Solar Imaging Radio Array

Kevin LangoneJesse Panneton

Sam WrightElizabeth Cantando

Steve SydnorAndrew VanVreede

Ling-Lun Bob Hsia

Aerospace and Ocean Engineering DepartmentVirginia Polytechnic Institute and State University

Blacksburg, Virginia

May 10, 2004

Contents

1 Problem Definition and Strategy 11.1 Solar Space Science Mission History . . . . . . . . . . . . . . . . . . . 21.2 Project Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Required Disciplines and Societal Sectors . . . . . . . . . . . . . . . . 31.4 Needs, Constraints, and Alterables . . . . . . . . . . . . . . . . . . . 31.5 Project Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Design of Value System 72.1 Science/Performance Objectives . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Maximize Angular Resolution . . . . . . . . . . . . . . . . . . 72.1.2 Maximize Dynamic Range . . . . . . . . . . . . . . . . . . . . 92.1.3 Maximize Lifetime . . . . . . . . . . . . . . . . . . . . . . . . 92.1.4 Minimize Relative Position Error . . . . . . . . . . . . . . . . 92.1.5 Maximize Data Transmission Reliability/Strength . . . . . . . 102.1.6 Maximize Data Transmission Rate . . . . . . . . . . . . . . . 102.1.7 Maximize Data Storage Capability . . . . . . . . . . . . . . . 102.1.8 Minimize Actual and Optimal Operating Temperature Difference 112.1.9 Minimize Maximum Load Factor During Launch . . . . . . . . 11

2.2 Cost Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.1 Minimize Mass . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2 Maximize Time in Sunlight . . . . . . . . . . . . . . . . . . . 122.2.3 Maximize Power System Efficiency . . . . . . . . . . . . . . . 122.2.4 Minimize Stationkeeping Requirements . . . . . . . . . . . . . 122.2.5 Minimize Initial Fuel Required . . . . . . . . . . . . . . . . . . 132.2.6 Maximize Specific Impulse of Propellant . . . . . . . . . . . . 132.2.7 Maximize Launch Vehicle Success Rate . . . . . . . . . . . . . 14

2.3 Computation of Objective Weights . . . . . . . . . . . . . . . . . . . 14

i

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 System Synthesis 173.1 Array Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3 Launch Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.4 Attitude Determination and Control . . . . . . . . . . . . . . . . . . 21

3.4.1 Attitude Determination . . . . . . . . . . . . . . . . . . . . . 223.4.2 Attitude Control . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5 Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.5.1 Bipropellant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.5.2 Hydrazine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.5.3 Hydroxylammonium Nitrate . . . . . . . . . . . . . . . . . . . 253.5.4 Cold Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.5.5 Solid Rocket Motors . . . . . . . . . . . . . . . . . . . . . . . 263.5.6 Electrical Propulsion . . . . . . . . . . . . . . . . . . . . . . . 27

3.6 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.6.1 Power Generation . . . . . . . . . . . . . . . . . . . . . . . . . 293.6.2 Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . 303.6.3 Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.7 Thermal Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.8 Communication, Command, and Data Handling . . . . . . . . . . . . 323.9 Formation Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.9.1 Redundant Microsatellites . . . . . . . . . . . . . . . . . . . . 343.9.2 Host Spacecraft . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 System Analysis 384.1 Array Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.1.1 Element Selection . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 Attitude Determination and Control . . . . . . . . . . . . . . . . . . 404.3 Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.4 Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.4.1 Power Generation . . . . . . . . . . . . . . . . . . . . . . . . . 464.4.2 Power Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.4.3 Power Regulation and Control . . . . . . . . . . . . . . . . . . 484.4.4 Sizing for the SIRA mission . . . . . . . . . . . . . . . . . . . 48

4.5 Thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

ii

4.5.1 Thermal Modeling . . . . . . . . . . . . . . . . . . . . . . . . 514.5.2 Multi-Layer Insulation . . . . . . . . . . . . . . . . . . . . . . 524.5.3 Radiator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.5.4 Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.6 Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.6.1 Command and Data Handling . . . . . . . . . . . . . . . . . . 544.6.2 Telemetry and Communications . . . . . . . . . . . . . . . . . 544.6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5 System Modeling 595.1 Synthetic Aperture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.2 Orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.3 Attitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.4 Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.5 Thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.6 Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6 Component Selection 746.1 Deployable Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.2 Attitude Determination and Control . . . . . . . . . . . . . . . . . . 77

6.2.1 Attitude Determination . . . . . . . . . . . . . . . . . . . . . 776.2.2 Attitude Control . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.3 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796.3.1 Solar Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796.3.2 Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.4 Thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.5 Communications and Data Handling . . . . . . . . . . . . . . . . . . 826.6 Launch Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846.7 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7 System Integration 887.1 Mission Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.2 Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.3 Microsatellite Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 917.4 Stack Deflection Calculations . . . . . . . . . . . . . . . . . . . . . . 92

iii

7.5 Component Placement . . . . . . . . . . . . . . . . . . . . . . . . . . 937.6 Total system mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

iv

List of Tables

1.1 Needs, alterables, and constraints. . . . . . . . . . . . . . . . . . . . . 41.2 Interaction between spacecraft subsystems. . . . . . . . . . . . . . . . 6

2.1 Objective key corresponding to Tables 2.2 & 2.3. . . . . . . . . . . . . 152.2 Analytical hierarchy process matrix. . . . . . . . . . . . . . . . . . . . 152.3 Analytical hierarchy process matrix, with final weights for each design

objective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1 Estimated sizes, weights, and power requirements for command sub-systems of varying complexity. . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Summary of system possibilities. . . . . . . . . . . . . . . . . . . . . . 37

4.1 Orbit comparison for fuel consumption (m/s). . . . . . . . . . . . . . 434.2 Propellant of various propulsion system parameters. . . . . . . . . . . 434.3 Propellant of various propulsion system parameters. . . . . . . . . . . 454.4 Typical solar cell parameters. . . . . . . . . . . . . . . . . . . . . . . 494.5 Standard space qualified batteries. . . . . . . . . . . . . . . . . . . . . 504.6 Operating Temperatures for Spacecraft Components (◦C). . . . . . . 524.7 Comparison of applicable transmitter options. . . . . . . . . . . . . . 56

7.1 Summary of mission operations . . . . . . . . . . . . . . . . . . . . . 907.2 System mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

v

List of Figures

2.1 Design objectives for the SIRA mission. Bold boxes are quantities tobe maximized; others are to be minimized. . . . . . . . . . . . . . . . 8

3.1 Random distribution of array. . . . . . . . . . . . . . . . . . . . . . . 183.2 Spherical distribution of array. Reprinted from [10]. . . . . . . . . . . 183.3 Ellipsoidal distribution of array. Reprinted from [9]. . . . . . . . . . . 18

4.1 Dipole array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 Turnstile array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.3 Loop array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4 Thermal conductivity versus MLI thickness. . . . . . . . . . . . . . . 53

5.1 Sample coordinates of array elements projected on the surface of asphere. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.2 Contour plot of relative signal intensity on the synthetic aperture. . . 625.3 Earth and spacecraft orbits, sun-centered inertial view. . . . . . . . . 635.4 Minimum and maximum formation range to Earth versus eccentricity. 645.5 Range to Earth for one orbit. . . . . . . . . . . . . . . . . . . . . . . 645.6 Attitude control schematic. . . . . . . . . . . . . . . . . . . . . . . . . 655.7 Sample power simulation. . . . . . . . . . . . . . . . . . . . . . . . . 675.8 Spacecraft diameter versus temperature. . . . . . . . . . . . . . . . . 675.9 Spacecraft temperature versus waste heat per radiator area. . . . . . 685.10 Solar array temperature vs. solar array size. . . . . . . . . . . . . . . 695.11 Bit Error Probability as a Function of Eb/No (reproduced from [7]). . 715.12 Optimization of high-gain antenna dish size for telemetry at a distance

of 3 million km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.13 Optimization of omni-directional antenna data rates of antenna diam-

eter 0.002 m, for communication Earth to SIRA at 3 million km. . . . 725.14 Optimization of omni-directional helix antenna. . . . . . . . . . . . . 73

vi

6.1 Deployable truss structure. . . . . . . . . . . . . . . . . . . . . . . . . 756.2 Storable Tubular Extendable Member. . . . . . . . . . . . . . . . . . 766.3 STEM cassette configuration. . . . . . . . . . . . . . . . . . . . . . . 766.4 Star tracker configuration. . . . . . . . . . . . . . . . . . . . . . . . . 786.5 Colloid microthruster [37]. . . . . . . . . . . . . . . . . . . . . . . . . 796.6 Cross section of MLI. . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.7 AeroAstro X-Band Transponder and operational block diagram [42]. . 826.8 Example of the omni-directional low gain antenna, to be mounted on

each face of SIRA microsatellites [43]. . . . . . . . . . . . . . . . . . . 836.9 Western Avionics Shuttle Bus PCI interface board [44]. . . . . . . . . 836.10 NEC Toshiba Space Sytems’ Onboard Computer, Data Handling Unit,

and Solid State Memory [45]. . . . . . . . . . . . . . . . . . . . . . . 846.11 Proton launch vehicle fairing dimensions. . . . . . . . . . . . . . . . . 856.12 Basic spacecraft structure. . . . . . . . . . . . . . . . . . . . . . . . . 86

7.1 SIRA insertion burn location. . . . . . . . . . . . . . . . . . . . . . . 897.2 Orthographic orbit views in rotating reference frame. . . . . . . . . . 897.3 First four satellites released from stacks. . . . . . . . . . . . . . . . . 917.4 L-beam component. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.5 Component placement. . . . . . . . . . . . . . . . . . . . . . . . . . . 947.6 Microsatellite stacks in launch configuration. . . . . . . . . . . . . . . 947.7 Two dimensional projection. . . . . . . . . . . . . . . . . . . . . . . . 95

vii

Chapter 1

Problem Definition and Strategy

When one thinks of bad weather, phenomena such as hurricanes, tornadoes, andblizzards usually come to mind. These storms all have the capability to cause severedamage to human-made assets, possibly resulting in serious injury or even death.Though considered much less often, solar storms and space weather also have thepotential to inflict serious damage to property.

Space weather is primarily a result of the sun’s weather cycle. The sun regu-larly expels mass as coronal mass ejections (CMEs). The interplanetary shocks fromcoronal mass ejections can cause large distortions in the Earth’s geomagnetic field.These distortions induce severe currents which can result in the failure of powergrids. Geomagnetic storms may also result in an expansion of the auroral zone anddangerous increases in particle flux to astronauts and high altitude pilots. Coro-nal mass ejections also have the potential to damage sensitive electronic equipmentaboard Earth-orbiting spacecraft. For these reasons, the accurate prediction of spaceweather has become a topic of increasing interest for space scientists.

The primary goal of the Solar Imaging Radio Array is to study the structure andevolution of coronal mass ejections. This objective includes more accurate predictionsof the arrival of CME shocks at Earth. Current data from missions such as theSolar and Heliospheric Observatory (SOHO), Wind, and the Advanced CompositionExplorer (ACE) are helping scientists to improve models of solar weather. SinceCMEs generally take several days to travel to Earth[1], real-time observations of theevents could provide significant early warning capability and allow preparations to bemade for a potential geomagnetic storm. Many CME events are coupled with solarflares, which can be detected at Earth just minutes after ejection since radiation fromthe flares travels at light speed. Current efforts are underway to correlate solar flaresand CMEs. Other objectives of the mission include an enhanced knowledge of solar

1

wind density and further understanding of the objects found in the low frequencyradio (< 30 Mhz) sources.

1.1 Solar Space Science Mission History

SIRA will not be the first satellite to study the Sun, although it will be the firstsatellite to use a cluster of microsatellites to gather solar data. Some of SIRA’spredecessors include SOHO, ACE, and Wind. SOHO is a joint mission betweenNASA and the European Space Agency (ESA) launched on December 2, 1995. It wasdesigned to study the corona, solar wind, solar oscillations, solar particles, and manyother aspects of the Sun. SOHO is still in operation today. WIND was launchedon November 1, 1994. WIND was designed to study the Sun’s effect on Earth’smagnetosphere and ionosphere, and to investigate the plasma processes occurring inthe near-Earth solar wind. ACE was launched on August 15, 1997 and was designedto sample low-energy particles of solar origin and high-energy galactic particles. ACEcan provide an advance warning (about one hour) of geomagnetic storms that candisrupt power and communications systems on Earth [2].

1.2 Project Scope

The scope of this project includes the design of a microsatellite dipole antennaarray to study solar weather. SIRA will be an interferometer composed of sixteenmicrosatellites. SIRA uses the array of satellites to act as a single long baselineaperture to study the sun. We will design the microsatellites, select a launch vehicle,and select orbits for the radio array. This design will include propulsion systemselection, power system sizing, orbital analysis, and the establishment of reliablecommunication links. The microsatellites will use onboard propulsion to maintainpositioning. They must communicate with each other and with the ground stationon Earth. The satellites will maintain a spherical formation with a diameter ofapproximately twenty five kilometers. The scope does not include design of specificsubsystem components (i.e. off-the-shelf hardware will be used when available) orthe post flight data analysis. Material selection, mass estimates, and stationkeepingpropellant requirements will be included in this design.

2

1.3 Required Disciplines and Societal Sectors

The design and operation of SIRA is a complex task requiring the expertise ofmany different classes of professionals. Aerospace engineers will choose the optimallaunch platform and configuration for the microsatellites. Aerospace experts willresolve orbital mechanics details, such as how to achieve the chosen orbit and maintainstationkeeping. Knowledge of formation flying will be especially helpful for the orbitaldynamics of the antenna array. Structural engineers will design and test cheap, lightweight materials for flight readiness. Electrical and computer engineers will designthe circuitry and power systems needed to operate the satellite electronics and sciencemission. Solar physicists will be needed in order to develop the scientific instrumentsonboard the microsatellites. Mathematicians and scientists will analyze and reducethe data to further the research of solar weather.

Outside contractors will be solicited for building and testing components of thespacecraft. They will play a large role in the success of SIRA. The National Aero-nautics and Space Administration (NASA) and its facilities will supervise and fundthe development and operation of SIRA.

Separate from the disciplines and professions involved in the design and imple-mentation of the mission, there are individuals with whom our design team will beworking. First and foremost, we will be working among ourselves. As a design team,the six members will work closely with each other. Dr. Hall will oversee and guidethe progress of the design throughout the entire process. The subsystem groups,comprised of members from each design team, will be integral parts of the designprocess. NASA personnel who are concurrently working on similar designs will bevaluable sources of information for the design team.

1.4 Needs, Constraints, and Alterables

The primary goal of the SIRA mission is to further understand space weather andits effects on our solar system. Three results needed to accomplish the goal includemapping the propagation of coronal mass ejections from the Sun towards the Earth,advancing space weather prediction abilities, and observing the interaction of theEarth’s magnetosphere with CMEs and other space weather.

The design is restricted by several predefined constraints. The radio receiver willhave a range of 30 kHz to 15 MHz to detect frequencies which no one has studiedpreviously. An adaptable sampling interval must vary with the frequency of eachCME. The total power must be sampled at 16 bit resolution every 5 seconds. Relative

3

positional accuracy between the microsats must be within 6 m. The overall missionlifetime will be at least five years. Three-axis stabilization and antenna pointingerror of less than 2.5 degrees are required for data processing [3]. Additionally, thebudgeting for the mission is limited to $300,000,000.

The optimal number of microsats in the constellation can be altered to fit theconstraints listed above. Other alterables include the size, shape, and location ofthe orbit. There are multiple material choices available for use. Transport methodoptions include a variety of launch vehicles and propulsions system. Many off-the-shelf components are available to construct the communication and data handlingsystem. Each subsystem must be designed with consideration of the interaction withthe other subsystems as well as the constraints.

Table 1.1: Needs, alterables, and constraints.

NeedsAdvance space weather prediction abilitiesMap propagation of coronal mass ejectionsObserve CME-magnetosphere interactionAlterablesNumber of satellitesOrbit locationMaterial selectionPower system designLaunch vehicleCommunication systemAttitude control systemPropulsion systemConstraintsFrequency between 30 khz and 50 MhzRelative position knowledge within 6 mMinimum 2 year lifetimePower sampled 16 bits every 5 secondsThree-axis stabilizationAntenna error 2.5 degrees or lessTotal Mission Cost <$300,000,000

4

1.5 Project Elements

There are many elements that constitute the design of this mission. All aspects ofthe project will be designed to support the science mission of imaging radio sources inthe solar corona and heliosphere. SIRA will image the corona using a synthetic aper-ture interferometer. The interferometer will consist of sixteen dipole microsatelliteantennas deployed from a commanding satellite. Communications and control mustbe established between the array, and the ground station. Each of the microsatelliteswill be identical, and their design will constitute the microsatellite element of SIRA.

The structural design element is focused on the safe transport and deploymentof the microsatellites as well as the integrity of all the satellites throughout theirlifetime. There will be structural aspects to the microsatellite element. Thermal andenvironmental controls work to maintain operating temperatures within subsystemlimits. An important structural element includes identifying the best materials touse for spacecraft construction. Extreme temperatures experienced by materials inthe propulsion system require the use state-of-the-art materials and manufacturingprocesses. Spacecraft materials must withstand the highest structural loads, whichoccur during launch.

The transfer of the system from Earth to service constitutes the launch logisticsand orbital maintenance element of SIRA. This element will include launch vehicle se-lection, propulsion system design, and microsat positioning. The mission ∆V budgetconstrains orbit selection. The attitude determination and control subsystems worktogether with ground communication and command teams to develop maintenanceroutines for attitude and orbit control. Design of thrusters and internal actuatorsdepends on the required positional accuracy as determined by the mission geometryteam. Many components of the system will require power, including but not limitedto the science, commanding and control, and propulsive elements. The power ele-ment will include the generation, storage, and distribution of power throughout thesystem. The subsystems of any spacecraft are not separate entities; they interact onmany different levels. Table 1.2 shows how strongly each subsystem interacts withthe others. A qualitative estimate is made of the relative interactions between eachof the spacecraft’s systems according to the following scale: no interaction (0), weakinteraction (1), or strong interaction (2).

5

Table 1.2: Interaction between spacecraft subsystems.

Subsystem (6) (5) (4) (3) (2)(1) Attitude Control 1 1 2 2 2(2) Propulsion 1 1 0 0 –(3) Communication 2 0 2 –(4) Instrumentation 2 2 –(5) Structure 1 –(6) Power –

1.6 Summary

Installation and operation of the Solar Imaging Radio Array will require the skillsof many professionals to successfully integrate all systems and ensure that all compo-nents meet mission requirements. The final design precisely observes space weather.The design accomplishes these tasks with minimal mass and cost.

6

Chapter 2

Design of Value System

Value system design is the process of creating the model by which the best designwill be determined. A list of mission objectives is established in Figure 2.1 along witha measure of effectiveness (MOE) for each. The desire is to minimize or maximizeall of the MOEs. However, the interactions between the different objectives limit theextent to which each can be optimized. Therefore, the importance of each objectiveneeds to be determined. An established method is used to compare the importanceof objectives in order to determine their corresponding weights. These weights areused in computation of the effectiveness of each design possibility.

2.1 Science/Performance Objectives

Since the mission goal is to gain knowledge of coronal mass ejections and othersolar weather phenomena, science objectives are certainly important. Several scien-tific objectives are established below that help to evaluate the scientific performanceof system possibilities.

2.1.1 Maximize Angular Resolution

The angular resolution of an interferometer is the minimum separation betweentwo objects, so that one can see both of them as separate images. Angular resolution isthe angle defined as the wavelength divided by the distance separating the antennasand is measured in arcminutes[4]. At 15 MHz, the wavelength is 20 meters. Theproposed antenna configuration is a 5-25 km sphere. Pairs of distant antennas willhave smaller angular resolution and will be able to resolve finer details. At the shortest

7

Figure 2.1: Design objectives for the SIRA mission. Bold boxes are quantities to bemaximized; others are to be minimized.

8

wavelength and the greatest separation, the angular resolution is 2.75 arcminutes.Keeping the antennas evenly spaced will ensure that they are the farthest distancepossible from all the other antennas at any given time. We desire random arraydistribution to reduce lobe grating. These conflicting objectives could be met withalternative array geometries such as the elongated ellipsoid as suggested by [5]. Theantennas could be randomly placed on the surface of the elongated ellipsoid, withsome antennas located great distances apart at either end of the spheroid.

2.1.2 Maximize Dynamic Range

The dynamic range of an interferometer is the ratio of the largest resolvable targetsize to the smallest resolvable target size [6]. It is similar to angular resolutionin that they are both measures of the array’s capability. The dynamic range isindicated in decibels (dB). The minimum dynamic range is specified as 90 dB, sothe largest resolvable object must be 109 times larger than the smallest resolvableobject. Satisfaction of this constraint requires sets of antennas both distantly spacedand closely spaced. The closely spaced antennas will easily resolve the larger targets,and the distantly spaced antennas will resolve the smaller targets.

2.1.3 Maximize Lifetime

Although SIRA has a minimum specified lifetime of two years, an objective isto maximize the mission lifetime. Increasing the mission lifetime will allow SIRA toincrease scientific gain and therefore the effectiveness of the mission. All systems willbe designed to work longer than the minimum two year mission. This objective is ofleast importance since a constraint has already been placed on mission lifetime.

2.1.4 Minimize Relative Position Error

An important aspect of formation flying is the accuracy of the relative positionof the satellites. A constraint for SIRA is to know the relative position of the mi-crosatellites to within 6 meters. The resulting error is only 0.024%, assuming theapproximate distance between the microsatellites is 25 km. Minimization of relativeposition error must be weighed against the price of the chosen sensors and the powerrequired by the sensors. Minimizing the relative position error beyond the 6 meterconstraint is not as important as other objectives, but can still improve the qualityof the data obtained by SIRA.

9

2.1.5 Maximize Data Transmission Reliability/Strength

Having reliable contact with the fleet of microsatellites is crucial due to the natureof the science mission. The fleet must maintain a strict formation in order for theinterferometer to work properly. These tight formation requirements will be metwith an onboard guidance and control system. This system will be monitored toensure it is functioning properly. Operators will need to know the exact status of theformation. It is possible that the ground station will only be in contact with the fleetfor several hours each day. The communication window will be critical to downloadthe gathered information and upload any new instructions. The ability to transmitwhen needed, along with the strength and integrity of the signal are crucial to themission. The signal-to-noise ratio (C/N) is measured in decibels, and bit-error rateis the percentage of data bits incorrectly received. These errors can be minimized byincreasing the transmitter power, the antenna gain, or decreasing data compressionprior to transmission.

2.1.6 Maximize Data Transmission Rate

Transmitting data from the fleet to Earth will use power and processing resources.The amount of time to transmit data from the fleet back to the Earth will be min-imized by maximizing the data transmission rate. The rate of data transmission ismeasured in bits per second (bps) and is determined directly from transmitter power(watts) and antenna gain (decibels). A lower transmitter power can be used with ahigh gain antenna to achieve high data rates with less power consumption; however,beam width will be sacrificed.

2.1.7 Maximize Data Storage Capability

The fleet may only be in contact with Earth for a limited time during any givenperiod. The fleet will not be able to continuously stream the data that it collects backto Earth; thus it will need to be stored onboard. The amount of data recorded andstored will be on the order of gigabytes. The objective is to maximize the availableonboard data storage capacity, allowing the system to store all of the data untiltransmission to Earth is possible. Data storage can be increased simply by addingwritable memory to the bus.

10

2.1.8 Minimize Actual and Optimal Operating TemperatureDifference

SIRA’s orbit likely places it in direct sunlight throughout the entire mission. Thefaces of the microsatellites which will be in direct sunlight will need to be protectedfrom the Sun’s heat, so as not to damage the sensitive scientific instruments onboard.Material selection will play a large role in protecting the microsatellites from the Sun’sheat and radiation. A lightweight material with acceptable insulation properties willbe needed to satisfy this need and also the mass constraint.

2.1.9 Minimize Maximum Load Factor During Launch

Evaluation and determination of the interactions between launch vehicle and pay-load give a better understanding of the strenuous environments produced by launch.During launch the combination of high accelerations and vibrations combined withhigh temperatures and rapidly changing pressures often produce the most severemission environments. Careful consideration of the launch environment is critical tospacecraft design. Load factors or acceleration loads involve the static and dynamicloads experienced at various times throughout a mission. Design of the payload towithstand these loads is critical to mission life and completion. The most severedynamic environments during launch are related to acceleration rate and aerody-namic smoothness of the launch vehicle. Typically maximum loads are experiencedduring the first burn stage. When the payload is near the launch pad acoustic exci-tation is at a maximum. Damping insulation can be added to the fairing to minimizeacoustic vibrations. During acceleration at low altitudes payloads are subjected tolarge dynamic pressure changes. These pressures changes are minimized by addingor increasing the size of vents on the launch vehicle fairing.

2.2 Cost Objectives

Costs need to be minimized over all aspects of this project without sacrificing dataquality, safety, or the scientific goals. SIRA must be built, launched, and maintainedduring its lifetime, while limited to a budget of $300,000,000. Excess costs can becut in the launch phase by minimizing mass. Since the design of new components isnot included in the scope, use of commercially available products will also cut costs.Careful orbit and propulsion system selection will also reduce costs associated withstationkeeping.

11

2.2.1 Minimize Mass

Minimization of the total system mass is a principal challenge in the design of anyspace mission. High mass generally results in increased launch and orbit stationkeep-ing costs. All launch vehicles have a maximum payload mass which they are capableof boosting into orbit; thus less mass results in a larger selection of rockets whichcan be used. The goal of minimizing mass is considered one of the most importantobjectives.

2.2.2 Maximize Time in Sunlight

Maximizing the time in sunlight will positively affect all aspects of the mission.Since the primary goal of the mission is to study coronal mass ejections and TypeIII bursts, the spacecraft must be able to see the sun. Batteries would be requiredduring eclipse if solar panels are used for electric power. The microsatellites are masslimited and batteries would potentially be the most massive component. Eliminationor minimization of batteries is an advantage of an eclipse-free orbit. Furthermore,thermal control will be aided by the constant thermal environment that results fromsuch an orbit. Active thermal systems require cooling and heating components tocontrol the temperature [7]. This objective is measured by percent of time spent insunlight, with the optimal value being 100%.

2.2.3 Maximize Power System Efficiency

The power subsystem traditionally constitutes a large portion of the total space-craft mass. The goal is to maximize the efficiency of the power system in order toreduce mass devoted to this potentially robust system. Since the minimization ofmass is already included, this objective is given secondary importance.

2.2.4 Minimize Stationkeeping Requirements

The amount of fuel needed to maintain SIRA’s orbit must be minimized. Themicrosatellites will not have large storage tanks to hold the excess fuel needed forstationkeeping. The units which will be used to measure the stationkeeping arem/s per year, also termed ∆V /year. The orbit location will have a direct influenceon this parameter. The distant retrograde orbit (DRO) requires no ∆V while theEarth-Moon Lagrange point orbits (EML4 and EML5) have a restrictively large ∆Vrequirement.

12

2.2.5 Minimize Initial Fuel Required

The fuel needed to place the microsatellites into orbit fulfills two roles. The firstcomponent is the Launch Vehicle Fuel Required (LVFR). The LVFR is the amountof fuel needed to move the satellites from the Earth’s surface to the location of theorbit. The second component is the Orbit Insertion Fuel Required (OIFR). TheOIFR is the amount of fuel needed to insert each microsatellite from the locationof the orbit into their individual orbits. Once again, the location of the orbit has adirect influence on the insertion fuel requirement. The LVFR does not need to becarried by the individual microsatellites. Note that each of these fuel requirementsare merely used to placed the satellites into an initial orbit; orbit stationkeeping costsare considered separately. A host satellite can transport the fleet of microsatellites tothe orbit location. However, the OIFR must be carried by each individual microsat.

2.2.6 Maximize Specific Impulse of Propellant

Specific impulse quantifies the efficiency of the propulsion system and how effi-ciently the chemical energy content of the propellant is converted into thrust. Thisvalue is proportionately related to the square root of the ratio between the combustionchamber temperature and the average molecular weight of the exhaust gases. Specificimpulse is maximized by matching the highest possible combustion temperature withthe lowest average molecular weight of the combustion products. Maximizing specificimpulse is of extreme importance on missions with severe mass constraints. Propul-sion system performance is directly related to the capability to produce a change invelocity. The rocket equation quantifies the relationship between change in velocityand specific impulse.

∆V = gIsp lnmo

mf

(2.1)

The following equation shows the relationship between specific impulse and the massof propellant required for a given change in velocity.

Mp = mo

[1− e

− ∆VIspg

](2.2)

Equations 2.1 and 2.2 prove that the importance of maximizing specific impulsecannot be overlooked. High specific impulse results in minimized propellant massand maximum ∆V capabilities. Both are essential to micro-spacecraft design.

13

2.2.7 Maximize Launch Vehicle Success Rate

Spacecraft design is futile if the launch vehicle fails to correctly insert its payloadinto the proper orbit. Launch vehicles with maximum reliability, production capacity,and minimum stand-down time after failure are chosen to maximize launch vehiclesuccess rate. Although launch vehicle success rate is important there is limited controlover some of its aspects.

2.3 Computation of Objective Weights

A method known as the Analytical Hierarchy Process [8] is used to determine theweight that corresponds to each objective. All of the objectives (which are listed andenumerated in Table 2.1) are placed in a matrix and the relative importance of eachobjective is entered in the corresponding entry of the matrix (Table 2.2). The entriescorrespond to the following values:

• 1/9 Absolutely less important

• 1/7 Very strongly less important

• 1/5 Strongly less important

• 1/3 Weakly less important

• 1 Equal importance

• 3 Weakly more important

• 5 Strongly more important

• 7 Very strongly more important

• 9 Absolutely more important

The values in each column are then normalized on the sum of the values in thatcolumn. The results of this computation are shown in Table 2.3. The last step isto average the values in each row, which yields the final weights. These weights areindicated in the last column of Table 2.3. Note that many of the science objectives areweighted heavily, as is the minimization of total mass. For each component design,the applicable measures of effectiveness will be normalized by the highest value for

14

Table 2.1: Objective key corresponding to Tables 2.2 & 2.3.

1 Minimize mass 10 Minimize launch load factor2 Minimize cost 11 Maximize data transmission reliability3 Minimize stationkeeping 12 Minimize temperature difference4 Maximize resolution 13 Maximize specific impulse5 Minimize relative position error 14 Maximize data storage capability6 Minimize insertion fuel cost 15 Maximize data transmission rate7 Maximize lifetime 16 Maximize dynamic range8 Maximize power system efficiency 17 Maximize time in sunlight9 Maximize launch vehicle success rate

Table 2.2: Analytical hierarchy process matrix.

15

all the designs, then multiplied by the correct weight. These values are summed toproduce the final rating for each component design possibility. Note that objectivesto be minimized will be counted as negative in the computations.

Table 2.3: Analytical hierarchy process matrix, with final weights for each designobjective.

2.4 Summary

The SIRA Value System helps to establish the system that best fulfills the designobjectives. It outputs quantitative measures of the effectiveness of each subsystemthat can be used by the decision maker to select the best component. Measures of ef-fectiveness quantify each objective pertaining to the individual component. Using theanalytical hierarchy process, numerical values are obtained which establish the bestcomponent selection. The next chapter will describe alternative design configurationscomposed of the different subsystem solutions.

16

Chapter 3

System Synthesis

The problem definition and value system design establish the basis for the actualsystems design. This chapter discusses different possibilities for each system param-eter/subsystem as well as complete designs of the spacecraft. Since there is morethan one option that can be used to fulfill each design objective, various solutions toeach problem need to be evaluated. Different options for the geometry of the microsatellite array, attitude determination and control, propulsion, power, and thermalcontrol are all discussed here. With all the alternative solutions in place, initial de-signs of the complete satellite can be put together and analyzed. With the objectiveweights established in Table 2.3, the different solutions can be analyzed to determinehow well they can complete each objective.

3.1 Array Geometry

SIRA will use a constellation of microsatellite dipole antennas to observe coronalmass ejection activity from 30 KHz to 15 MHz. These frequencies occur at half-wavelengths equal to 5 km and 10 meters, respectively. Thus, the individual dipoleantennas must be no shorter than ten meters in length, and the two most distantdipoles must separate by at least 5 km. Several geometries are being considered forthe synthetic aperture array.

The simplest geometry would be a random distribution in three dimensional space.The minimum separation requirements would have to be established and maintainedin conjunction with initial deployment. A downside of this geometry is the probabilitythat two or more of the microsatellites will cluster and never separate fully. Theclosely grouped satellites will contribute less resolving power to the array than the

17

more distantly spaced satellites. To maintain optimal spacing the antennas will mostlikely be distributed over the surface of some imaginary shape.

Figure 3.1: Random distribution of array.

Figure 3.2: Spherical distribution of array. Reprinted from [10].

Figure 3.3: Ellipsoidal distribution of array. Reprinted from [9].

The second geometry under consideration is the distribution of the microsatellitesover the surface of an imaginary sphere. The sphere will have a radius of 5 km atthe beginning of the constellation lifetime, expanding to 25 km at the end of itslifetime. The ordinate locations of each satellite would be selected to minimize lobe

18

grating and maximize angular resolution. A modification of the spherical shell is theellipsoidal shell suggested by Oberoi [5].

The ellipsoid would have circular cross sections 2.5 km in radius perpendicular tothe major axis. The major axis itself would be 25 km in length and perpendicular tothe Sun vector. The ellipsoid size would be fixed throughout the mission lifetime andwould satisfy all resolution requirements. Proper insertion geometry will minimizecorrective positioning and the subsequent propulsive cost.

3.2 Orbit

The orbit choice has an effect on almost every subsystem of the satellite. Theattitude and control requirements are dependent upon the variable environmentaldisturbance torques. The power subsystem will have to include batteries if the satel-lites experience eclipse. Orbits outside geostationary altitude can create difficultchallenges for the communication subsystem. All of the propulsion requirements forSIRA will stem from the orbit selection. Finally, the performance of the scientificinstruments and the data they record depend directly on where they are in the solarsystem.

The scientific objectives of SIRA limit the orbit possibilities. The microsatellitesmust be placed far enough away from Earth to avoid interference from the magneto-sphere. Three logical orbit choices which satisfy the minimum distance requirementare the Sun-Earth L1 point, Earth-Moon L4 or L5 point, and the Distant Retro-grade Orbit (DRO). Each of these orbits is described and analyzed in the followingparagraphs.

The Sun-Earth L1 is a libration point about which a halo orbit is flown. The L1

point is collinear with the sun and earth and is located between the two of them. Thedistance to L1 is approximately 1.5 million km from Earth. Compared to the otherorbit options the orbit insertion cost is much less. The fuel required for formationkeeping is on the same order of magnitude as the DRO, but substantially less thanthe EM-L4/L5.

The EM-L4/L5 orbit would be much closer to Earth than the SE-L1, but wouldstill be in a halo trajectory. Although the initial energy to get the microsatellitesto EM-L4/L5 is much less than the other orbits the orbit insertion and formationkeeping requirements are considerably larger. The initial energy can be carried bysome type of ’host’ to move the microsatellites into the vicinity of the orbit. However,each microsatellite must carry enough propellant to insert the spacecraft into orbit,maintain the orbit, and maintain formation throughout the lifetime of the mission.

19

This option will most likely prove to be unsatisfactory due to the massive on-boardfuel requirements.

The DRO is a heliocentric orbit with the same period as the Earth [11]. The orbitshape, however, is not the same as that of the Earth. The eccentricity is slightlyincreased which causes a circular motion relative to the Earth. The maintenancerequirements, both formation and orbit, are less for the DRO than either of the otherorbits[11]. The problem is in the large insertion fuel requirement. If the insertionfuel can be carried by the host then this option is promising. The DRO is locatedapproximately 1.9 million km from Earth.

3.3 Launch Vehicle

Launch system selection is essential to the success of any space mission. Thelaunch system’s job is to accelerate the payload from Earth to the desired orbit.Spacecraft design is constrained by the nature of the launch process. During launchthe combination of acceleration, vibrations, high temperatures, and rapidly changingpressures produce the most hostile environments experienced by the payload. Theability of the payload to withstand these loads is critical to mission success. Launchvehicles with maximum reliability, production capacity, and minimum stand-downtime are chosen to maximize launch vehicle success rate [7].

There is a variety of launch vehicles to choose from depending on desired perfor-mance, trajectory, and launch site. One option considered for SIRA is an L1 haloorbit. NASA is currently conducting a science mission from L1 dubbed SOHO or So-lar and Heliospheric Observatory. The launch vehicle used to successfully launch theSOHO spacecraft to an L1 orbit was the two stage Atlas-IIAS. The Atlas program hasoperated since 1958 and carries an 87% launch success rate. The Atlas-IIAS consistsof a solid rocket booster stage powered by four Thiokol Castor IVA solid rocket boost-ers and a core vehicle stage (booster and sustainer) powered by Rocketdyne MA-5Aliquid propellant engines using RP-1 fuel and liquid oxygen propellants. Maximumthrust at liftoff is approximately 2.98 MN. The multiple firing Centaur is powered bytwo Pratt and Whitney (RL10A-4) liquid hydrogen and liquid oxygen engines withextendible nozzles. The payload fairing features a maximum diameter and length of3.65 m and 10 m respectively. Maximum load factors experienced during launch andascent are 6.0 gs axially and ±2.0 gs laterally. Acoustic levels reach 138 dB whilemaximum pressure change in the fairing is 5.4 kPa/s. Launch takes place at LC-36A or B at Cape Canaveral Air Force Station in Florida. The estimated launch priceranges from $95 to $105 million [12].

20

An alternative orbit considered for SIRA is a DRO or distant retrograde orbit. ADelta II 7925 is being proposed by NASA to launch SIRAs sixteen satellites into aDRO. The 7925 carries a 95% success rate and features a single start liquid bipropel-lant Rocketdyne RS-27 main engine, two Rocketdyne LR101-NA-11 vernier engines,and a strap-on third stage solid propellant motor. The Delta II delivers a takeoffthrust rating of 2.63 MN with a maximum payload compartment diameter of approx-imately 3.0 m. The maximum length of the aluminum payload storage area is around6.0 m and contains acoustic absorption blankets to buffer out any harmful vibrationsduring takeoff and ascent. During ascent payloads experience +6.0 gs axially and±2.0 gs laterally. A maximum acoustic level of 145 dB is felt during liftoff with themaximum dynamic pressure change in the payload fairing being 3.45 kPa/s. Launchoccurs from Launch Complex 17(LC-17) at Cape Canaveral Air Force Station inFlorida [3]. The third orbit being considered in the SIRA mission is a L4/L5 Earth-moon orbit. Either of the two launch vehicles discussed above should be sufficient tolaunch SIRAs payload to this orbit.

If more room is needed to fit SIRAs satellites into the fairing the Titan IV shouldbe considered. A liftoff thrust of 14 MN is provided by two solid rocket motors. Stageone utilizes a LR87 hypergolic liquid propellant rocket engine while stage two uses asimilar LR91 liquid propellant rocket engine. There are several different options forthe upper stage with the Centaur engine being the largest and most powerful. Thepayload fairing has a maximum diameter and length of 4.6 m and 24 m respectively.Launch occurs from LC 40 or 41 at Cape Canaveral Air Force Station and will costaround 248 million dollars. Maximum load factors experienced during launch andascent are +3.0 gs axially and ±1.5 gs laterally. Acoustic levels reach 140 dB with amaximum pressure change in the fairing of 3.5 kPa/s [12]. The Titan IV was designedto carry space shuttle sized payloads and may be a good fit for the SIRA missiondepending on the mass of each microsatellite.

3.4 Attitude Determination and Control

The design of a spacecraft is influenced by the accuracy to which the attitude isknown. Spacecraft and the instrumentation onboard must be aligned in the correctdirection to function properly. Solar panels must be positioned perpendicular to thesun rays to increase efficiency, and antennas and receivers must be pointed correctlyto send and receive signals.

21

3.4.1 Attitude Determination

The spacecraft’s orientation must be established before any control can be applied.There are a number of standard instruments used for attitude determination. Sunsensors, horizon sensors, star trackers, and magnetic field sensors are some examplesof attitude determination instrumentation. The sun sensors and horizon sensorsdetermine the direction from the center of the body to some other point in space. Thedirection provides knowledge of the attitude about two axes. For complete attitudedetermination more than one sensor may be employed. Star trackers operate on thesame principles as the previous two examples. The relative location of the stars isknown, so many vectors can be formed. The star tracker provides a high degree ofaccuracy. The magnetic field sensor has dipoles which detect the direction of thesurrounding magnetic field. The limitation on this instrument is that the magneticfield must be known to a high degree. Therefore, it may only be used in orbits aboutthe Earth.

3.4.2 Attitude Control

Many factors are considered when designing the optimal control system. Someinstruments need more pointing accuracy than others. More instrumentation leadsto more attitude control requirements. Either the individual component or the entirespacecraft must be positioned for successful operation of the system. The spacecrafthas to be aimed in the correct direction before a thrusting maneuver can be performed.The control system is also used to overcome environmental disturbances.

Three main categories of control can be identified. These are spin-stabilization,gravity-gradient (GG) stabilization, and 3-axis control [7]. Each category has ad-vantages and disadvantages associated with the complexity and effectiveness of thecontrol system. The spin-stabilization and GG stabilization are both forms of pas-sive attitude control. Spin stabilization keeps the angular momentum vector ap-proximately constant in inertial space by spinning about one axis. GG stabilizationemploys the fact that a long, skinny body will align itself with the gravitationalfield. Three-axis control is much more complex than the passive forms mentionedpreviously. The possible actuators used for 3-axis control are described below.

Three-axis control is more complex and expensive than passive control, but itallows for greater control and pointing accuracy. The complexity results from the ac-tuators needed to provide the control. Possible actuators include momentum wheels,control moment gyros (CMGs), thrusters, and magnetic torquers. The control systemusually consists of some combination of these actuators.

22

Momentum wheels are used when a high degree of accuracy is needed. Eachwheel can provide a control torque about one axis leading to the need of three wheelsfor complete control. The wheels are activated by environmental disturbances andcontinue to spin at a constant speed until further disturbances are experienced. Thewheels will spin up and then back down if the disturbances are periodic. However, ifthe disturbances are secular the wheel will eventually reach a saturation (maximum)speed. A process called momentum dumping is then required. This is accomplishedusing thrusters or magnetic torquers.

A Control Moment Gyro (CMG) is another form of a momentum storage device.CMGs work in the same manner as momentum wheels except that it can be rotatedabout an axis to provide angular momentum change in multiple directions. CMGscan provide much larger torques and faster slew rates than momentum wheels, buttypically are heavier and more expensive.

Thrusters are almost always necessary when using 3-axis control. They can beused for quick slew maneuvers but cannot be used if high pointing accuracy is needed.Thrusters can be used for orbital transfer maneuvers in addition to coarse attitudecontrol. An important application for thrusters is momentum dumping. When themomentum wheels or CMG reach their saturation speed an external torque mustbe applied to spin them down. Typically, the thrusters are initially used for orbitinsertion and then used as momentum dumping devices.

Magnetic torquers use the naturally occurring magnetic field of the central bodyto produce a torque. The torque produced is limited in strength and direction. Thetorque is always perpendicular to the surrounding magnetic field. The small magni-tude reduces the application of magnetic torquers. They can be used to compensatefor residual dipole moments of the spacecraft or for momentum dumping. Usingmagnetic torquers for momentum dumping requires a longer dumping period thanthrusters and cannot always be completed due to the limited direction of the torque.

3.5 Propulsion

The propulsion subsystem contains all components involved in creating a force ofthrust to move a vehicle or rotate it about its center of mass. Some of the compo-nents include thrusters, propellant, propellant tanks, power conditioning units, anda propellant feed system. Main functions of the propulsion system are launch, or-bit insertion, orbit maintenance, and attitude control [13]. There are many types ofpropulsion technologies currently available for use in space applications.

The SIRA mission is designed to employ microsatellites. Microsatellites are classi-

23

fied into four categories by overall mass. Spacecraft with masses between 100 and 25kg are characterized by subsystem architecture following traditional design in bothcomponent design and integration techniques. Class I spacecraft ranging in massbetween 5 and 25 kg make use of the smallest propulsion hardware available or cur-rently under development. [14]. SIRA micro-spacecraft fit into the Class I category,therefore only propulsion systems that can be integrated into the Class I size andmass requirements are considered.

3.5.1 Bipropellant

Chemical propulsion is currently the most widely used form of spacecraft propul-sion involving a variety of techniques. These techniques include bipropellant engines,monopropellant engines, cold and warm gas thrusters, as well as any combinationof these systems. Bipropellant engines, typically considered for primary propulsionapplications, are often used on missions requiring high ∆V maneuvers. Bipropel-lant engines experience much higher specific impulses than other chemical systems,leading to propellant mass savings. Their disadvantage is the complexity of bothengine construction and feed system layout, resulting in high cost. The need forseparate feed systems for fuel and oxidizer leads to unwanted extra mass. Conse-quently, bipropellant engines are typically used on missions requiring ∆V greaterthan 1 km/s. Significant advances are currently under development in the miniatur-ization of bipropellant engines, however, efforts are focused on attitude control ratherthan primary propulsion applications. Emphasis on pulsing performance rather thanlong-duration burns rules out the possibility for primary propulsion applications onmicro-spacecraft. Challenging issues confront integration of bipropellant engines intoa Class I micro-spacecraft. Examples include combustion efficiency losses, injectordesign, and thermal control issues. Due to the limits of current bipropellant enginetechnology such as the lower component part count, the need for only a single pro-pellant tank, and lower overall cost make a monopropellant propulsion system bettersuited for Class I spacecraft [15]. The possibility of a duel mode Hydrazine/NTObipropellant engine where Hydrazine is also used for attitude control in monopropel-lant thrusters may be an option. This option would eliminate the need for separatepropellant tanks.

3.5.2 Hydrazine

Monopropellant engine technology is substantially simpler than that of bipro-pellant engines with added reliability, relatively simple feed systems, and moderate

24

performance characteristics. For state of the art hydrazine thrusters a specific im-pulse of 220 s is attainable. Hydrazine thrusters are used extensively on conventionalspacecraft for attitude control and as primary propulsion for intermediate to low ∆Vmaneuvers (about 1 km/s or less). The smallest available hydrazine thrusters producethrust in the 0.9 to 4.45 N range. These engines could conceivably be used for primarypropulsion on micro-spacecraft. Currently there is development of a miniature hy-drazine thruster capable of impulse bit performances of 50-100 mN. Impulse bits thissmall are well suited for fine attitude control and formation flying in constellations[15]. The replacement of cold gas thruster technology is the main goal of miniaturehydrazine thruster development, consequently eliminating leakage concerns on longmissions. The need for momentum wheels could also be eliminated saving weight,power, and cost.

Current hydrazine thruster technology allows for easy integration into a Class Imicro-spacecraft bus due to minimal engine size, weight, and thrust levels. Also,minimal redevelopment is required for integration in Class I spacecraft due to theconsiderable flight time experienced by hydrazine thrusters. In the past, small hy-drazine thrusters have been used mainly for attitude control purposes where fast valveaction is needed for short impulses. Greater than 50% of the engine’s weight can beattributed to the valve. Since primary propulsion applications usually do not requireshort impulses slower, less efficient valves may be implemented greatly reducing totalengine weight. There are some disadvantages to using hydrazine thrusters, however.Hydrazine itself is highly toxic and flammable resulting in high ground handling andpropellant loading costs. Also, if higher ∆V maneuvers are needed monopropellantsystems become increasingly heavy due to propellant storage. The concern of space-craft component contamination in missions requiring formation flying is also relevant.However, it must be addressed that for missions requiring ∆V maneuvers less than1km/s monopropellant systems have an advantage over bipropellant systems due toreduced cost, system complexity, component part count, volume and mass [14].

3.5.3 Hydroxylammonium Nitrate

Another form of monopropellant technology involves the use of (hydroxylammo-nium nitrate)-based propellants (HAN). HAN-based propulsion technology offers sig-nificant advantages over hydrazine systems. The propellant used is a mixture of anoxygen rich component called HAN and a fuel rich component, both diluted in wa-ter. The propellant and its reaction products are relatively nontoxic to spacecraftcomponents, resulting in an ease of ground handling and loading costs. HAN-basedpropellants offer 40% higher storage densities than hydrazine allowing for smaller

25

propellant tanks. HAN-based mixtures also contain the ability to operate at lowertemperatures than hydrazine. High storage densities and improved thermal operat-ing conditions make HAN-based propulsion techniques extremely favorable for useon micro-spacecraft. Smaller and lighter storage tanks can be used and the need fortank and line heaters is possibly eliminated, reducing overall power requirements.One issue with HAN-based propellants is the high flame temperatures experiencedin the engines. Similar to small bipropellant engines, special attention must be paidto thermal design of the chamber. Proper materials must be selected that will with-stand these high temperatures. HAN-based thrusters offer an attractive alternativeto hydrazine thruster technology for Class I spacecraft for primary propulsion appli-cations, due to reduced toxicity, easier handling procedures, and increased propellantstorage densities [14].

3.5.4 Cold Gas

Cold gas thrusters represent the smallest rocket engine technology currently avail-able. They are valued for their simplicity, small impulse bit capability, and low space-craft contamination qualities. There are valve leakage concerns which could possiblylead to catastrophic loss of propellant on longer missions. For most cases cold gassystems are characterized by low specific impulse. Only with the use of extremelylight propellant gas can higher specific impulses be obtained. However valve leak-age may be a concern when extremely light gases are used. Nitrogen is by far themost commonly used cold gas propellant due to reasonable storage density, perfor-mance, and lack of contamination concerns. The low specific impulse characteristicsof cold gas thrusters eliminate the possibility of its use for primary propulsion onmicro-spacecraft. However, its use for attitude control is still an option. Size, mass,and power requirements adhere well to Class I micro-spacecraft constraints, howeverthere does not seem to be any real advantages over using a monopropellant system.Required large heavy tankage and propellant leakage concerns make cold gas systemsunattractive for micro-spacecraft, especially on long missions [14]. Cold gas systemsare currently being considered for attitude control applications where only limitedspacecraft lifetimes are required.

3.5.5 Solid Rocket Motors

Solid rocket motors are a common form of propulsion used for orbit transfer andorbit insertion maneuvers. They combine compact size with high specific impulseperformance. These values are comparably lower than bipropellant engines but higher

26

than monopropellant engines. The use of solid propellant eliminates any leakageconcerns. The disadvantage is that a solid rocket motor’s engine can only be firedonce, not allowing for any orbit trimming [14]. State of the art solid rocket motorsappear quite suitable for Class I spacecraft, however thrust levels are much too highand burn times are generally short. Neither result is desirable for micro-spacecraftapplications. If ongoing efforts to obtain longer burn times and lower thrust values canbe met solid rocket motors could be an attractive option for future micro-spacecrafttravel.

3.5.6 Electrical Propulsion

Electrical propulsion offers several different techniques for propulsion. One tech-nique is the ion engine. The typical propellant for ion engines is xenon. Ions areextracted from a gaseous plasma discharge by electrostatic forces and acceleratedacross an electric potential difference. The accelerated ions achieve speeds of around300 km/s corresponding to a specific impulse of 3000 s. Ion propulsion subsystemsconsist of several components, all of which will need to be miniaturized for micro-spacecraft applications. Components include the thruster, the power conditioningunit (providing voltage to the engine), and the feed system. High specific impulse,which results in significant propellant savings and overall mass reduction is a definiteadvantage. This is of extreme importance to micro-spacecraft, especially on missionsrequiring high ∆V maneuvers. Compared to chemical bipropellant systems ion en-gines offer the possibility of lighter spacecraft and shorter mission times. Reducedpropellant requirements due to high specific impulses result in reduced propellantrequirements, allowing for extremely compact propellant storage. Also, xenon is aninert gas and is completely non-contaminating to all spacecraft materials and com-ponents. An important disadvantage to using ion propulsion systems is the additionof its electrical power requirements which may add considerable overall mass to thespacecraft. To reduce this disadvantage an optimal operating point must be selectedallowing for both significant propellant savings and low power system masses. Typ-ically the optimum operating point seems to be 3000 s Isp [15]. All current ionengines are too large for use on Class I spacecraft with respect to both mass andpower requirements. New technologies will have to be developed in order to integrateion engine technology into Class I micro-spacecraft. Thruster miniaturization andsmaller power requirements are key areas in development of these new technologies.Thus micro-ion engines are to be considered highly advanced micro-propulsion con-cepts that still have many challenges to overcome before their use on micro-spacecraftbelow 25 kg may be realized.

27

Another form of electric propulsion using electrostatic propulsion is the Hallthruster. Using xenon as a propellant, Hall thrusters use plasma generation andion beam acceleration which results in more compact thrusters than obtainable withion engines. Hall thrusters are more compact than ion engines, yet deliver the samethrust. Their specific impulse capabilities of around 2000 s fall short of the ion en-gines specific impulse of 3000 s. However a 2000 s specific impulse is still suitablefor orbit transfers, repositioning, and other intermediate ∆V maneuvers. AlthoughHall thrusters are more compact than ion engine thrusters they are much too heavyfor use on Class I spacecraft and consume too much power [14]. Currently, they fitbetter into near-Earth applications rather than interplanetary.

Similar to ion engines and Hall thrusters, Field Emission Electric Propulsion(FEEP) systems generate thrust by accelerating ions by means of electrostatic forces.The advantage to FEEP is that the ionization mechanism does not require a gaseousdischarge, resulting in high miniaturization possibilities. They are also able to de-liver extremely small impulse bits. The downside is the field emission process requireslarge voltage sources (up to 10 kV). This leads to very high specific impulses around10,000 s, resulting in high mass penalties associated with the power conditioning unit.Spacecraft component contamination is also an issue considering the propellant com-monly used is liquid metal Cesium. With concerns over contamination and severepower constraint issues, current technology in the FEEP propulsion field does notlend itself to Class I spacecraft for attitude control or primary applications [14].

Colloid thrusters function similarly to FEEP devices, featuring emitter tips andaccelerating electrodes. Thrust is produced by electrostatically accelerating finecharged liquid droplets ejected from a capillary. Several trade-offs have to be made incolloid thruster design to optimize performance. One challenge is to offset the extramass associated with the addition of the power conditioning system used to drivethe system. This can be done by optimizing specific impulse performance. Carefulselection of propellant is also necessary to avoid thruster corrosion. Glycerol is foundto fit system needs and constraints better than other tested propellants. Specificimpulses as high as 1450 s have been achieved during testing at voltages of 12.3and -2.0 kV. Colloid thrusters lend themselves to a high level of miniaturization byavoiding gaseous plasma discharges. Colloid thrusters appear to fit well within theClass I micro-spacecraft size and power constraints, possibly better than any othercurrent electric propulsion concepts. However, colloid propulsion system’s low spe-cific impulse limits its use for primary propulsion applications. For this reason colloidthrusters are limited to missions requiring low ∆V maneuvers [14].

A unique type of electrical propulsion device is the pulsed plasma thrusters (PPT).In a PPT, the propellant is ionized and electromagnetically accelerated in a pulsed

28

mode of operation. The fuel used is a solid bar of Teflon. PPTs are valued for theirrelative simplicity of operation, simple propellant feed systems, and compact (solid)propellant storage, featuring no moving parts with the exception of the Teflon fuelbar. PPTs are capable of providing minute long impulse bits suitable for fine attitudecontrol. However, PPTs have been associated with low thruster efficiencies and lowthrust-to-power ratios. Component contamination does not seem to be an issue withPPTs; however, further investigation into the matter is underway. PPTs are currentlyable to produce specific impulses up to 5000 s with typical values ranging between1000-1500s. Impulse bits as low as 22mN/s have been generated and power levelsbetween 1 and 30 W are needed [14]. Pulsed plasma technology for Class I spacecraftis still under development.

3.6 Power

The electrical power subsystem will be responsible for collecting, storing, anddistributing power as needed to all subsystems. The following tasks must be fulfilledby the power subsystem:

• Generate continuous power during the mission.

• Distribute power to bus and payload.

• Provide additional power to support times of peak loading.

• Protect system components from harmful anomalies such as voltage spikes.

There are several common technologies available for each component of the powersubsystem. These options are discussed in further detail below.

3.6.1 Power Generation

There are four main classes of technology for power generation aboard on-orbitspacecraft: photovoltaic, static, dynamic, and fuel cells. Photovoltaic power comesfrom solar panels which convert incident radiation into electric current. These panelscan be either affixed to the body of the spacecraft or attached to separate appendages.Solar photovoltaic power generation is relatively inexpensive and reliable, making itthe power generation system of choice for many spacecraft (other than deep spaceinterplanetary missions away from the Sun). However, solar panels are susceptibleto damage from orbital debris as well as radiation. They also degrade significantly

29

over the spacecraft’s lifetime and can be sensitive to attitude. Several materialsare available for construction of solar panels, including silicon, gallium arsenide, andindium phosphide. Silicon is cheaper and its properties are more well-known; howeverit is relatively inefficient at converting incident radiation into electrical power. Indiumphosphide is more efficient than silicon and is much less susceptible to degradationbut is more expensive. Gallium arsenide is the most efficient material but is alsoexpensive [7].

Static power sources use a nuclear heat source to convert thermal energy to elec-tric energy. Common technologies include the thermoelectric couple and thermionicenergy conversion. Static power sources are minimally affected by the space envi-ronment, do not rely on sun-pointing, and suffer from little degradation. However,these technologies are considerably more expensive than photovoltaic sources andpresent radioactive pollution concerns. For these reasons, this type of power sourceis generally used for interplanetary missions.

Dynamic power sources use a working fluid heated by energy from either thesun or a nuclear power source to produce power through a thermodynamic cycle [7].Dynamic sources using nuclear power suffer from the same drawbacks as mentionedabove. Solar thermal dynamic sources are capable of providing more power thanphotovoltaic systems but require more mass per unit power.

Fuel cells convert chemical energy to electricity through an oxidation reaction.Fuel cells are capable of producing significant amounts of power for a given mass.In addition, lifetime degradation is low and they are not severely affected by spaceenvironment. However, the need to carry all fuel onboard makes them prohibitive forlong duration missions. Thus fuel cells are generally used for manned (short term)missions.

3.6.2 Energy Storage

Most spacecraft powered by solar energy require some stored energy for eclipseperiods or peak power demands. While SIRA is expected to not experience eclipses,extra power may be required for subsystems demands such as communications dumpsand formation-keeping maneuvers. Chemical batteries are typically used for storage,though flywheels and other methods are being considered for future missions.

Some spacecraft carry primary batteries, which are generally used for short-term,high power tasks at the beginning of the mission. Secondary batteries can convertchemical energy to electrical energy and back. Nickel cadmium and nickel hydrogenare two battery technologies commonly in use at present. Nickel cadmium cells arerelatively inexpensive and reliable, though they suffer from the problem of memory

30

(i.e. if not discharged completely some power capability can be lost). Nickel hydrogenbatteries are more efficient and have no memory but are more expensive. Other moreefficient cells are under development including lithium-ion and sodium-sulfur. Thesehave the potential of reducing spacecraft mass devoted to power.

The use of flywheels to store electric energy is another option. Electric energy canbe converted to mechanical energy in the wheel for storage. When power is required,the wheel spins down and the motor becomes a generator, producing electric power.Flywheels have the advantage of high efficiency relative to batteries and a nearlyunlimited lifetime [16]. However, they do affect the attitude of the spacecraft andthis must be taken into account.

3.6.3 Power Control

The power control system for the spacecraft is responsible for preventing batteryovercharging and spacecraft overheating due to extra power production. The twomain power control methods currently in use are peak-power tracking and directenergy transfer. A peak-power tracker is a non-dissipative mechanism that extractsonly the necessary power to the bus. This type of power control is commonly usedon shorter missions. Direct energy transfer systems dissipate excess power throughshunts. The advantages of such a system include less breakable parts, lower mass,and better effectiveness for long missions [7].

3.7 Thermal Control

Thermal protection will be an integral part of SIRA due to its orbit placing it incontinuous sunlight. Cycling effects need not be taken into effect.

The use of multi-layer insulation (MLI) on the outside of the spacecraft is theprimary hardware component for thermal control. The MLI can be coated withdifferent materials to produce the desired thermal effect. Optical Solar Reflectors(OSRs) have a highly reflective surface to produce a low solar absorptivity, anda transparent quartz cover to create a high emissivity. OSRs produce the lowesttemperature when irradiated by solar energy, but are both fragile and expensive.Silver-coated Teflon can also be used to coat the MLI and have similar properties toOSRs. Silver-coated Teflon does not provide as low a temperature as OSRs, but theyare much less expensive and much more durable [7].

Another requirement is to dissipate heat from the electrical equipment. SIRA is alow mass satellite and therefore will not produce much electrical heat. Passive space

31

radiators can be used to dissipate the heat out into space. These components areinexpensive since they consist of no moving parts. The use of cold plates is anotheralternative which can be used to dissipate heat away from electrical equipment. Coldplates are simply mounted onto the equipment and have fluid pumped through themwhich carries waste heat to a radiator which dispels the waste heat out into space.They are inexpensive, but add weight due to the necessary plumbing and the needfor a pump. Heat pipes are sealed pipes with a phase changing fluid inside whichcarries heat from electrical equipment to space radiators. Heat pipes have low massand size, yet exhibit high heat transfer capabilities [7].

Some components of SIRA may need to be temperature regulated. This can beaccomplished by the use of thermistors or resistance thermometers. Thermistorsare cheap, small, and relatively accurate. They have a very small response timeand consume minimal amounts of power. They operate in the range of −50o C to+300o C. In contrast, resistance thermometers are extremely accurate but are muchmore expensive. They operate in the range of −260o C to +600o C. Resistancethermometers are mainly used on solar arrays due to the fact that a solar cell’sefficiency increases as temperature decreases, and this temperature value will need tobe monitored closely.

3.8 Communication, Command, and Data Han-

dling

The communications and command subsystem is integral to the satellite designbecause it allows all of the other subsystems to interact with each other and with thehuman element at ground control. This subsystem manages all of the informationcoming in and going out of the satellite. This subsystem’s job is to gather and studyall of that information, which is the ultimate goal of the mission.

There are many variables to be determined in the design of a communications,command, and data handling system for SIRA due to the uniqueness and the mission.This system will need to be lightweight and possibly very technically complex. Thesatellite command system must be able to control the other subsystems, such as thepropulsion, ACS, and power systems. The fleet of microsatellites will all need tocommunicate freely with each other for fleet-keeping purposes. The fleet will alsotransmit the collected data back to the ground station, over 50 Earth radii away,using relatively low-power transmitters and small aperture antennas.

Communication within the fleet and with ground control can be achieved using

32

a combination of wide-beam antennas around the satellite structure, and possibly ahigher-gain directional antenna. The wide-beam antennas allow the microsatellites tosend and receive fleet-keeping commands to each other without pointing requirements.In order to relay the collected data back to the ground stations, directional antennasmay need to be pointed at Earth to achieve a high data rate transmission. Availablefrequencies for space communication are S, X, and Ku bands, at about 2, 8, and12 GHz respectively. Data communication over a high bandwidth may require ahigh gain directional antenna. For this reason, S or X-band frequencies will be moresuitable to a non-pointing solution. A typical 2 W S-band system, transmitting 1,000bits/sec, consumes 4.4 W and weighs 5.9 kg [7]. Power requirements and overall massof this subsystem can add up very quickly, with the need for digital encoders, relays,and command computers.

The command and data handling subsystem onboard each microsatellite must per-form two main functions: “it receives, validates, decodes, and distributes commandsto other subsystems”; and “gathers, processes, and formats spacecraft fleetkeepingand mission data for downlink or use by an onboard computer” [7]. Inherent featuresto this subsystem are timekeeping and system monitoring. The size of this subsystemis usually proportional to the complexity of the spacecraft. Due to stringent massrestrictions on SIRA, this subsystem will be required to handle potentially complex at-titude control and data handling procedures, using minimal power and weight. Table3.1 includes estimated size and masses for command systems of varying complexities.SIRA will be a combination of simple and complex elements.

Table 3.1: Estimated sizes, weights, and power requirements for command subsystemsof varying complexity.

Simple Typical ComplexVolume (cm3) 2500–6000 6000–9000 13000–15000Weight (kg) 2.75–5.5 4.5–6.5 9.5–10.5Power (W ) 7–12 13–18 15–25

Complexity of the command system is determined by processing command re-quirements, telemetry data processing requirements, bus constraints, reliability ClassS parts, time clock and watchdog requirements.

33

3.9 Formation Configuration

The primary design decision for SIRA is the inclusion or exclusion of a hostsatellite to be maintained for the mission lifetime. One option is to maintain a hostsatellite to command and administrate the antenna array. The host satellite in thiscase would perform all data compression and transmission to Earth. The alternativeis to dispose of the host satellite after orbit insertion. In this case the array wouldfunction entirely as a single instrument, performing both transmission and receivingoperations. This second configuration has fewer single points of failure and will bedesigned to function even if one of the microsatellites stopped working. The singlepoint of failure argument can be summarized as follows: The probability of any oneof the array elements failing is less than the probability of multiple elements failing.

3.9.1 Redundant Microsatellites

The autonomous satellite array will perform many of the same functions that thehost craft would perform. Each satellite must know its precise position with respectto every other spacecraft. This will result in twice as many measurements than arenecessary but will reduce the relative position error. The magnetic field observationsand the ranging data both must be compressed and reformatted for transmission.Image forming will be performed on the ground, where computing power is not massconstrained. The array must broadcast the data to Earth. Eliminating the hostsatellite translates into reduced station keeping and propellant requirements as wellas improving the reliability of the mission.

The mission strategy will progress as follows:

1. The microsatellites will be identical in their construction. Each will house itsown power, thermal, and propulsion system. Each microsatellite is autonomousand independent of its comrades.

2. The satellites will be launched simultaneously as a single unit within a protectivehousing. The housing will cushion and protect the microsatellites from the loadsat launch. The housing will transport the microsatellites to their final orbit.

3. After full orbit insertion into the destination orbit, the transport craft willinitialize the satellites and release them one at a time. The release mechanismmay resemble a spring and may propel them into the array configuration.

4. The transport craft will then thrust away.

34

5. The microsatellites will then perform small position corrections and assumetheir functional positions.

6. The microsatellite will make observations while maintaining constant positionknowledge of itself with respect to the other satellites.

7. This information will be transmitted to the other elements of the array and willbe compressed into a single, transmittable unit.

8. The single signal will be transmitted back to Earth periodically utilizing theentire array as a single large, high power antenna.

9. The array will continue to perform its mission until so many of the array ele-ments fail that the observations provide no useful information.

Elimination of the host spacecraft increases the lifetime of the instrument. Nofunctionality is lost, while the support system requirements are lessened. The hostsatellite no longer has to be maintained throughout the mission lifetime. The powerrequired to compress and transmit the data between the array elements in additionto Earth is substantial. In the system analysis chapter of this report we will weightthe costs and gains of the host satellite for the SIRA mission.

3.9.2 Host Spacecraft

The advantage of using a host satellite is that it vastly reduces the complexity,mass, size, cost of each individual microsatellite. Also, the host satellite can perform asignificant portion of the data reduction, image forming, and data compression beforetransmission. The data transmission rate could be one or two orders of magnitudehigher than that of the array without a host satellite, increasing the flexibility ofground station selection and design. If the host satellite can compile all of the dataand transmit to Earth, in the time it takes a single ground station to come in andout of view, then there will be no need for DSN.

The mission strategy for the host satellite configuration will progress as follows:

1. The microsatellites will be identical in their construction, except for the hostsatellite which will be the remainder of the insertion vehicle. Each will houseits own power, thermal, and propulsion system. Each microsatellite is underthe direct surveillance and control of the host satellite.

35

2. The satellites will be launched simultaneously as a single unit. Each microsatel-lite attached to the host satellite, comprising the launch vehicle payload.

3. After inserted into the destination orbit by the launch vehicle, the host satellitewill propel itself and the microsatellites (as one spacecraft) to their final orbitallocation.

4. The host satellite will release each of the microsatellites by means of a spring-loaded mechanism. The microsatellites will use their own propulsion to establishthe predetermined array shape and assume their functional positions.

5. Once all of the microsatellites have been released and positioned, the host satel-lite will orient itself for optimal communication with the array and for high datarate transmission with the ground station.

6. The microsatellites will make observations while obeying position and rangingcommands from the host satellite.

7. Data gathered from each microsatellite will be transmitted by means of omni-directional low gain antenna to the host satellite for reduction, compression,and storage.

8. Periodically, as the ground station becomes visible, the host satellite will trans-mit the stored data through a directional high gain antenna.

9. The array will continue until so many of the microsatellites fail that the obser-vations provide no useful information.

A design incorporating a host satellite will simplify certain aspects of this mission,while possibly complicating others. The host satellite would cause a potential singlepoint of failure to the design, but there are measures that can be taken to greatlyreduce that possibility. The technology and methodology already exist for a relativelycheap solution using a host satellite design, whereas further development is requiredto design a completely autonomous microsatellite array capable of such powerfultransmission capabilities.

3.10 Conclusion

SIRA’s components must work together to complete the objectives of the mission.This chapter evaluated these systems and put together scenarios of crude completed

36

spacecraft. These two scenarios are creating the satellite array with and without acentral host satellite. With this initial information established further progress canbe made in analyzing these systems to determine how well they will complete themission objectives. Table 3.2 summarizes the different design possibilities for eachsubsystem and mission parameter as discussed in this chapter.

Table 3.2: Summary of system possibilities.

System/Parameter OptionsFormation Configuration Central Satellite Redundant Small SpacecraftArray Configuration Random Spherical EllipsoidalOrbit Solar L1 Lunar L4/L5 Distant RetrogradeAttitude Control Thrusters Reaction Wheels

Control Moment GyrosPropulsion HAN PPT Electric ColloidSolar Panels Silicon Indium Phosphide

Gallium ArsenideEnergy Storage None Nickel Cadmium Nickel HydrogenCooling Cold Plate Radiation Heat Pipes

37

Chapter 4

System Analysis

Chapter 3 discusses possible solutions that may be used for each subsystem andpossible orbital array configurations. This chapter takes these ideas further by an-alyzing the specific ideas governing each subsystem. Equations for modeling eachsystem are presented that will enable the design and sizing of each subsystem to therequirements of the SIRA mission. This chapter does not describe the final design ofSIRA but acts as a good starting point.

4.1 Array Analysis

SIRA will be designed to maximize dynamic range and receiving power and tominimize angular resolution. Considering an array consisting of many antenna pairs,any pair of antennas can be analyzed simply as a single interferometer. The spacingbetween the two antennas is the foremost parameter governing their combined perfor-mance. The surface area of a 25 km sphere is 7850 km2. This required coverage areais representative of the separation between antenna pairs. The ellipsoidal array thatis 5 km in radius at the center of the major axis and is 25 km in length has a surfacearea less than 785 km2. The ellipsoidal configuration synthesizes a larger aperturearea compared to the spherical configuration for the same maximum separation.

The spherical array is more three dimensional than the ellipsoidal array. Aninterferometer is most sensitive to signals perpendicular to its baseline; therefore, thespherical array can detect signals equally in all directions. Conversely, the ellipsoidalarray is predisposed to measurements within a single plane; that formed by the majoraxis and the signal path.

The maximum separation between elements in the array determines angular res-

38

olution of the array. The angular resolution for a larger aperture is greater than theangular resolution for a smaller aperture given the same number of elements. Theellipsoidal configuration images three dimensional fields less effectively because it isless three dimensional than the sphere. Therefore SIRA will observe coronal massejections in a spherical configuration.

The receiving power of the microsatellite array will determine the strength andclarity of the data. Receiving power for a field of unit brightness is [18]:

P = B̄Aθ2π

4(4.1)

Increasing the area and the angular resolution of the array will improve the array’sperformance.

4.1.1 Element Selection

The elements of the antenna will be selected to maximize signal coverage andpower. The beam pattern produced by the antenna is computed using Biot Savart’slaw.

B =µ0

4π

∫ Idl × (r − r′)

|r − r′|3(4.2)

The magnetic field produced by a conducting wire varies as the inverse of theradial distance from it. The dipole antenna consists of two parallel conductors linedup end to end, separated by an insulator. This configuration produces two beam lobessurrounding the conductors, with a dark, insensitive region produced by the insulationmaterial. The typical beam pattern produced by a dipole antenna is shown in Figure4.1.

Figure 4.1: Dipole array.

This dark spot in the field pattern can be alleviated by the addition of a seconddipole oriented orthogonal to the first. Two dipoles combined in a single antenna

39

form a turnstile antenna. The typical beam pattern for a turnstile antenna is shownin Figure 4.2.

A third possible antenna element is the loop antenna. The loop antenna is asingle conducting element, generally circular, with a break for the signal line. Theloop antenna has a beam pattern shape similar to the dipole antenna with the nulllocated near the conductor and lobes extending outward normal to the plane of theloop. The dark spots in the pattern are smaller than those seen in the dipole pattern.Additionally, the loop antenna may reduce the noise produced by the microsatellitecomputer and other electronics.

Design must not interfere with the effectiveness of the antenna, the design mayrequire the displacement of the antenna element from the other components. TheBroadband Loop antenna manufactured by Wellbrook boasts a 30 dB rejection oflocally radiated noise compared to similar dipole antennas (Wellbrook). This wouldbe particularly advantageous for SIRA in reducing interference from the microsatelliteelectronics.

Figure 4.2: Turnstile array.

Figure 4.3: Loop array.

4.2 Attitude Determination and Control

The ADCS will be designed to minimize the weight while still fulfilling the controlrequirements. The SIRA mission consists of two phases, the transfer orbit and mission

40

orbit. The microsatellites will all be connected during the transfer orbit. A mainpropulsion system will be used for locomotion. The attitude must also be looselycontrolled during the transfer to insure the thrust vector is pointing in the correctdirection. The microsatellites will separate upon arrival at the mission orbit location.Once separated, each microsatellite will need independent attitude determination andcontrol capabilities.

The transmitter and antenna pointing requirements are used to decide the min-imum attitude determination accuracy needed. The strength and beamwidth of thetransmitter will determine the required accuracy. Also, the relative position of themicrosatellites must be known to within 6 m. Assuming a 25 km diameter sphericalformation, the accuracy required is 0.0138 degrees. Star trackers are able to providebetween 0.0003 and 0.01 degree accuracy. Sun sensor accuracy has a range from 0.005to 3 degrees [7]. The power requirement is much less for sun sensors than for startrackers. Magnetometers and horizon sensors are not suitable for the SIRA mission.The magnetic field is not known and there are no horizons visible from SIRA’s orbit.

The most demanding pointing requirement for SIRA is caused by the high gaindownlink antenna. The dipole radio antennas must be kept perpendicular to thesun at all times during observation. Also, the relative positions of the formationalong with the orbit must be maintained. The high gain antenna can be chosento be self-articulating to remove the restriction of maneuvering the entire satellite.Increased complexity and weight are the undesired side effects of a self-articulatingcomponent. A thruster system will be required onboard each microsat for positioningmaneuvers. Designing the thrusters to fulfill all of the attitude control requirementswould eliminate the weight of another actuator such as reaction wheels. However, thepropellant adds weight and volume to the microsat. Reaction or momentum wheelsare another possible control actuator for SIRA.

The disturbance torque experienced by the microsats must be sized in order tochoose the type of actuator. The gravity effects of the Earth and Moon, as wellas solar radiation pressure, will contribute the most to the disturbance torque. Theworst case disturbance from any celestial body must be taken into account. The solarradiation pressure produces a torque given by Equation 4.3 [7].

Tsp =Fs

cAs(1 + q) cos i(csp − cg) (4.3)

Where the solar constant Fs ≈ 1,367 W/m2, the speed of light c=3 ×108 m/s, As isthe surface area, csp is the location of the center of solar pressure, cg is the centerof gravity, q is the reflectance factor, and i is the angle of incidence to the sun. Thesizing of momentum wheels can be done using Equations 4.4 and 4.5. Equation 4.4

41

is used to determine the necessary torque the wheel must produce. Equation 4.5 isused to find the minimum momentum storage capability of the wheel.

Trw = TD × safety factor (4.4)

TP

4= hθa (4.5)

Thruster characterization includes determining the force, the number of pulsesto be performed throughout the life of the mission, and the amount of propellantneeded. The required force is simply the disturbance torque divided by the momentarm from the center of mass. An estimation must be made as to how often attitude,formation, and orbital correction maneuvers are needed. For each maneuver thereare two pulses, one to start and one to stop. The total mass of propellant can befound using Equation 4.6.

mpr =Ft

Ispg(4.6)

Where F is the force from the thruster, t is the duration of the thrust, Isp is thespecific impulse of the propellant, and g is the gravitational constant.

The sizing of possible actuators along with a selection of the best attitude deter-mination sensor is the next step in the design process. The properties of each systemwill be placed into the values system design. The best design will be chosen andoptimization will follow.

4.3 Propulsion

Minimizing mass and power requirements on SIRA’s microsatellite propulsionsubsystems is integral to mission success. Succeeding in both areas leads to maximumreliability at minimum cost. SIRA’s mission geometry involves several different phasesof propulsion. Each phase requires a propulsion system that accommodates particularperformance, power, and mass constraints. The following is an analysis of propulsionsystems from Chapter 3 that could conceivably meet all of SIRA’s mass, power, andcost constraints while simplifying overall design.

To simplify design and minimize mass of SIRA microsatellites, an upper stageor IPS (integral propulsion system) will be used to insert the microsatellites into theselected orbit. Each microsatellite contains a set of microthrusters for attitude controland a main micropropulsion system for station and formation keeping. The propulsion

42

system chosen for each phase of the mission must meet thrust and ∆V requirementswhile minimizing propellant mass and storage. Table 4.1 shows the ∆V requirementsof each propulsion phase for the orbits being considered. The information in Table4.1 is taken from a presentation given by NASA on SIRA trajectory and formationanalysis [11].

Table 4.1: Orbit comparison for fuel consumption (m/s).

Mission Phase DRO Solar L1

Mission Orbit Insertion 444 10Orbit Maintenance 0 5Formation Maintenance 0.22 0.63

The following relationship is used along with data from Table 4.1 to calculate themass of propellant needed to meet the ∆V requirements for each phase of the mission[13]:

mp = mf [exp(∆V/Isp)− 1] = mo[1− exp(−∆V/Isp)] (4.7)

where mo is the initial vehicle mass, mf is the final vehicle mass, ∆V is the requiredchange in velocity, and Isp is the specific impulse of the propellant.

Several of the propulsion systems discussed in Chapter 3 appear to be viableoptions for the upper stage or IPS which performs the mission orbit insertion phase.With an estimated microsatellite mass of 30 to 40 kg, the mass of the entire arraywill be between 480 to 640 kg. The upper stage or IPS is solely responsible theinsertion maneuver of SIRA’s microsatellites into the final orbit. Table 4.2 shows thepropellant mass required by three IPS options for orbit insertion using Equation 4.7,a maximum microsatellite mass of 40 kg, and information given in Table 4.1.

Table 4.2: Propellant of various propulsion system parameters.

DRO (444 m/s) Solar L1 (10 m/s)Bipropellant 42.83 kg 1.03 kgHydrazine 58.31 kg 1.44 kgIon Engine 4.79 kg 0.12 kg

Bipropellant engines offer high performance characteristics associated with highthrust-to-mass ratios. Typically used on larger spacecraft, state-of-the-art technology

43

now offers much smaller low thrust bipropellant engines capable of achieving the small∆V requirements for insertion into the orbits considered. However, there is the issueof high complexity leading to high cost with bipropellant engines. Table 4.2 showsthat the cost issue may not be a significant factor due to significant propellant masssavings compared to other chemical systems. The bipropellant system appears tobe an excellent option for insertion of SIRA’s microsatellites into the DRO orbit. Abipropellant system is not feasible for the L1 halo orbit insertion. Since propellantmass is not an issue for L1 insertion the possibility of using a much cheaper andreliable system may be more applicable.

Another chemical system being considered for SIRA’s orbit insertion phase is ahydrazine monopropellant system. The hydrazine system offers reliability and a highlevel of development and flight experience. The problem is a low specific impulseleading to extra propellant mass as shown in Table 4.2. The issue of large storagetanks associated with hydrazine must also be considered. Propellant mass constraintsmay be ignored for the L1 insertion maneuver due to the small ∆V requirement. Ahydrazine IPS is a favorable option for L1 if high ground handling and loading costsare acceptable.

The possibility also exists for SIRA to use electrostatic propulsion for the up-per stage or IPS. An ion engine offers an extremely high specific impulse resultingin significant propellant mass and cost savings compared to the chemical systemsconsidered. The propellant Xenon, an inert gas, eliminates high ground handlingand loading costs associated with chemical propellants. A dedicated power supplyis needed to drive the ion engine which is separate from the power supply for eachmicrosatellite. The extra mass associated with the ion engines power system is notan issue, since microsatellites leave the upper stage behind after they are insertedinto their final orbit. The risks of using an ion engine for the insertion phase of themission are a high complexity combined with minimal development. Final orbit de-termination and further investigation of all three systems is required to ascertain theoptimum choice for SIRA’s IPS. The main issues to resolve are mass over cost andcomplexity over reliability.

SIRA’s microsatellites contain a set of microthrusters for attitude control and amain propulsion system for stationkeeping and orbit maneuvering. The same type ofsystem is used for primary as well as attitude control propulsion applications. Thisconfiguration eliminates the need for separate propellant storage tanks minimizingoverall mass and volume of the spacecraft. Pulsed plasma thrusters and colloid spraythrusters are being considered for propulsion duties in this phase of the mission.Their high miniaturization capabilities along with adequate performance character-istics conform well within SIRA’s microsatellite design constraints. Table 4.3 shows

44

the propellant mass required by both systems for primary and ACDS functions usingEquation 2.2, a maximum microsatellite mass of 40 kg and a mission lifetime of fiveyears.

Table 4.3: Propellant of various propulsion system parameters.

DRO Solar L1

Colloid Spray Thruster 0.58 kg 2.45 kgPulsed Plasma Thruster 0.38 kg 1.65 kg

Colloid microthrusters offer moderately high performance characteristics at lowpower consumption. Colloid thrusters weighing only 0.5 kg are capable of producing0.1 mN of thrust using a maximum of 4 watts with a specific impulse of 1000 s [19].This allows for extreme miniaturization of the propulsion system. Table 4.3 showsthat on a five year mission SIRA’s microsatellites need a maximum 0.6 to 2.5 kg ofpropellant. Total subsystem mass for each microsatellite, including the propellant, isestimated between 2 and 4.5 kg depending on the orbit chosen. The only foreseeableissue is the colloid systems complicated design which could lead to high costs. Overall,the colloid spray system appears to be an excellent choice for SIRA’s microsatellitepropulsion applications.

Another propulsion system being considered for the mission orbit phase is a pulsedplasma thruster or PPT. The PPT offers slightly higher performance characteristicsover colloid thrusters with a much simpler design. Typical specific impulse num-bers are around 1500 s at minimal power consumption compared to most electricpropulsion systems. The PPT holds a small advantage over the colloid system in thearea of propellant mass needed as shown in Table 4.3. There is possibly an issuewith PPTs not being able to carry enough propellant along for the mission. Fur-ther investigation of this issue is necessary to determine if the problem exists. Bothmicropropulsion systems are well suited for this phase of SIRA’s mission. Extensiveresearch in cost analysis and reliability may help to determine the optimal choice forthe SIRA mission.

4.4 Power System

As mentioned in the previous chapter, there are several options available for eachaspect of the power system. The best option from each class is selected based on

45

mission constraints and the value system. Once the systems are chosen, the corre-sponding components must be sized to meet the requirements of other subsystems.

4.4.1 Power Generation

As discussed previously, the principal sources of power generation are photovoltaic,static, dynamic, and fuel cells. Static nuclear sources are expensive, risk pollution,and are not energy dense (low W/kg). Since cost and mass are the two largestconcerns for SIRA, nuclear power sources do not fit within the requirements or valuesystem. Nuclear dynamic sources suffer from the same drawbacks. Solar thermaldynamic cycles are less expensive, but are heavy and thus more effective for largerspacecraft. Fuel cells are prohibitive for long duration missions since all fuel must becarried on board. Photovoltaic sources suffer from none of the above restrictions: theyare inexpensive, energy dense, and well proven through use in many space missions.In addition, any orbit choice for SIRA will result in constant sunlight exposure.For these reasons, a photovoltaic source is the best alternative for use on the SIRAspacecraft.

The photovoltaic solar cells are sized so as to provide the required power at aminimum of mass and cost. The general expression for the power that must beprovided by the solar arrays is:

Psa =

(PeTe

Xe+ PdTd

Xd

)Td

(4.8)

where P , T , and X represent power, time per day, and path efficiencies respectivelyand the d and e subscripts are for daylight and eclipse respectively [7]. For anorbit always in sunlight (dropping the previous subscripts), the above equation easilyreduces to:

Psa =Preq

X(4.9)

The solar cells can be sized once the power requirement is known. The firstcalculation is the power density produced by the cell at the beginning of the spacecraftlife:

PBOL = ηFsId cos θ (4.10)

Here η is the cell material efficiency, Fs is the incident energy per area, Id is theinherent degradation due to manufacturing and shadowing, and θ is the worst case

46

sun angle. The end-of-life power is then found by multiplying the value at beginningof life by a lifetime degradation constant:

PEOL = PBOLLd (4.11)

The degradation constant is computed by:

Ld = (1− degr)life (4.12)

where degr is the degradation rate per unit time and life is the mission lifetime in thesame time units. In order for the solar cells to produce the required power throughoutthe mission, the end-of-life power must be equal to or greater than the required power(Psa). The following simple relationship determines the required solar array area:

Asa =Psa

PEOL

(4.13)

4.4.2 Power Storage

Although SIRA will rarely, if ever, experience eclipse, additional power may beneeded at certain times to satisfy peak power demands from other subsystems. Com-munications downlinks to Earth, for example, may require more power than the solararrays provide. The additional power can come from rechargeable chemical batteries.The procedure for sizing the batteries is outlined in this section.

Sizing of batteries is based simply on the total energy that must be providedduring the peak power loading. The total energy is the product of the power loadingand the time of loading. Another factor is the depth of discharge (DOD), which is thepercentage of the battery that can be discharged each cycle. The DOD is primarilybased on the number of charge-discharge cycles that the battery will have to endureduring its operational lifetime. The total required energy storage for a battery isgiven by the relation: [7]

Cr =P T

DOD n(4.14)

where P is the power required, T is the time that power must be provided, and n isthe transmission efficiency. The required mass of the battery is then given by:

mbatt =Cr

Ed

(4.15)

47

Here Ed is the energy density of the battery. In general this mass should be dividedup between at least two batteries in order to provide for the possibility of batteryfailure.

4.4.3 Power Regulation and Control

As mentioned in the previous chapter, the two main methods for power controlare peak power tracking and direct energy transfer. Peak power tracking systemsare more useful for missions that require more power at the beginning of their lifethan at the end. SIRA is expected to require approximately constant peak powerlevels throughout its lifetime. Furthermore, direct energy transfer systems requirefewer parts and less mass (a main consideration for this mission). For these reasons,a direct energy transfer system will be used for SIRA’s power control.

4.4.4 Sizing for the SIRA mission

Each SIRA microsatellite is expected to consume approximately 100 W of poweron average. For direct energy transfer systems, a typical value for the path efficiencyis 0.85. Thus, the power required from the solar arrays is:

Psa ≈ 120 W

Typical values for solar cell efficiencies and annual degradations are given in Table4.4. Recall that indium phosphide and gallium arsenide cells are approximately threetimes as expensive as silicon. While cost is an important constraint on the mis-sion, the minimization of power system mass is critical. The superior efficiency andresistance to degradation of indium phosphide and gallium arsenide cells result in con-siderable mass reduction compared to silicon. The choice between indium phosphideand gallium arsenide is more complicated. From Equations 4.10 through 4.12, thepower produced by the solar array is dependent upon the efficiency and degradationof the cells:

PEOL ∼ η(1− degr)life (4.16)

Using the appropriate values from Table 4.4 and a lifetime mission goal of five years,computations of the above equation give:

PEOL ∼ 0.1787 (InPh2) PEOL ∼ 0.2092 (Multi GaAr)

48

Thus the superior efficiency of gallium arsenide cells overcomes indium phosphide’sresistance to degradation: gallium arsenide cells produce more end-of-life power perunit area then do indium phosphide cells.

Table 4.4: Typical solar cell parameters.

Indium Gallium MultijunctionSilicon Phosphide Arsenide GaAs

Efficiency 14.8% 18% 18.5% 22%Annual Degradation 2.5% 0.15% 1% 1%

The next task is to size the gallium arsenide cells to produce the required 120 Wat the spacecraft’s end of life. Since the spacecraft will be 3-axis stabilized with aconstant orientation with respect to the sun (with the exception of communicationdownlinks), the solar panels can be mounted so that they are always nearly perpen-dicular to the sun’s rays. Thus, the worst case sun angle is approximated as tendegrees. Furthermore, it is assumed that the cells will lose about 20% of their effi-ciency due to manufacturing, shadowing, and the array temperature. Substitutingthe appropriate numbers into Equation 4.10 yields:

PBOL = 0.22× 1367W

m2× 0.8 cos 10◦ ≈ 237

W

m2(4.17)

Using the above results with Equations 4.11 and 4.12 gives the following:

PEOL = 237W

m2× (1− 0.01)5 ≈ 225

W

m2(4.18)

Finally, Equation 4.13 gives:

Asa =120 W

225 W/m2≈ 0.5m2 (4.19)

The next task is to size the batteries. The peak power load is approximately 80W and that this additional power must be provided for a period of four hours. Thisapproximation is intended to simulate a powerful communications dump. Also, it isassumed that this load will be required once a day for the five year mission lifetime,which computes to approximately 2000 cycles. Since mass is the principal concernfor SIRA, a battery with high energy density is required. Table 4.5 gives the valuesfor the most common battery types. Lithium batteries are newer technology but canbe used in missions outside Earth orbit [20]. Due to their high energy density, they

49

are the battery of choice for SIRA. For the number of cycles described above, it isassumed that the batteries will discharge up to 70% each cycle.

Table 4.5: Standard space qualified batteries.

Battery Type Specific Energy Density (W·hr/kg)Nickel Cadmium 40Nickel Hydrogen 100Lithium 200

Using Equation 4.14 with the above assumptions gives:

Cr =(80 W )(4 hr)

(0.7)(0.95)≈ 480 W · hr (4.20)

Using nickel hydrogen batteries and Equation 4.15 yields:

mbatt =480 W · hr

100 W · hr/kg≈ 5 kg (4.21)

The addition of batteries requires a small increase in the size of the solar panelsto charge the batteries during non-peak loading times. In order to fully recharge theabove battery system during a 20 hour period, an additional 5 W of power will needto be generated by the solar cells. In later chapters the exact specifications for finalsize and mass of these components will be given.

4.5 Thermal

The thermal analysis of SIRA is important so that all of its components are keptwithin their operating temperature limits. To model SIRA, the spacecraft is modeledas three sections: the spacecraft bus, MLI, and the solar cell panels. At L1 or in theDRO, SIRA will be in continuous sunlight, so thermal cycling effects will not haveto be taken into account. This condition eliminates the job of analyzing materialfatigue due to cycling effects, but introduces the problem of material performancedegradation due to constant solar radiation.

50

4.5.1 Thermal Modeling

Placement of SIRA at either L1 or DRO puts it well out of range of thermal effectsfrom the Earth and Moon. The only thermal effects to take into account are thoseof the Sun. Before thermal modeling can begin, the radiation flux at 1.5 million km.from Earth must be found. Using the radiation flux equation [7]:

Gs =Ls

4πr2L1

(4.22)

where the luminosity constant of the sun is Ls= 3.826×1026 W, and the radius fromthe sun to L1 is rL1=148.1×106 km. This computation reveals that the radiation fluxat 1.5 million km. is 1388 W/m2. This value is used at the major source or radiationin the space environment for further thermal modeling calculations.

To begin the modeling of the spacecraft bus it is assumed that the satellite is asmall sphere. It is also assumed that there is uniform energy dissipation over thesurface of the sphere. Although the final spacecraft design will most likely not bespherical, this model will serve as a good starting point to predict what types ofthermal control will be necessary. As stated above, the internal components willneed to be kept within their operating temperature range, which is nominally roomtemperature (300 K). To find the temperature SIRA will encounter, assumed to beconstant, the following equation may be used [7]:

Tmax =[AcGsα + Qw

Aσε

]1/4

(4.23)

whereAc = cross sectional area of the satelliteα = solar absortivity of the sphereQw = electrical power dissipationA = surface area of the sphereσ = Stefan-Boltzmann constant (5.670x10-8 Wm-2K-4)ε = infared emissivity of the satellite

Typical operating temperature ranges of many important spacecraft componentscan be found in the Table 4.6 [7].The temperature of the bus must be maintained in the range of operating temper-atures for the electronics since they are the most sensitive components onboard thespacecraft.

51

Table 4.6: Operating Temperatures for Spacecraft Components (◦C).

Component Min. Temperature Max. TemperatureComputer -10 50Solar Arrays -105 110Momentum Wheels -5 45Star Trackers -20 50Thrusters 7 65MLI -160 250Radiators -95 60Electric Motors -45 80Antennas -95 70

4.5.2 Multi-Layer Insulation

The use of MLI will likely serve as the main component of thermal control. Theperformance of the MLI can be modeled by the following equations:

Q = kT2 − T1

∆X(4.24)

where Q is the heat transfer through the MLI, k is the thermal conductivity of theMLI, and ∆X is the thickness of the MLI. The thermal conductivity of the materialis calculated using equation 4.25,

k =1

N/∆X

[hs +

(σεT2

2− ε

)[1 +

(T2

T1

)2](1 +

T1

T2

)](4.25)

Figure 4.4 shows how the thickness of the MLI corresponds to the thermal conduc-tivity, k2.

4.5.3 Radiator

Heat generated by SIRAs components will need to dissipated away from the space-craft to keep the components within their operating temperature range. The radiatorcan be sized from the following equation:

Qw

Ar

= σ e T 4 −Gsα cos θ (4.26)

where Qw is the heat generated by the spacecraft and Ar is the area of the radiator.

52

Figure 4.4: Thermal conductivity versus MLI thickness.

4.5.4 Solar Cells

The first step of modeling the solar arrays is to assume that they are rigid flatplates. It must also be assumed that the worst-case solar flux is at a zero degree Sunincidence angle. The solar radiation energy absorbed by the solar array is dependenton the absorptivity of the solar cell material normal to the Sun’s radiation, and thearea of the array. This energy can be found by using equation 4.27 [7]:

QSA = GSAα (4.27)

Use equation 4.28 [7] to calculate the maximum temperature that the solar cellswill encounter,

Tmax =[Gsαt − ηGs

σ(εb − εt)

]1/4

(4.28)

where αt is the absorptivity of the top of the array, h is the efficiency of the solarcells, and εt and εb are the emissivity of the top and bottom of the array respectively.To keep the maximum temperature under the maximum operating temperature ofthe solar array, the absorptivities and emissivities of the array can be changed.

4.5.5 Conclusion

All components of a spacecraft must work correctly in order to complete a givenmission. If the temperature of a component is out of its operating range then itmay not work properly or fail completely. For this reason, thermal modeling of the

53

spacecraft is important to ensure that all of the equipment onboard works correctly.The next step of the thermal modeling process is to choose materials and thermalcontrol components that will ensure correct operation of all SIRAs equipment.

4.6 Communications

The next step in the design of the communications and command and data han-dling systems is to begin analyzing their specific requirements as they relate to SIRA.The procedures outlined here will be used later for system modeling and optimiza-tion. An introduction to the technical and mathematical aspects of design for thissystem will be presented, including basic theory and some key equations.

4.6.1 Command and Data Handling

The scope of this design does not include the design of specific system components,or the mapping of specific interactions within the command and data handling system.The C&DH system functions will be designed according to the unique needs of theSIRA fleet.

SIRA requires a relatively complex C&DH system due to the extremely redundantand autonomous nature of the design. The complexity is caused by the way themicrosatellites may be designed to autonomously maintain their formation, as wellas share, store, and downlink the scientific data.

The C&DH system acquires the status of the microsatellite from onboard sen-sors. Also, commands are processed from the ground station or from within thefleet, by routing them to the appropriate subsystems (i.e. attitude control system).It routes science or subsystem data to and from the receivers and transmitters ordata storage devices. SIRA microsatellites will be continuously monitoring their ownrelative positions and attitudes, and communicating this information to the fleet.Large computational power will be required to achieve those real-time solutions. Thecomponents chosen will need to be cutting-edge, high speed, low mass, and have lowpower requirements.

4.6.2 Telemetry and Communications

Parameters to consider when modeling this subsystem include data rates, datavolume, data storage, frequency, bandwidths, power, mass, and beamwidth. These

54

variables ultimately determine the size and mass of all communications-related com-ponents that will satisfy the mission needs of SIRA.

A nominal value of 7 Gb is given in the RFP as the amount of data that needs tobe stored after each scientific observation. Eventually the stored data must be trans-mitted back to the ground station. If there are 16 microsatellites, each microsatellitemust be capable of storing (7 Gb)/16 = 440 Mb. Since only two microsatellites arerecording data at a time, they must be able to transmit the data among the rest ofthe fleet for storage, as it is being recorded, in real time. Assuming an observationperiod of 10-20 minutes, the two recording satellites would need to transmit at arate of 3-5 Mb/s. That is an extremely high data transfer rate, orders of magnitudehigher than will be needed to transmit the data back to Earth in the given time of4 hours. Another option would be to make each microsatellite capable of storingseveral gigabytes of their own data, until transmission back to Earth.

Data transmission from the fleet to the ground station will turn out to be muchless difficult than originally planned. The nominal value of 7 Gb to be transmittedback to Earth is relatively low with current communications technology, even for useon microsatellites. A relationship between quantity of data, D, and data rate, R, isshown is Equation 4.29 [7]:

D =R(F Tmax − Tinitiate)

M(4.29)

where Tmax is the maximum time in view, F is the fractional reduction in viewingtime, and M is the margin needed to account for missed passes. The RFP specifiesa daily transmission time of 4 hours, so Tmax is assumed to be (4*60*60)= 14400seconds, Tinitiate is assumed to be zero, a nominal value for M of 2, and 1 for F. Thissimplifies Equation 4.29 to

D =R Tmax

M(4.30)

which gives a nominal data rate of 1 Mb/s from the fleet to ground station. Thisdata transmission rate is easily achieved with new low power, low mass, high-speedS-band and X-band transmitters. However, if two or more of the microsatellites aretransmitting simultaneously, the required data rate is lowered by a factor of two ormore.

As previously described, the most strenuous load on the communications systemwould be during scientific observation. Designing each microsatellite with more stor-age capacity would greatly reduce intra-fleet communication data rate requirements.In this case, each microsatellite would simply store all recorded data onboard and

55

would be capable of transmitting it all back to Earth in far less time than required.More detailed modeling and optimization will need to be done in the following chap-ters.

The communication system hardware that enables the microsatellites to transmitand receive the necessary volumes of data, under such stringent mass and size restric-tions, are state of the art transmitters. Shown in Table 4.7 is the comparison of threepossible transmitters that will be considered for use on the SIRA microsatellites.

Table 4.7: Comparison of applicable transmitter options.

AeroAstro AeroAstro JPL SmallX-Band S-Band Deep Space

Transponder Transmitter TransponderCompatibility DSN, STDN DSN, STDN DSN

TDRSSDiplexer & Modulator Yes No YesTx data rate < 0.75 Mb/s 1-10 Mb/s < 1 Mb/sMass 1.4 kg 0.18 kg 3 kgPower Consumption (Tx) 14 W 6-30 W 12.9 W

These three pieces of hardware were chosen for further analysis due to their extremelylow mass and size, and high data transmission rates from deep space.

The specified data rates from Table 4.7 are also dependent on antenna design.High gain, parabolic directional antennas will be needed in order to achieve the max-imum transmission data rates. Each microsatellite may be equipped with one suchantenna for the high rate daily data dump to the ground station. Each microsatellitewill have several low gain, omni-directional antennas in order to communicate rang-ing and command information among the fleet without a pointing requirement. Thisconfiguration is a typical satellite-antenna arrangement because of the redundantaccess coverage created by the omni-directional antennas. Also, due to the three-dimensional arrangement of the microsatellites within the fleet, the microsatellitesmust have the ability to communicate in many directions at once without reorientingthe whole spacecraft. The high gain antenna will be a parabolic reflector. The onlyparameter to be determined for this type of antenna is the diameter. Peak gain andbeamwidth can be calculated for this antenna using Equations 4.31 and 4.32.

Gt = 17.8 + 20 log(D) + 20 log(f) (4.31)

56

θ =21

fD(4.32)

Here, Gt is the transmitter gain, D is the diameter, f is the frequency in GHz, and θis the beamwidth. Assuming an antenna diameter of 0.5m for a microsatellite, peakgain would be 28.7 dBi, antenna efficiency of 0.55. These results can be used with thelink equation [7], which relates all of the parameters needed to compute the signal-to-noise ratio, Eb/No. The signal to noise ratio ultimately determines the achievabledata rate.

Eb/No =PLlGtLsLaGr

kTsR(4.33)

Here, P is the transmitter power, Ll is the transmitter-to-antenna loss, Gt is thetransmit antenna gain, Ls is the space loss, La is transmission path loss, Gr is thereceive antenna gain, k is Boltzmann’s constant, Ts is the system noise temperature,and R is the data rate. Equation 4.33 can be rewritten as,

Eb/No = P + Ll + Gt + Lpr + Ls + La + Gr + 228.6− 10 log Ts − 10 log R (4.34)

where all variables are in units of dB, K, or bps. For example, SIRA broadcastingwith AeroAstro X-band Transponder to the Deep Space Network would be capableof a data rate equal to 0.531 Mb/s, assuming:Eb/N0 = 9.6 dBP = 1.76 dBW (1.5W transmit power)Ls+Ll+La = -240 dB (at 1.5 million km from Earth)Gt = 28.7 dB (0.5m SIRA antenna)Gr = 72.7 dB (70m DSN antenna)Ts = 300 K (nominal Earth temperature)

These preliminary calculations demonstrate the feasibility of a communicationssystem capable of transmitting the required data from the SIRA fleet to the groundstation in the required time limit. Further modeling and optimization are the nextphases of design for this subsystem.

4.6.3 Conclusion

The first steps in the analysis of each subsystem are presented here in Chapter 4.Equations needed to model each subsystem are shown that will serve as the beginning

57

of the subsystem design and sizing phases. The next step will be to optimize eachsystem and their individual components. This phase will be presented in Chapter 5.

58

Chapter 5

System Modeling

The previous chapter introduces mathematical equations important for modeling eachof SIRAs subsystems. Chapter 5 applies these equations to each subsystem in the formof mathematical models. These models created in MATLAB help to gain a betterunderstanding of particular characteristics important to the design of each subsystemand its components. This chapter begins the process of subsystem optimization andis the next step in the finalization of SIRAs design.

5.1 Synthetic Aperture

SIRA consists of a constellation of microsatellite antennas to observe coronal massejection activity from 15MHz to 30 KHz. The CME produces temporal density gra-dients and a subsequent shock. Type II radio bursts observed at the shock tend to becircularly polarized, to about 70% [21]. The circularly polarized signal is best detectedby crossed dipoles. Three orthogonally crossed dipoles will provide omni-directionalcoverage while relieving the burden previously placed on pointing accuracy.

The two crossed dipole configuration, or turnstile, suffers signal loss when theplane of the cross is not orthogonal to the incoming signal. This degradation ofthe radiation pattern falls off as the exponential of the cosine of the angle off theorthogonal axis, becoming negligible parallel to the antenna axis [22]. The threecrossed dipole configuration counteracts this effect. When one dipole is parallel tothe signal, the other two are perpendicular. In any orientation, the triad will provideat least the performance of the best-case turnstile antenna.

The dipole length will not change as a result of the additional third axis, andwill remain solely dependant upon wave length. The radiation pattern of the sixteen

59

element array is the sum of the patterns for each individual element [22]. There aretwo apparent radiation behaviors for typical antenna, a near field and a far field.Since the minimum near field distance is on the order of half a wavelength, or 10meters [24], the array elements were modelled using the far field radiation pattern.The far field pattern represents the distribution of the electric field in space [25].

The far field radiation pattern for the three orthogonal dipole configuration isuniform in all directions. The intensity of the signal diminishes according to the in-verse squared law [24]. Computer codes were created in MATLAB 6.1 to model thesebehaviors. The first step in modeling SIRA’s antenna array involves selection of acoordinate system and generates realistic positions for each element. The insertionprocess for the microsatellites will originate from a central cluster. Each microsatel-lite will translate radially from the cluster, and position itself on the surface of atheoretical spheroid.

Recall that random, non-symmetric antenna placement is desired to achieve evenaperture coverage and to avoid lobe grating. Coordinates.m generates semi-randomspherical coordinates for each of the sixteen microsatellites. Element locations arespecified by the two spherical angles, phi and theta, used in a standard sphericalcoordinate system [26]. To create the spherical shape, two elements are placed in eacheight octants. MATLAB’s random number generator selects phi and theta within theboundaries of a particular octant. Cartesian.m converts these spherical coordinatesto rectangular for convenient manipulation at any specified radius. Typically, a unitradius is used throughout.

Sphering.m produces visual confirmation of the random coordinate generationalgorithm. First MATLAB’s sphere generation function, Sphere generates coordinatetriples for a unit sphere with a specified grid size. The coordinates of the sphereare plotted as a surface. Then the coordinates of each microsatellite are plotted,superimposed upon the sphere. Typical results can be found in Figure 5.1.

A benefit of this algorithm is a new random set of element coordinates with eachsimulation. Running the simulation for a variety of initial conditions demonstratesthe consistency of the results.

The next step in modeling a synthetic aperture antenna array is to identify theaperture and project the signal contributions from each element on to the aperture.For SIRA, the synthetic aperture is the projected area of the sphere, or a circle.The planar circle is perpendicular to the sun vector and passes through the sphericalcenter. Signalcontour.m generates coordinate triples for the aperture plane of theantenna array. The sample plane is square with symmetric, uniform grid sizing.Signalcontour.m then calls elementpattern.m to calculate the signal intensity due toeach array element. For each grid point, elementpattern.m calculates the distance to

60

the one of the microsatellites. The intensity of the signal is calculated according to theinverse squared law. The signal intensity is summed over all sixteen microsatellites,at each grid point.

Broadband adaptive arrays implement adaptation algorithms to impose weightson each element signal and to correct for phase shifting [22]. For ground based arrays,the weighting algorithm may manifest as physical hardware. Elementpattern.m usesreal valued distances as an example of an adaptation algorithm. SIRA will alwaysknow relative element positions, which is all that is necessary to combine the signalsof each element.

The position knowledge will come from a combination of the Deep Space Net-work and omnidirectional antennas. The DSN uses radiometric tracking to makemeasurements to allow determination of the state vector. New improvements to theDSN will provide SIRA with position accuracy to within 100 meters [23]. Given twosatellites at a distance of 25 km apart, the resulting uncertainty is 0.23 degrees. Theerror is well within the requirements of the dipole antenna’s angular uncertainty. Therange of the satellites is another issue which must be addressed. The omnidirectionalantennas will provide the distance between all of the microsatellites to within 0.8 m[7].

This information will be embedded in the data stream, and available for analysis.

Figure 5.1: Sample coordinates of array elements projected on the surface of a sphere.

61

Signalcontour.m maps the weighted signal strength to the synthetic aperture plane.Sample results can be found in Figure 5.2.

Repeated iterations of the array simulation demonstrate full coverage over a circu-lar aperture with high signal integrity at the center of the array. The wide outer bandof the contour map halos the array, identifying the outer region of signal detection.The weak spot in the first quadrant of the contour map identifies a bare spot in ourarray. Identification of weakness is the first step towards improvement. The initialelement placement will be more or less random. It is expected that the microsatel-lites will be repositioned to improve array performance after insertion. Once uniformcoverage has been established, computational techniques will be employed to tweakthe array and combine the signals.

Figure 5.2: Contour plot of relative signal intensity on the synthetic aperture.

5.2 Orbit

The Distant Retrograde Orbit (DRO) for SIRA is a heliocentric orbit with thesame semi-major axis as Earth. SIRA will orbit Earth in a retrograde manner exactlyonce per year. The period of Earth and SIRA are the same because the semi-majoraxes are equivalent. The eccentricity e of the DRO can be varied to change thedistance from Earth to SIRA (Figure 5.3). The nearest approach of SIRA must

62

remain outside the Earth’s sphere of influence to minimize station keeping. At thesame time, the smallest maximum distance is also desirable to ease communication.

Figure 5.3: Earth and spacecraft orbits, sun-centered inertial view.

A computer program provides quantitative dynamic analysis of SIRA’s DRO. Atwo-body model with SIRA and the sun was employed [27]. The orbit was assumedto be coplanar with Earth’s orbit. The eccentricity is the only variable orbital pa-rameter under the aforementioned assumptions and constraints. To avoid makingcommunications too difficult the eccentricity was not set higher than 0.03. The vari-ation in distance between Earth and SIRA over the course of one period is shownfor a generic orbit with e=.0255 (Figure 5.4). The relative similarity of Earth’s orbitand the DRO can be seen in Figure 5.5.

The transfer orbit for SIRA to the DRO was also modeled as a two-body problem.A minimum energy transfer orbit is desired. The time for a minimum energy transferis prohibitively long due to the similarity between the orbits. An iterative method wasemployed to solve for the transfer orbit. The position vectors of the Earth and SIRA,along with time of transfer, are the inputs for the method. The resulting transferorbit is only the heliocentric part of the transfer. Patched conic approximations donot apply to the DRO insertion since SIRA will only be within the sphere of influenceof the sun. The ∆V obtained at the beginning of the heliocentric transfer orbit isused to determine the earth escape orbit. A lunar swingby may be a method to

63

improve performance, but it was not modeled in the MATLAB code.

Figure 5.4: Minimum and maximum formation range to Earth versus eccentricity.

Figure 5.5: Range to Earth for one orbit.

64

5.3 Attitude

Two mission models have been considered for attitude control. The first modelconstantly points the data transmitter at Earth. Attitude adjustments will be lessthan one degree/day. However, articulating solar panels are required to provide thenecessary power. The second model involves two attitude burns every day. The firstburn points the data transmitter at earth and the second realigns the dipole antennasto be perpendicular to the sun. Attitude adjustments will be as large as 90 degrees.Body mounted solar panels may be used for the second model.

The disturbance torques on each spacecraft in the DRO are negligibly small. Alinear feedback controller provides the necessary control for the microsatellites (Figure5.6). The initial attitude is given by the attitude determination system, namely startrackers. The desired attitude is dictated by the communication subsystem. The ac-tuators, thrusters, are fired and the new attitude is compared to the desired attitude.If the two attitudes match within the tolerance as specified by the communications,the control loop is finished and the downlink is performed.

Figure 5.6: Attitude control schematic.

5.4 Power System

A series of programs written in MatLab constitute the computer modeling of thepower subsystem over a representative period during the spacecraft’s lifetime. Thecode is written as a script file, with several function files that simulate discrete events.The goal of this code is to accurately simulate the time history of power usage andenergy storage of each microsatellite. The power usage is broken down into subsys-tems. Each subsystem is assigned a nominal power usage based on the specifications

65

provided by other subsystem designs. An estimate of the power provided by the solarpanels during nominal operation is also included.

Several discrete events that drastically effect the spacecraft’s power usage areincluded as well. Communications dumps are one example. The communicationssystem is expected to require large additional amounts of data for downlink to Earth.In addition, additional power may be needed by ADCS for slewing maneuvers andthe solar panels may produce less power due to the reorientation.

Formation keeping maneuvers may also require some additional power. A majorityof this power is dedicated to the propulsion system, though ADCS may need to makecorrections to make sure the thrust occurs in the correct direction.

During some power-intensive events the power required by spacecraft subsystemswill exceed the power generated by the solar arrays. For these situations batterieswill compensate for the deficit. The amount of energy drained from the batteriesduring an event is given by

Edrained =∫ T

0(Preq − Psa)dt (5.1)

where the term inside the integral represents the power shortage as a function oftime. When the batteries are not fully charged and excess power is provided by thesolar arrays, the batteries recharge in the same manner as they are drained, as givenby the equation above.

5.5 Thermal

The Matlab code SiraThermal.m comprises the computer aided design of thethermal components. Due to SIRA’s distance from Earth, the albedo of direct solarradiation and the Earth infrared radiation are neglected. This leaves the direct solarradiation flux as the only energy SIRA receives.

SIRA’s dimensions are constrained to a volume of one cubic meter or less due tolaunch considerations. The temperature of the spacecraft can be found as a functionof the size of the spacecraft using Equation 4.23. Using absorptivity and emissivityvalues of white paint (a = 0.6; e = 0.8), the spacecraft temperature can be found asa function of the size of the spacecraft, as seen in Figure 5.8.

As the spacecraft becomes infinitely small the temperature asymptotically risesto infinity. SIRA will most likely be between 0.5 m3 and 1.0 m3, and if this is thecase the spacecraft will see temperatures ranging from 295K to 275K. This range

66

Figure 5.7: Sample power simulation.

Figure 5.8: Spacecraft diameter versus temperature.

67

falls between the freezing point of water and room temperature, where all of SIRA’scomponents will function normally.

A radiator will also be needed to dissipate the heat produced from the electronicequipment inside the spacecraft. The code written for the thermal aspects of SIRAassumes a worst-case sun angle of no more than five degrees, and assumes that SIRAwill dissipate between 50W and 150W. The sizing of the radiator can be done byinspection of Figure 5.9.

Figure 5.9: Spacecraft temperature versus waste heat per radiator area.

Figure 5.9 proves that as the temperature of the spacecraft rises more heat needsto be rejected. This figure also shows that the area of SIRA’s radiator will be smallrelative to SIRA’s surface area.

The solar cells must be at a temperature of no more than about 380K (110C), forproper operation of the solar cells. The solar cells are assumed to be rigid flat plates.Figure 5.10 shows how the equilibrium temperature of the solar cells changes as thesize of the array changes.

It can be seen that even an array of about 0.8 m2 will be below the solar cellsmaximum operating temperature.

5.6 Communications

A series of programs written in MatLab constitute the computer-aided modelingof the communications subsystem. These codes model, and allow optimization of, all

68

critical components and factors associated with the space communications betweenground stations and SIRA. Components that are modeled include the type and size ofcommunications antennas and the ground station. Environmental factors associatedwith the communications are modeled to determine the expected signal degradationdue to inevitable losses.

The “link budget” is the most basic and crucial information that must be deter-mined for any space flight. The link budget includes all vital parameters associatedwith the spacecraft communications system. The link budget equation (Equation5.2) is used to model the communication link and design the link budget.

Eb/No = P + Ll + Gt + Ls + La + Gr + Lθ − 228.6− 10log10Ts − 10log10R (5.2)

P is transmitter power (dBW), Ll is line loss (dB), Ls is space loss (dB), La istransmission loss (dB), Eb/No is signal-to-noise ratio (dB), Lθ is pointing error loss(dB), Gr and Gt are receiver and transmitter gains respectively (dB), Ts is systemnoise temp (K), and R is data rate (bps). Transmitter power is limited by thetransponder hardware selected. The sum of the line loss Ll and transmission loss La

is assumed to be nominal value of 10dB. Space loss Ls is,

Ls = 147.55− 20log10(s)− 20log10(f) (5.3)

where s is the propagation length (m), and f is the frequency (Hz). Pointing errorloss Pθ is,

Figure 5.10: Solar array temperature vs. solar array size.

69

Lθ = −12(e/θ)2 (5.4)

where e is the pointing error (deg), and θ is the half power beamwidth. Pointingerror e is prudently assumed to be equal to the half power beamwidth θ, a typicalassumption is e=θ/2. Half power beamwidth θ for a semi-hemispherical antenna is,

θ = 21/fD (5.5)

where f is the frequency (GHz), and D is the diameter of the antenna dish (m).Antenna gains Gr and Gt are found by,

Gr/t = 17.8 + 20log10(D) + 20log10(f) (5.6)

where D is the diameter of the antenna dish (m), and f is the frequency (GHz).In modeling the communications system, the object is to minimize mass and

weight by keeping the onboard antennas as small as possible while maintaining therequired data rate and bit error rate to support the mission. Each microsat in SIRAwill have 440 Mb of stored data that will have to be transmitted to Earth in a fourhour period, which requires a minimum data rate R of 30 kb/s.

The only feasible ground station for use with SIRA is the Deep Space Network(DSN), which consists of 70m diameter dishes around the globe, using BPSK andQPSK digital modulation types (SMAD). In order for SIRA to communicate on thisnetwork, the transponders selected for use must also be BPSK/QPSK compatible.This type of forward error correction digital encoding requires a bit error rate (BER)of 10−5 to 10−7, or one bit error per ten million. A signal-to-noise ratio EbNo ofabout 10 is required for a bit error rate of 10−7 with those modulation types. Thebasis for these results are illustrated in Figure 5.11.

Using the information and equations given above, a model is constructed andoptimized by varying data rate and antenna size. The plots created by the modelingprogram show signal-to-noise ratio plotted against data rate, at a given maximumanticipated distance from Earth. Several different antenna sizes are plotted on thesame space. The smallest antenna size that can achieve 30.4 kb/s while still main-taining Eb/No of 10 is the optimal choice. An example run of the modeling programis shown in Figure 5.12. The point where the two bold lines intersect determines theoptimal size for the high gain antenna dish.

A system of omni-directional antennas must also be designed for emergency com-mand, intra-fleet ranging, and fleet-keeping. The distance between each microsatis negligible compared to the distance from the fleet to the Earth, so preliminary

70

Figure 5.11: Bit Error Probability as a Function of Eb/No (reproduced from [7]).

Figure 5.12: Optimization of high-gain antenna dish size for telemetry at a distanceof 3 million km.

71

modeling shows that intra-fleet data rates will be more than sufficient. The omni-directional antennas therefore are only modeled to support the emergency commandand ranging functions. Command and ranging communications typically require adata rate of 5-10 kb/s. Equations 5.7 and 5.8 calculate gain Gt/r and beamwidth θ,for helix low-gain antennas, respectively.

Gt/r = 10.3 + 10log10(C2L/λ) (5.7)

θ = 52/(C2L/λ3)(1/2) (5.8)

where Gt/r is gain in (dB), C = pD (m), L is antenna length (m), λ is wavelength(m). Figure 5.13 shows an example of an antenna with 0.002 m diameter, of varyinglengths, plotted against signal-to-noise ratio and data rate, for communications linkwith Earth to SIRA. The optimal length occurs where the two bold lines intersect.

Figure 5.13: Optimization of omni-directional antenna data rates of antenna diameter0.002 m, for communication Earth to SIRA at 3 million km.

In addition to modeling the required data rate, the omni-directional antennas aredesigned with a half angle beamwidth wide enough for 360o coverage. Each antennashould have a half angle beamwidth of at least 90o. Figure 5.14 shows an exampleof different antenna lengths plotted against antenna diameter and beamwidth. Theintersecting bold lines specify an antenna of length 0.05 m, diameter of 0.002 m, anda half angle beamwidth of about 75o.

72

The modeling programs described above and detailed in the Appendix will be usedto further model and optimize the antenna sizes, signal quality, and desired data ratesfor each mode of communication. Final decision and optimized communication linkbudget are discussed in later chapters.

5.7 Conclusion

Analysis performed in this chapter is extremely important to the process of obtain-ing a successful design. SIRAs subsystems performance characteristics are modeledand analyzed to gain a better understanding of a possible final design. The next steptoward a final design involves detailed descriptions of SIRAs subsystem parts andconfigurations needed to meet Chapter 5 design and performance specifications.

Figure 5.14: Optimization of omni-directional helix antenna.

73

Chapter 6

Component Selection

This chapter outlines the physical components to be included as part of each sub-system. Components for each subsystem are sized using models developed in earlierchapters, and then components are selected based on how well the manufacturer’sproduct specifications meet SIRA’s requirements. For components which are notreadily available, custom designs are used and compared to off-the-shelf products.

6.1 Deployable Antennas

SIRA requires one time deployable dipole antennas. The constellation of 16 mi-crosatellites modeled as 1 m cubes satisfy launch size constraints. The stowed antennais of sufficiently small size to fit within a 1 m cube. Several deployment mechanismsare scrutinized for feasibility, simplicity, and low mass requirements.

Deployable Truss StructureSpacecraft truss structures are frequently found within solar arrays and antennas.

Sections of the structure are folded at hinge points. Pulleys or gears extend the foldedbeam to its straight configuration. The deploying antenna has a non-zero probabilityof catching on the spacecraft frame. The mechanisms necessary for deployment aremore massive than is practical for a microsatellite. Additionally, the hinge pointsresult in a deviation from the ideal dipole antenna, which consists primarily of a longstraight conductor.

Shape memory alloyA shape memory alloy is deformed in its cooled, martensitic phase. This state has

low yield strength. When heated the alloy returns to its original shape. Examples

74

given do not illustrate a significant change in shape so as to warrant their use. Ideally,a stowed coil would deploy to a straight mast, but this does not appear possible givencurrent physical limitations.

Storable Tubular Extendable MemberThe storable, tubular extendable member will be highly effective for antenna ap-

plications. Also referred to as tape-springs, advantages include continuous conductor,no hinge points, and high ratio of deployed length to stowed length. The material canbe thickened to prevent flapping that may be associated with overextension. Futureresearch may reveal a rigidizing temperature transition. Ideally the stowed coil couldbe insulated and thermally controlled. The metal will cool and harden when exposedto the space environment.

STEMs were invented by George Klein for scientific applications first implementedon Alouette, Canada’s first satellite. Those first STEM dipole antennas measured 11meters and 22 meters in length and were successfully deployed and later used on USsatellites. Tape-springs are thin, transversely curved strips similar to tape-measuresand can be made from copper beryllium (CuBe) alloy.

Recent work on STEMs has been led by S. Pellegrino at the University of Cam-bridge. Seffen and Pellegrino gives physical properties of age hardened copper beryl-lium in the context of tape-spring applications [31]. Young’s modulus for age hardenedcopper beryllium is 131 GPa. Its yield stress is 1.175 GPa [31].

Kebadze, Guest, and Pellegrino then rigorously examine the formation processfor bistable, rolled composite materials [29]. Understanding the internal stresses andsupport of this understanding establishes credibility. The process described producesa stable coiled configuration that does not require an external constraining force [29].

Figure 6.1: Deployable truss structure.

75

A requirement of twenty to thirty meter separation could only be met by a Stain-less Steel bi-STEM tubular boom [30]. SIRA requires a five meter conductive cylin-drical beam for use as a dipole antenna. This can be accomplished with a copperberyllium STEM contained in a deployment cassette. Rolatube Technology Ltd.produces bi-stable reeled composite structures suitable for SIRA.

STEM SpecificationsThe bi-stable antenna will be manufactured from a Copper Beryllium alloy as

specified by the proposal. The density of this alloy is 8.36 g/cm3. Each microsatellitewill be equipped with six STEM deployment cassettes, joined to form the dipole triad.Each STEM cassette will deploy a five meter tube, five centimeters in diameter and0.25 mm thick. Such a cylinder has sufficient moment of inertia to not buckle underthe maximum attitude control torque. The total mass per microsatellite of CopperBeryllium is ten kg.

Figure 6.2: Storable Tubular Extendable Member.

Figure 6.3: STEM cassette configuration.

76

Six STEM cassettes will lie on one edge of the microsatellite cube in the clusteras shown in Figure 6.3. The darkened faces are those faces from which the antennamembers will deploy. For a cylinder five centimeters in diameter and 0.25 mm thick,the stowed configuration has a rectangular cross section 0.25 mm thick and 16 cmwide. The five meter strip rolls up with a minimum diameter equal to the deployeddiameter. Each successive layer is approximated by a 1.2 mm thickness. This resultsin a fully stowed cylinder 16cm tall and 10cm in diameter. This is the minimum sizefor each cassette. The cassette assembly dimensions will be 0.45 m x 0.45 m x 0.3 m.This will extend 0.3 m exterior to the crate. Thus the crate will be reduced in sizeto accommodate this extrusion.

6.2 Attitude Determination and Control

The attitude determination and control subsystem is most directly influenced bythe need to minimize mass and power requirements. According to the Value SystemDesign the minimization of mass is most critical to the mission. Selection of theattitude determination and control systems will also consider the power requirementand fulfillment of mission objectives.

6.2.1 Attitude Determination

Two scenarios were considered to fulfill the requirements of the SIRA mission.The first implements the use of a sun sensor and rate gyro. Sun sensors provideattitude knowledge about two axes. Rate gyros are able to supply angular velocitymeasurements which may be integrated to produce measurements of the attitudes forall three axes. An adequate sun sensor manufactured by Astro-Iki has a weight of 0.2kg and a power consumption of 0.25 W [32]. The sun sensor may also serve a dualpurpose of aligning the solar panels with the sun vector. A corresponding rate gyrohas a weight of 6 kg and power consumption of 40 W [32]. A preventative factor forthis configuration is that the knowledge of the third axes attitude will continuallydrift throughout the mission. Also, the need for a sun sensor for the solar panels isnegated by the implementation of body mounted solar panels. The resultant massand power requirements total a mass of 6.2 kg. and 40.25 W.

The alternative method of determining the attitude employs only a star tracker.Star trackers have been used more recently on spacecraft as the only means of attitudedetermination. A current star tracker suitable for the SIRA mission is the CT-633Stellar. The current model consists of a wide field camera which masses 2.5 kg. and

77

consumes an average of 8 W of power [33]. Another applicable star tracker, STSC,currently under development, which should be available before SIRA launches, weighsonly 0.29 kg. and has a power consumption of approximately 6 W [34]. The STSCcombines a wide angle camera with the ability to perceive and distinguish stars towithin mv 4.5. The algorithm used by STSC involves comparing perception of triadsof stars (Figure 6.4). The relative attitude between known triads yields the attitudeof the spacecraft.

Figure 6.4: Star tracker configuration.

The SIRA mission has minimal rotational rates and must minimize mass. Theimplementation of rate gyros will therefore not be necessary. Attitude measurementsmay be differentiated, albeit at a loss of information, to obtain attitude rates if therates are necessary for any other subsystem. The STSC system provides the optimumsolution to the SIRA attitude determination problem.

6.2.2 Attitude Control

The four most common forms of attitude control actuators are thrusters, controlmoment gyros, reaction/momentum wheels, and magnetic torquers. Two of theseactuators can be eliminated immediately based on the constraints of SIRA. Magnetictorquers require a magnetic field and an accurate model of the magnetic field sur-rounding the satellite. Control moment gyros are typically used on spacecraft whichrequire rapid attitude maneuvers. Large mass is also characteristic of CMGs. Theremaining options, reaction wheels and thrusters, were researched and evaluated.

Honeywell manufactures ”micro” reaction wheels that weigh 1.3 kg and have anaverage power consumption of 8 W. At least four of these reaction wheels must beused in order to eliminate a single point of failure. Furthermore, reaction wheels areonly able to provide pure torques and not translational maneuvers. An additionalthruster would be required for any station or formation keeping. For an individualattitude maneuver, operating under worst case scenario of one failed wheel, 16 W of

78

power will be consumed. The total weight of all four wheels would be 5.2 kg. TheVSD for the reaction wheel configuration is 16*7.5%+5.2*13.5%=141.

A colloid micro thruster has been developed at Stanford University [36]. Eachthruster weighs 0.4 kg and requires an input power of 4 W while operating (Figure6.5). Full attitude control requires twelve thrusters. Two thrusters will be oriented inthe same direction for each of the six body-fixed directions at an equivalent distancefrom the center of mass. Under normal operating conditions the simultaneous firingof two thrusters would produce a pure torque about one axis without translation. Theconfiguration of 12 thrusters also allows for multiple points of failure. In addition, thethrusters can be used to perform the station and formation keeping maneuvers therebyeliminating the need for an additional propulsion system. No more than two thrusterswould be fired at the same time resulting in a power consumption of 8 W. The totalmass of the thrusters would be 4.8 kg. Applying the VSD for power consumptionand mass results in 8*7.5%+6*13.5%=142.2. The colloid micro-thrusters provide abetter solution to SIRA’s attitude control problem.

Figure 6.5: Colloid microthruster [37].

6.3 Power

6.3.1 Solar Arrays

Due to the complexities associated with articulated solar arrays requiring mechan-ical actuators and the realization that sufficient room is available on the sides of thespacecraft, photovoltaic cells will be mounted to the body of each satellite. Severalmanufacturers are available that can produce solar arrays customized to particularmissions. Able Engineering offers a fan-like deployable array capable of producing150 kW/kg; however the circular nature of this product precludes its use on the cube-shaped design of the microsatellites. The same company also offers rigid panels but

79

these panels have a minimum power production of 500 Watts, which is far more thanrequired for the mission [38].

Spectrolabs offers rigid panels that can be sized to any specification. Their mostefficient product is a triple junction cell comprised of several compounds, includinggallium arsenide, indium phosphide, and germanium. These panels provide 330 W/m2

and demonstrate reliability better than 0.999. The average distributed mass is 2.06kg/m2 [39].

Emcore also produces scalable solar panels composed of triple junction technology.Emcore’s panels produce a minimum 26.5% (362 W/m2) efficiency and mass only0.84 kg/m2 [40]. Due to the superior mass efficiency, Emcore panels are chosen to bemounted on the body of each spacecraft.

6.3.2 Batteries

Several battery technologies are available that would be viable for this mission.Nickel hydrogen batteries are a reliable, space tested technology and are more efficientthan nickel cadmium cells. EaglePicher produces nickel hydrogen cells in a wide rangeof sizes [41]. One or two of these batteries would provide the power necessary foroperations when the solar cells are insufficient. Many companies also have lithiumion batteries under development, which provide more mass-efficient energy storage.For a future mission such as SIRA these cells may be a better choice than the currentlyavailable nickel hydrogen batteries.

Assuming that lithium ion batteries are not sufficiently reliable for a deep spacemission, (3) 1.25 V EaglePicher cells are chosen for energy storage. Each is approxi-mately 8 cm in diameter and has mass less than 1 kg. The batteries connected to abattery charge regulator and a DC-DC converter to match the 28 V bus. Solid statepower switches turn the individual hardware on or off.

6.4 Thermal

SIRA microsatellites are spacecraft with low power consumption. SIRA’s thermalneeds are relaxed enough that a passive thermal control system is all that is required.Also, most of the spacecraft’s components fall into the same operating temperaturerange, so no one instrument needs special attention. The only two components thatwill be thermally controlled are the batteries and the CPU.

The main component of thermal control will be MLI. The MLI will be used towrap the batteries and the CPU. This will be done because these two components

80

have the most strict thermal operating range. The entire spacecraft need not bewrapped in MLI. The outside of the spacecraft will consist mostly of solar panels,which will reflect most of the sun’s energy. The panels will not reach a high enoughtemperature where dangerous levels of heat will be conducted through the panels intothe bus.

The MLI which will be used on SIRA will be manufactured by Swales Aerospace,Inc. The MLI will consist of 15 layers of 1/4 mil aluminized Mylar. Between eachaluminized layer is a 1/4 mil web of Dacron. The Dacron is used to thermally isolateeach layer of aluminized Mylar. The Dacron web creates small pockets of still airbetween each layer that inhibits convection resulting in an insulating effect. On theoutermost layers is a 1 mil layer of insulating Kapton film. A cross-section of theMLI can be seen in Figure 6.6. The density of the MLI is 0.3 kg/m3 and and itseffective emissivity is 0.03. The performance of the MLI relies heavily on the detailsof its configuration. Any discontinuity in the MLI such as attaching points, seams,and folds are a source for heat leakage.

Figure 6.6: Cross section of MLI.

To radiate the heat necessary to keep the components within their operatingtemperature range a 0.45 m2 radiator will be used. The radiator will be made byFoster-Miller, Inc. and will be made from graphite-aluminum. The graphite fiberpanels provide a higher thermal conductivity with lower mass. The radiator will beplaced on the top face of the cube where there is less sunlight absorbed by the radiatorwhich will yield a lower operating temperature. All thermal lines will be made fromflexible copper tubing with a thermal resistance of 2 K/W.

A low solar absorptance paint coating will also be applied to the radiator andcommunications dish to help keep SIRA’s temperature controlled. With all thesemeasures put into effect the spacecraft will maintain a temperature of -10C to 25C.

81

6.5 Communications and Data Handling

The main components of the communications system are the high gain antenna,the low gain antennas, and a transponder. The main components of the commandand data handling system are the central processing unit, the satellite data bus, anda data handling and storage unit. Component selection and component details areas follows.

TransponderEach microsatellite in SIRA will use the AeroAstro Corp. X-Band Transponder

to send and receive data from the high gain and low gain antennas. This transponderhas modulation and demodulation capabilities built into it, which includes Dopplercorrection and the ability to generate the necessary beacon tone for ranging purposes.It transmits on 8.4-8.5 GHz, receives on 7.145-7.235 GHz, and uses bi-phase filteredBPSK and QPSK modulation methods, both compatible with DSN ground stations.The transponder’s dimensions are 15.2 cm x 7.6 cm x 7.6 cm, and it weighs 1.135kg. The high power amplifier add-on that will be required is 15.2 cm x 6.65 cm x 6.1cm, and weighs 0.272 kg. Together they will consume approximately 100 W duringtransmission, at 6-8.5 VDC [42].

Figure 6.7: AeroAstro X-Band Transponder and operational block diagram [42].

High and Low Gain AntennasThe high gain antenna used on SIRA will be the same type and generation of that

used on the 2004 Mars Rovers. Computer modeling and analysis specifies the highgain antenna diameter of 0.35 m, almost identical to the Rovers’ 0.38 m diameter.The dish will have a half-power beamwidth of 3.5 degrees with a maximum gain of73.3 dBi, which will produce a nominal data rate of 30 kbs. The dish will be mountedto the body of the microsat and will not be gimbaled.

82

The low gain antennas will be simple vertical omni-directional devices, mountedon each face of the microsats. There are multiple manufacturers of these products,and specific sizing of these antennas will not pose a problem. These antennas willtransmit and receive at the same frequencies as the high gain antenna; this is so thatonly one transponder needs to be used, in order to minimize mass. The low gainantennas will have a half-power beamwidth of 116 degress with a maximum gain of3.35 dBi.

Figure 6.8: Example of the omni-directional low gain antenna, to be mounted oneach face of SIRA microsatellites [43].

Satellite Data BusThe satellite data bus selected for use is the Western Avionics’ Shuttle Bus PCI

interface card [44]. This is a very capable yet compact piece of hardware. ThePCI card provides all launch data bus, ground data bus, and MUX multiple remoteterminal capabilities to the Shuttle Bus. The dimensions of the card are 175 mm x107 mm, and it weighs 0.550 kg. Operating temperature is required to be 0-50 C.

Figure 6.9: Western Avionics Shuttle Bus PCI interface board [44].

Data Handling and Storage UnitNEC Toshiba Space Systems’ Onboard Computer and Data Handling Unit will

be used on SIRA to control all system functions and to store the gathered radiodata. The Onboard Computer was developed as a multi-purpose computer for largesatellites, however it can be sized appropriately and used for SIRA. These computersadopt the C-MOS 16bit CPU and C-MOS I/O Processor.

83

The Space Systems’ data handling unit manages all subsystems of the spacecraft.It provides command control, autonomous control of a satellite, and telemetry for-matting and encoding. Its main functions are decoding and executing the uplinkcommand. It also collects and edits fleet-keeping and mission data via the ShuttleBus [45].

These central processing units will be matched with modern solid-state data stor-age devices from Space Systems. These memory units provide a large volume of datarecording (the required 450 Mb is easily achieved) with high data rate and multi-channel recording and reproducing capability.

Figure 6.10: NEC Toshiba Space Sytems’ Onboard Computer, Data Handling Unit,and Solid State Memory [45].

6.6 Launch Vehicle

The Proton launch system manufactured by ILS or International Launch Servicesis the chosen launch vehicle for SIRAs mission. The Proton vehicle is one of the mostcapable commercial expendable launch systems in use today. As of the end of 2001the Proton attempted 265 launches with a success rate of 96%. The program offersa variety of launch configurations including a wide range of orbit possibilities. TheProton launch complex, consisting of two commercial launch pads, is located at theBaikonaur Cosmodrome in the Republic of Kazakstan. The Proton features a yearround launch schedule with a minimum time between launches of around 25 days.

The Proton M/Breeze M is chosen to perform SIRAs launch duties due to itswide range of payload fairing size and state of the art fourth stage. A standardascent trajectory performed by three stages is used to place the upper stage andpayload into a 170-230 km circular parking orbit. Once in the parking orbit thepayload may be transferred into the final orbit by the upper stage or Breeze M.

84

Maximum flight loads experienced by SIRA during launch are during liftoff and1st/2nd stage separation. At lift off a longitudinal load of 2.6 gs is felt with 4.6 gsbeing felt longitudinally at 1st/2nd stage separation. The lateral loads experiencedduring lift off and 1st/2nd stage separation are ±1.7 gs and ±1.2 gs respectively.These loads and acoustics loads felt during liftoff must be taken into account in thedesign of SIRA microsatellite structure.

ILS offers several high volume payload fairings which accommodate the height ofSIRA’s payload. The Proton M/Breeze M standard commercial fairing features ausable diameter and height of 4 and 4.2 meters respectively. An overall height of 11.6meters allows for the payload and the fourth stage to be completely encapsulatedinside the payload fairing which is attached directly to the third stage.

The fourth stage or Breeze M is responsible for accelerating and positioning SIRAinto its transfer trajectory. The Breeze M is also be responsible for inserting SIRAs16 microsats into the final orbit. Propulsion for the Breeze M consists of one gimbaledmain engine developing 19.62 KN of thrust, four impulse adjustment thrusters of 396N of thrust each for fine adjustments, and 12 attitude control thrusters of 13.3 N each.The main engine is capable of firing up to eight times per mission with a back upstarter included. Also included on the Breeze M is a control system consisting of anon board computer and three-axis gyro stabilized platform and navigation system.An angular pointing accuracy of ±10 degrees and an angular velocity accuracy of±0.5 degrees can be maintained.

Separation of SIRAs payload from the Breeze M once inserted into the final orbit

Figure 6.11: Proton launch vehicle fairing dimensions.

85

can be performed in any of three modes. Three-axis stabilization, longitudinal spin-up, and transverse spin-up are the three options. Two adapter systems equipped withseparation mechanisms are available depending on the type, number, and position ofseparation springs desired. The mass of the 1194 mm adapter if chosen is 110 kgand the mass of the 1164 mm adapter is 120 kg. The microsats themselves will beattached by separation mechanisms designed by Planetary Systems Corporation andwill not be utilized until SIRAs payload is successfully inserted into its final orbit.

6.7 Structure

The purpose of the spacecraft structure is to protect and contain all componentsfor the specified lifetime of the satellite. It should not buckle under normal loads, andthe internal stresses should not exceed the yield strength of the material. The massof the structure should be minimized, as it should for all space-based applications.Finally, the cost of the structure should be minimized. Structure cost includes theraw material cost and assemblage. The structural design should be easy to modifyon paper, and easy to work with in postproduction. These constraints are ranked inimportance from the essential to the desirable. Each will be discussed in detail inthis section.

The spacecraft structure is constrained only by launch loads and design drivento be low mass. During launch, the sixteen microsatellites will be stacked four tall.Therefore the lowest satellite must support the compressive force of the entire stack.Each satellite has a current upper bound mass of 40 kilograms. The maximum loadfactors during launch will be 4.65 g’s axially and plus or minus 1.70 g’s laterally,where g is the gravitational acceleration at the surface of the Earth [46].

Figure 6.12: Basic spacecraft structure.

A 0.8 meter, reinforced, thin-walled cube was chosen for the SIRA spacecraftstructure, shown in Figure 6.12. The structural frame was analyzed for three different

86

materials: 7075 aluminum, a nickel alloy, and a type one carbon fiber composite.Specific calculations were performed using the densities, moduli, yield strength, andcost per kilogram. The mass of the structure was estimated from the volume of thebeams. Integration hardware, like bolts, will increase the mass by a negligible amount.The structure was analyzed for yielding under centric loading, and buckling. Acomposite material produced the least massive spacecraft structure at 4.3 kg, while analuminum structure totals 6.6 kg. Despite a higher mass, aluminum was selected forthe structure because carbon fiber composite materials experience strength reductionwhen holes are drilled in them.

The L-shaped beams that compose the crate structure provide improved strengthper unit mass compared to rectangular beams. The previously described antennamodule will fit securely on the edge of the cube and will deploy externally in threeorthogonal directions. Thrusters are positioned along the edges of the cube at anglesconducive to attitude control.

6.8 Conclusion

Information provided in this chapter reveals the final design of SIRA. All subsys-tem components were sized and selected. In certain cases custom-made componentswere discussed, compared, and chosen to meet SIRA’s specific needs. This chapterforms the last step before SIRA is assembled in its entirety.

87

Chapter 7

System Integration

The previous chapter detailed the components of SIRA and how they functionindependently. This chapter will illustrate how those components will be put to-gether and detail the interaction between components. This chapter also includesCAD drawings of the completed spacecraft, mass estimates, deployment sequences,mission operations timetable, launch configuration, and stack deflection at launch.All segments of the mission, from launch to completion, are as follows.

7.1 Mission Operations

After launch, the vehicle will place the satellite stack into a retrograde parkingorbit of altitude approximately 250 km. Over the equator, at a geodetic longitudeof approximately 180 degrees, the third stage of the rocket will perform a ∆V of3.19 km/s to place the stack into the transfer orbit. The transfer takes a total ofapproximately 67 days. At the end of this period the satellite stack is in the vicinityof the line joining the Sun and the Earth. At this point the fourth stage of therocket ignites, giving the stack another ∆V of 446 m/s to insert the stack into thedistant retrograde orbit. Once the burn is complete the fourth stage separates andthe spacecraft begin their deployment and prepare for the mission phase. No furtherorbit stationkeeping is required; the spacecraft will maintain a retrograde motionabout the Earth for the duration of the four year mission. The formation maintainsa distant of approximately 1 million km from Earth throughout the mission phase.Orthographic views of the spacecraft orbit are shown in Figure 7.2. Note the body-body rotating coordinate system in which the x-axis is the line joining the Sun andthe Earth, the z-axis points to ecliptic north, and the y-axis completes the right hand

88

triad. A summary of the major mission events is included in Table 7.1.

Figure 7.1: SIRA insertion burn location.

After initial analysis using Matlab simulations, the Satellite Tool Kit softwarepackage was used to create a model of higher fidelity. The model includes gravita-tional forces from both the Sun and the Earth, as well as solar radiation pressure. Allmaneuvers are impulsive burns. Although initially believed that a more distant orbitwould increase the ∆V budget, analysis suggests that significantly more fuel is re-quired to insert into a closer orbit. This was not discovered using the Matlab modelsbecause they failed to simultaneously incorporate both gravity fields. Furthermore,the difference in maximum and minimum radius is significantly less than expected.

Figure 7.2: Orthographic orbit views in rotating reference frame.

89

Table 7.1: Summary of mission operations

Event Time CommentLaunch 0 Nighttime launchTransfer Orbit Burn (3rd stage) Launch +60 minutes 3.19 km/sTransfer Orbit Stowed configurationInsertion Burn (4th stage) Launch +67 days 445 m/sMission Average distance from

Earth 1 million km

7.2 Deployment

The 16 microsatellites of SIRA will be stacked into four columns of four satel-lites inside the payload faring of the launch vehicle. The microsatellites are to bemounted to the payload floor and to one another by means of Planetary Systems’”Lightband” release mechanisms. The microsatellites will be electronically connectedto each other and the fourth stage by means of the Lightband separation mechanisms.Upon launch, a simple electrical signal will be sent through the Lightband to triggerthe initialization of essential systems. The only systems active at this point are thoseresponsible for sending out very low rate health information, and listening for basicstartup commands from the ground station.

Upon completion of the third stage of the launch vehicle, several minutes afterlaunch, the fourth stage and payload separate from the rocket motors. The payloadfairing is discarded from the fourth stage section and the fourth stage rocket engineand guidance computers are initialized to take the satellites to their separation pointin the Distant Retrograde Orbit. System checks will be performed en route so thatthey are ready to separate.

Sixty-seven (67) days after launch the fleet will receive commands from ground tobecome active and initialize their main systems. Shortly thereafter the fourth stagewill initialize a burn to complete the transfer, then the fleet will separate from thefourth stage four at a time. The release mechanisms and sequencing will be automatedby the fourth stage computer. The microsatellites at the top of each stack will bereleased first, simultaneously. The microsatellites’ guidance and propulsion systemswill take over once released, moving them safely away from the fourth stage. Whenthe first four microsatellites are 20 meters away, the next top four will be released inthe same manner. A distance of 20 meters is a safe distance based on propellant andcommunication interference considerations. This process will repeat until the whole

90

fleet has separated from the fourth stage and moved safely away. The fourth stagewill do a final burn maneuver to position itself farther away from the fleet.

It will take almost one full day for the fleet to move into position around therandomized spherical configuration. Upon release, the microsatellites are fully activeand are therefore flying themselves almost completely autonomously for the remainderof the mission. En route to their positions, the microsatellites will perform final teststo ensure the operation of the Dipole antennas and the high gain communicationsdish.

Approximately 69 days after launch the fleet will be in position. Once in position,the dipole antennas will be deployed and scientific observations can begin.

Figure 7.3: First four satellites released from stacks.

7.3 Microsatellite Structure

Recall that the SIRA crate structure is composed of aluminum L-shaped beams.The structure was analyzed for yielding under centric loading and buckling. Thedimensions of the L-beams necessary to sustain launch were determined throughcomputations. The symmetric L-beam legs are 50 mm long and 3 mm thick. Eachof twelve beams is 0.8 meters long to form the 0.8 meter cube crate structure. Thetotal mass of aluminum structure will be 7.5 kg. At each corner the L-beam faces

91

overlap, and each of the three members can be joined to the other two using weldsor bolts.

Figure 7.4: L-beam component.

The cube crate structure must have functional rigid faces to secure componentsand to mount solar cells. The Proton launch vehicle is subject to minimum naturalfrequencies of 15 Hz laterally and 30 Hz longitudinally. The faces of the cube mustbe suitable to tolerate such a vibrating launch environment. Honeycomb compositesprovide the best high strength, low-density solution honeycomb material.

UCF Ultracor 68-3/8-2.0 will be installed externally to all faces of the cube. Thehoneycomb panels are 20 mm thick and were developed using a space qualified, tough-ened, polycyanate matrix resin [47]. Each panel will be sandwiched between a 1.5mmthick layer of epoxy 7781 fiberglass to improve strength in bending. The materialdensity is 0.029 g/cm3 and Ultracor has compressive yield strength of 0.9 MPa. Theinstallation of honeycomb adds 2.0 kg to each microsatellite. The honeycomb will becut away so as not to obstruct the star tracker’s line of sight.

7.4 Stack Deflection Calculations

At launch, four stacks of four microsatellites will be assembled adjacently. Eachmicrosatellite will be identical; therefore each satellite must be designed to supportthe entire 160kg stack. Four axially loaded L-beams provide support. The axial stressis two orders of magnitude less than the critical stress of the material. The momentof inertia of the beams about the structural center is sufficient to prevent bucklingwith a factor of safety of 1.2.

The moment of inertia of each vertical beam is summed together to find theeffective bending moment of inertia of the stack to be 1.74x10-4 meters4. The stack

92

is 4 meters tall. The modulus of elasticity for anodized aluminum is 7 x 1010 N/m2.We model the lateral launch loads as side force at the mid height. The side force isequivalent to a 2.0 g acceleration of the entire 160 kg stack, or 3136 Newtons. Usingthe maximum deflection equation for a cantilevered beam

δmax =PA2(3L− A)

6EI(7.1)

where d max is the maximum deflection of the stack, P is the side force, A is thedistance from the cantilever to the application of the force (2 meters), L is the length,E is the modulus of elasticity of the material, and I is the moment of inertia of thestack [48]. The maximum deflection of the microsatellite stack is 1.9 mm at thetop of the stack. This deflection complies with launch vehicle specifications and issufficiently small so as not to endanger the mission. These computations are merelya first step towards determining the vehicles’ response to launch. After constructionfurther testing will be done to obtain all information needed to ensure a safe launch.

7.5 Component Placement

Figure 7.5 is a model of one SIRA microsatellite including all components asinstalled prior to launch. Twelve thrusters are installed interior to the satellite onthe edges of the cube to provide three-axis stabilization. The radiator encompassesan entire face of the cube and is reinforced by the honeycomb composite panel. Thecomputational hardware is positioned adjacent to the radiator in the center of thespacecraft. This location provides optimal thermal insulation reinforcing the effects ofthe MLI. The batteries are mounted opposite the radiator to the honeycomb panelingnext to the power distribution module. The large dipole antenna and the downlinkdish are mounted on opposite faces. The star tracker is installed with a clear view ofthe stars.

Figure 7.6 depicts the SIRA satellite array in its launch configuration. Four stacksof four microsatellites are stacked on top of the fourth stage propulsion module. Thelarge dipole antennas (not shown) lie exterior to the stack, with the radiator face onthe interior.

Figure 7.7 shows a two dimensional projection of the cube faces and major com-ponents. The release mechanisms are fitted to the perimeter of the spacecraft so theydo not have to be bolted to the solar panels.

93

Figure 7.5: Component placement.

Figure 7.6: Microsatellite stacks in launch configuration.

94

Figure 7.7: Two dimensional projection.

7.6 Total system mass

The mass estimate Table 7.2 shows the dipole antenna hardware and the structureconstitute the primary mass of SIRA. The total mass of each spacecraft is 37.1 kg.The total launch vehicle mass is 691,115 kg, and the total mass at launch is 691,708kg. The total payload mass launched on the Proton M vehicle is 593.6 kg.

7.7 Conclusion

The precluding paragraphs showed what a completed SIRA spacecraft will consistof and look like. This chapter represents the culmination of all the research that sup-plemented the design of the spacecraft. The CAD drawings of the completed space-craft, mass estimates, deployment sequences, mission operations timetable, launchconfiguration and the stack deflection at launch show what SIRA will endure through-out the duration of its mission. This concludes our discussion of SIRA.

95

Table 7.2: System mass.

Component Mass (kg) Dimensions (m)Launch VehicleStage 1-Inert 31,000-Propellant 419,410Stage 2-Inert 11,715-Propellant 156,113Stage 3-Inert 4,185-Propellant 46,562Breeze M-Inert 2,370-Propellant 19,800

Thrusters 4.8 0.1 x 0.1 x 0.2Radiator 2.0 0.78 x 0.78 x 0.03MLI 0.5 0.01 thickBatteries 2.0 0.089 D x 0.15Star Tracker 0.29 0.2 D x 0.1Structure 7.5 0.8 x 0.8 x 0.8Honeycomb 2.0 0.8 x 0.8 x 0.02Comm. Dish 1.5 0.35 DTransponder 1.14 0.152 x 0.076 x 0.076Amplifier 0.272 0.152 x 0.067 x 0.061Computer 0.55 0.175 x 0.107 x 0.03Data Storage Unit 0.5 0.15 x 0.1 x 0.1Solar Panels 2.0 2.4 m2

Power Distribution 2.0 0.15 x 0.15 x 0.10Dipole Antenna 10.0-Stowed 0.45 x 0.45 x 0.3-Deployed 5.0 x 0.00025 (thick) x 0.05 D

Spacecraft Mass: 37.1 kg (each)Launch Vehicle Mass: 691,115 kgTotal Launch Mass: 691,708

96

Bibliography

[1] N. Gopalswamy et al, “Predicting the 1-AU arrival times of coronal mass ejec-tions,” Journal of Geophysical Research, Vol. 106, No A12, 2001, pp. 207-217

[2] D. Dunham, Libration-Point Missions 1978-2000, Libration Point Orbits andApplications Conference, Girona, Spain, June 2002.

[3] R.J. Macdowall, Solar Imaging Radio Array, NASA Proposal VM03-0022-0006,September 8, 2003.

[4] Carrol and Ostlie, An Introductory to Modern Astrophysics, New Jersey: Addi-son Wesley, 1996.

[5] D. Oberoi, “PARIS - A Design for a very low frequency space borne radio inter-ferometer,” SIRA Workshop, Lanham, Maryland, May 2003.

[6] B.D. Steinberg Microwave Imaging with Large Antenna Array. New York, NewYork: Wiley-Interscience Publication, 1983.

[7] J.R. Wertz and W.J. Larson (editors), Space Mission Analysis and Design, ElSegundo: Microcosm Press, 1999.

[8] E.H. Forman, Decision by Objectives, avail.http://mdm.gwu.edu/Forman/DBO.pdf.

[9] Surpac Software International. ”Ellipsoid Visuallizer.” 2001. Availwww.surpac.com/refman/blockmod/ellpvis.htm

[10] Pragt, Erik. ”Photoshop Tutorials: Wireframe Sphere.” Updated 27 May 2003.http://62.166.32.154/tutorials/photoshop/shapesandobjects/wireframesphere/index.jsp

97

[11] D.C. Folta, B. Naasz, and Vaughn, “Trajectory and Formation Analysis” SIRAWorkshop Presentations, May 13-14, 2003 avail.http://lep694.gsfc.nasa.gov/sira workshop/1

[12] S.J. Isakowitz, International Reference Guide to Space Launch Systems,Washington: American Institute of Aeronautics and Astronautics, 1995.

[13] R.W. Humble, G.N. Henry, and W.J. Larson, Space Propulsion Analysis andDesign, New York: McGraw-Hill Companies, 1995.

[14] M.M. Micci and A.D. Ketsdever, Micropropulsion for Small Spacecraft, Reston:American Institute of Aeronautics and Astronautics, 2000.

[15] P.J. Turchi, Propulsion Techniques Action and Reaction, Reston: AmericanInstitute of Aeronautics and Astronautics, 2000.

[16] P. Tsiotras, H. Shen, and C.D. Hall, “Satellite Attitude Control and PowerTracking with Energy/Momentum Wheels,” Journal of Guidance, Control, andDynamics, Vol. 24, No. 1, January-February 2001, pp. 23-34.

[17] Wellbrook Communications. ”Active Loop Antennas.” December 12, 2003.Avail. http://www.wellbrook.uk.com/ALA1530.html

[18] J. Holmes. Radio Astronomy. Curtin University of technology Applied PhysicsWeb Server. December 12, 2003. Avail.www.physics.curtin.edu.au/teaching/units/Ast201/Lectures/A201-10.ppt

[19] F. Pranajaya, “Colloid Micro-Thruster Experiment,” Stanford University, avail.http://ssdl.stanford.edu/Emerald/experiment/thruster/doc/Thruster DesignDoc.doc

[20] W.C. West, J.F. Whitacre, V. White, and B.V. Ratnakumar, “Fabrication andtesting of all solid-state microscale lithium batteries for microspacecraftapplications,” Journal of Micromechanics and Microengineering, Vol. 12, 2002,pp. 58-62.

[21] Thejappa, Zlobec, and MacDowall, ”Polarization of Fragmented Solar Type IIRadio Bursts,” The Astrophysical Journal, Volume 592, Issue 2, pp. 1234-1240.

[22] E. Nicolau and D Zaharia, Adaptive Arrays. Amsterdamn: Elsevier. 1989.

98

[23] “Deep Space Network Home Page”http://deepspace.jpl.nasa.gov/dsn/index.html.

[24] J. Carr, Practical Antenna Handbook, 4th ed. New York, NY: McGraw-Hill.2001.

[25] K. Mack and Sandler, Arrays of Cylindrical Dipoles. Cambridge: At TheUniversity Press. 1968.

[26] G. Arfken, Mathematical Methods for Physicists, 3rd ed. Orlando, FL:Academic Press. 1985.

[27] R. Bate, et al. Fundamentals of Astrodynamics, Dover Publications, 1971.

[28] Iqbal and Pellegrino. ”Bi-Stable Composite Shells.” Department ofEngineering, University of Cambridge. AIAA 2000-1385.

[29] Kebadze, Guest, and Pellegrino. ”Bistable Prestressed Shell Structures.”University of Cambridge, Department of Engineering. 2003.

[30] Pellegrino, Kukathasan, Tibert, and Watt. ”Small Satellite DeploymentMechanisms.” University of Cambridge, Department of Engineering. November9, 2000.

[31] Seffen and Pellegrino. ”Deployment of a Rigid Panel by Tape-Springs.”University of Cambridge, Department of Engineering. August 1997.

[32] Astro-Iki. 04/02/04 ”Optico-Electronic Instruments”http://wildcat.iki.rssi.ru/ASTRO 1 E.htm

[33] Ball Aerospace and Technologies Corp. 04/02/04 ”Attitude Sensor”http://www.ball.com/aerospace/pdf/ct633.pdf

[34] LLNL 04/02/04 ”Star Tracker Stellar Compass (STSC)”http://www.llnl.gov/sensor technology/STR45.html

[35] Honeywell. 12/4/03 ”Momentum Control Systems”http://content.honeywell.com/dses/products/.htm

[36] Stanford. 04/02/04 ”Colloid Micro-Thruster Experiment”http://ssdl.stanford.edu/Emerald/experiment/thruster/pdf/ThrusterDesignDoc.PDF

99

[37] Stanford. 04/02/04 ”Colloid Micro-Thruster Research”http://ssdl.stanford.edu/uThruster/

[38] Able Engineering Inc. www.aec-able.com.

[39] Spectrolabs. www.spectrolab.com.

[40] Emcore. www.emcore.com.

[41] EaglePicher. www.epi-tech.com.

[42] ”X-Band Transponder”, AeroAstro Corporation, 2003. www.aeroastro.com

[43] RadioLabs Incorporated, 2004. www.radiolabs.com

[44] ”Configurable Databus Solutions”, Western Avionics, 2004.http://www.western-av.com/

[45] NEC Toshiba Space Systems, Ltd., 2004. www.ntspace.jp

[46] American Institute for Aeronautics and Astronautics. International ReferenceGuide to Space Launch Systems. AIAA, Washington DC, 1991.

[47] Automation Creations, Inc. ”Material Property Data.” Avail.http://www.matweb.com April 13, 2004.

[48] F.P. Beer, E.R. Johnston, and J.T. DeWolf, Mechanics of Materials, ThirdEdition, McGraw Hill: 2001.

100

Appendix - Matlab CodesSynthetic Aperture

% Elizabeth Cantando% SIRA% coordinates.m% February 3, 2004

% For a fixed radius sphere, 16 element array.% Selects random coordinates for two elements per octant.% coordinates(theta,phi)% onetwo identifies the first or second coordinate of each element.

function [coordinates] = script

coordinates(16,2)=0; element = 1; onetwo = 1;

while element <= 16while element <= 8

coordinates(element,onetwo) = pi/2*rand;element = element + 1;

endcoordinates(element,onetwo) = (pi/2*rand) + pi/2;element = element + 1;

end

element = 1; onetwo = 2;

while element <= 8while element <= 6

while element <= 4while element <= 2

coordinates(element,onetwo) = (pi/2*rand);element = element + 1;

endcoordinates(element,onetwo) = (pi/2*rand) + pi/2;element = element + 1;

endcoordinates(element,onetwo) = (pi/2*rand) + pi;

101

element = element + 1;endcoordinates(element,onetwo) = (pi/2*rand) + 3*pi/2;element = element + 1;

end

while element <= 16while element <= 14

while element <= 12while element <= 10

coordinates(element,onetwo) = (pi/2*rand);element = element + 1;

endcoordinates(element,onetwo) = (pi/2*rand) + pi/2;element = element + 1;

endcoordinates(element,onetwo) = (pi/2*rand) + pi;element = element + 1;

endcoordinates(element,onetwo) = (pi/2*rand) + 3*pi/2;element = element + 1;

end

% Elizabeth Cantando% SIRA% cartesian.m% February 3, 2004

function [cart_coord] = cartesian(coordinates)% Produces x,y,z for spherical given% Simple coordinate transformation

R = 1.0; %specifies raduis of arrayelement = 1;

while element <= length(coordinates)cart_coord(element,1) = R*cos(coordinates(element,1))*

102

sin(coordinates(element,2));cart_coord(element,2) = R*sin(coordinates(element,1))*sin(coordinates(element,2));cart_coord(element,3) = R*cos(coordinates(element,2));element = element + 1;

end

% Elizabeth Cantando% SIRA% sphering.m% February 16, 2004

[X,Y,Z] = sphere(17); mesh(X,Y,Z);% generates and plots coordinate triples for a unit sphere, 17 grid points

axis equal hold on

coords = coordinates; cart_coord = cartesian(coordinates)

for count = 1:16plot3(cart_coord(count,1),cart_coord(count,2),cart_coord(count,3),’kx’)count = count + 1;

end% plots 16 array elements on the surface of a unit sphere

% Elizabeth Cantando% SIRA% signalcontour.m% February 16, 2004

% generates points of observation in a plane parallel to any% diameter of the sphere.

103

% all dimensions considered relative to unit radius% plots contours of signal intensity at planes of intrest

function [pattern, YY] = signalcontour

coords = coordinates% generates polar coordinates of antennas

cart_coord = cartesian(coordinates)% converts coordinates from spherical to cartesian

d = .0; % d is the distance from the center of the arrayw = 1; % w is the half width of the square planeN = 6; % N is the number of grid points per half sidedx = w/N;

P = zeros(4*N*N,3);P(:,1) = d; % x coordinateP(:,2) = 0; % y coordinateP(:,3) = 0; % z coordinate

[YY,ZZ] = meshgrid(-N:dx:N, -N:dx:N); point = 1;% generates sampling grid

for count2 = 1:length(YY)for counter = 1:length(YY)

P(point, 2) = YY(count2,counter);P(point, 3) = ZZ(count2,counter);point = point +1;

endend% generates coordinate triples for pattern calculation

pattern = elementpattern(cart_coord,P);% generates signal pattern for each coordinate triple

ind3 = 1; for ind = 1:length(YY)for ind2 = 1:length(YY)

ZZZ(ind,ind2) = pattern(ind3,4);ind3 = ind3 + 1;

104

endend% reorders resulting vector into usable matrix

contour(ZZZ)% plots signal strenth for specified planar grid

% Elizabeth Cantando% SIRA% elementpattern.m% February 3, 2004

% Each element produces a pattern as 1/radius^2% at some location P(x,y,z)

function [pattern] = elementpattern(cart_coord,P)

pattern = zeros(size(P,1),4);

for count = 1:size(P,1)x = P(count,1);y = P(count,2);z = P(count,3);

element = 1;for element=1:16

xo = cart_coord(element,1);yo = cart_coord(element,2);zo = cart_coord(element,3);

% determine the position to each element in the arraytheta(element) = atan2(((y-yo)^2+(z-zo)^2)^0.5,(x-xo));R(element) = ((x-xo)^2+(y-yo)^ 2+(z-zo)^2)^0.5;

% determine the signal from that element at PSignal(element) = xo*xo/R(element)/R(element);

105

element = element + 1;enddirect(count) = sum(Signal(1:16));% Sum the signal from all elements to determine signal at P

pattern(count,:) = [x y z direct(count)];end

Orbit

% function which takes the postion vectors (r1)Earth and (r2)DRO,% the gravitational coefficient(SUN) and the transfer time (dt)% and solves for the semi-major axis (aT) of the transfer orbit,% the semi-latus rectum (pT) of the transfer orbit.

function[aT,pT,dtT] = piterationT(r1,r2,mu,dt)

Tol = 10d-14; Maxit = 20; Itnum = 0;

r1m = sqrt(dot(r1,r1)); r2m = sqrt(dot(r2,r2));

dnu = acos(dot(r1,r2)/(r1m*r2m)); k = r1m*r2m*(1-cos(dnu)); l =r1m+r2m; m = r1m*r2m*(1+cos(dnu));

pi = k/(l+sqrt(2*m)); pii = k/(l-sqrt(2*m)); po =(1/3)*(2*pi+pii); ao = (m*k*po)/((2*m-l^2)*po^2+(2*k*l*po)-k^2);fo = 1-(r2m/po)*(1-cos(dnu)); fdoto =sqrt(mu/po)*tan(dnu/2)*((1-cos(dnu))/po-1/r1m-1/r2m); go =(r1m*r2m*sin(dnu))/(mu*po); sindEo = (-r1m*r2m*fdoto)/sqrt(mu*ao);cosdEo = 1-(1-fo)*(r1m/ao); dEo = atan2(sindEo,cosdEo); dtgo =go+sqrt(ao^3/mu)*(dEo-sin(dEo)); Fo = dtgo-dt; p1 =(1/3)*(pi+2*pii); a1 = (m*k*p1)/((2*m-l^2)*p1^2+(2*k*l*p1)-k^2);f1 = 1-(r2m/p1)*(1-cos(dnu)); fdot1 =sqrt(mu/p1)*tan(dnu/2)*((1-cos(dnu))/p1-1/r1m-1/r2m); g1 =(r1m*r2m*sin(dnu))/(mu*p1); sindE1 = (-r1m*r2m*fdot1)/sqrt(mu*a1);cosdE1 = 1-(1-f1)*(r1m/a1); dE1 = atan2(sindE1,cosdE1); dtg1 =g1+sqrt(a1^3/mu)*(dE1-sin(dE1)); F1 = dtg1-dt;

106

while(abs(F1)>Tol&Itnum<Maxit)dp = -((po-p1)*F1)/(Fo-F1);pn = p1+dp;an = (m*k*pn)/((2*m-l^2)*pn^2+(2*k*l*pn)-k^2);fn = 1-(r2m/pn)*(1-cos(dnu));fdotn = sqrt(mu/pn)*tan(dnu/2)*((1-cos(dnu))/pn-1/r1m-1/r2m);gn = (r1m*r2m*sin(dnu))/(mu*pn);sindEn = (-r1m*r2m*fdotn)/sqrt(mu*an);cosdEn = 1-(1-fn)*(r1m/an);dEn = atan2(sindEn,cosdEn);dtgn = gn+sqrt(an^3/mu)*(dEn-sindEn);Fn = dtgn-dt;po = p1;p1 = pn;Fo = F1;F1 = Fn;Itnum = Itnum+1;

end

aT = an; pT = pn; T = -dtgn

close all clear all

% tol is the error tolerance for convergence when% using the function newton_orb to find the% eccentricic anomaly E% rs is the radius of the Sun% muS is the suns gravitational coeficient% Eday is the nimber of solar days in one Earth period

Mo1 = 0; Mo2 = 0;tol = .1e-014; rS = 696d3; muS = 1.326d11; Eday =365.242199;

% Semimajor axis (a), period (P), and mean angular motion (n)% for Earth and DRO orbits

107

a = ((Eday*24*3600)^2*(1/(2*pi))^2*muS)^(1/3); n = sqrt(muS/a^3);P = 2*pi/n;

% eE is an approximation of the current eccentricity of Earths orbit% eD is the chosen eccentricity of the DRO orbit in order to% keep SIRA the proper distance away from the Earth

eE = 0.0167; eD = 0.0255;

% periapsis (rp) and apoapsis (ra) distances for Earth and DRO orbits% semi-latus rectum (p) for Earth and DRO orbits

rpE = a*(1-eE); rpD = a*(1-eD); raE = a*(1+eE); raD = a*(1+eD); pE= a*(1-eE^2); pD = a*(1-eD^2);

% vector of Earth and DRO period in seconds (dt)

dt = 0:100000/2:P; f = 0:(2*pi)/length(dt):2*pi;

% Time rate of change Mean (M),Eccentricic (E),and True% anomaly (f) angles for DRO and Earth orbits over one period

for u=1:length(dt)M1(u)=Mo1+n*dt(u);M2(u)=Mo2+n*dt(u);E1(u)=newtorb_ell(eE,M1(u),tol);E2(u)=newtorb_ell(eD,M2(u),tol);f1(u)=(atan2((1+eE)^.5*tan(E1(u)/2),(1-eE^2))*2);f2(u)=(atan2((1+eD)^.5*tan(E2(u)/2),(1-eD^2))*2);

end

% r1 and r2 are the radius’s of each orbit at any time t% drEDRO is the distance of SIRA from the Earth at any time t% x’ and y’ are points at any time t used to plot the orbits% and the motion of SIRA and the Earth% v1 is the orbit velocities at any time t for Earth% v2 is the orbit velocity at any time t for the dro

108

% r1v and rv2 are the position vectors for each orbit% rv1 being used for the Earth and rv2 being used for the DRO% dv12 is the difference in orbit velocity between Earth and DRO

for i=1:length(dt)r1(i) = pE/(1+eE*cos(f1(i)));r2(i) = pD/(1+eD*cos(f2(i)));drEDRO(i) = sqrt((sqrt(dot(r1(i),r1(i)))^2+sqrt(dot(r2(i),r2(i))^2))-...2*(sqrt(dot(r1(i),r1(i)))*sqrt(dot(r2(i),r2(i)))*cos(f2(i)-f1(i))));x1(i) = r1(i)*cos(f1(i));y1(i) = r1(i)*sin(f1(i));x2(i) = r2(i)*cos(f2(i));y2(i) = r2(i)*sin(f2(i));x4(i) = rS*cos(f(i));y4(i) = rS*sin(f(i));v1(i) = sqrt(muS*(2/r1(i)-1/a));v2(i) = sqrt(muS*(2/r2(i)-1/a));dv12(i) = abs(v1(i)-v2(i));r1v(i,:) = [x1(i) y1(i)];r2v(i,:) = [x2(i) y2(i)];

end

% mm ia the minimum value for the difference between% the Earths orbits velocity and the DRO orbit velocity% dvmin is the row number of the minimum difference between% their velocities chosen from the array dv12% w is the point picked out of the Earths position vector to launch from% u is the point picked out of the DRO posotion vector for insertion% r1vT is the position vector of launch(2 body problem) from Earth% r2vT is the position vector of insertion(2 body)to DRO% r1m is the magnitude of r1vT% r2m os the magnitude of r2vT% dfT is the change in angle for the transfer% dtT is the time the transfer manuever must be completed in% in order to insert in the DRO close to the Earth

%mm = min(dv12);%dvmin = find(dv12==mm);w = 225;u = 515; r1vT = r1v(w,:); r2vT = r2v(u,:); r1m =

109

sqrt(dot(r1vT,r1vT)); r2m = sqrt(dot(r2vT,r2vT)); dfT =acos(dot(r1vT,r2vT)/(r1m*r2m)); dtT = dt(u)-dt(w);

% the function pplot plots time vs. the min and max values for the% semilatus rectum (p)(used if the function piterationT does not converge)% nT is the mean angular motion of the transfer orbit% PT is the period of the transfer orbit% aT is the semi-major axis of the transfer orbit% eT is the eccentricity of the transfer orbit% rpT and raT(periapsis and apoapsis distances of transfer orbit% piterationT is a function used to find and return aT and pT,

%pplot(r1vT,r2vT,muS,dtT) % use if piterationT does not converge[aT,pT,T] = piterationT(r1vT,r2vT,muS,dtT) nT = sqrt(muS/aT^3); PT= (2*pi)/nT; eT = sqrt(1-(pT/aT)); rpT = aT*(1-eT); raT =aT*(1+eT);

% C is the chord length of the transfer orbit% v1Tv is the velocity vector of the launch point from Earth orbit% v1TO is the magnitude of v1Tv% v2Tv is the velocity vector of the insertion point into DRO% v2TO is the magnitude of v2Tv% dvT1 is the delta-v launch% dvT2 is the delta-v insertion% f11 is the angle of the launch point% f22 is the angle of the insertion point

C = r2vT-r1vT; v1Tv =(sqrt(muS*pT)/(r1m*r2m*sin(dfT)))*(C+(r2m/pT)*(1-cos(dfT))*r1vT);v1TO = sqrt(dot(v1Tv,v1Tv)); v2Tv =(sqrt(muS*pT)/(r1m*r2m*sin(dfT)))*(C-(r1m/pT)*(1-cos(dfT))*r2vT);v2TO = sqrt(dot(v2Tv,v2Tv)); dvT1 = v1TO-v1(w); dvT2 = v2(u)-v2TO;dvTotal = abs(dvT1)+abs(dvT2); f11=f1(w)*180/pi; f22=f2(u)*180/pi;

% the next section may not be right, i am trying to get points% to plot the transfer orbit, but have been unsuccesful

sinfoT = pT/(eT*rpT); cosfoT = ((pT/rpT)-1)/eT; foT =atan2(sinfoT,cosfoT); sinf1T = pT/(eT*r1m); cosf1T =((pT/r1m)-1)/eT; f1T = atan2(sinf1T,cosf1T); EoT =

110

atan2(tan(foT/2),sqrt((1+eT)/(1-eT)))*2; E1T =atan2(tan(f1T/2),sqrt((1+eT)/(1-eT)))*2; MoT = (EoT-eT*sin(EoT));

% still below just trying to plot the transfer orbit

tT = 0:100000/2:PT;

for j = 1:length(tT)M3(j) = MoT+nT*tT(j);E3(j) = newtorb_ell(eT,M3(j),tol);sinf(j) = (sqrt(1-eT^2)*sin(E3(j)))/(1-eT*cos(E3(j)));cosf(j) = (cos(E3(j))-eT)/(1-eT*cos(E3(j)));f3(j) = atan2(sinf(j),cosf(j));r3(j) = pT/(1+eT*cos(f3(j)));x3(j) = r3(j)*cos(f3(j));y3(j) = r3(j)*sin(f3(j));v3(j) = sqrt(muS*(2/r3(j)-1/aT));

end

%plots the orbits and the motion of DRO and the Earth

for c=1:length(dt)eangle=atan2(y1(c),x1(c));sangle=atan2(y2(c),x2(c));sangle=sangle-eangle;relstate(c,1)=sqrt((x2(c))^2+(y2(c))^2)*cos(sangle)-sqrt((x1(c))^2+(y1(c))^2);relstate(c,2)=sqrt((x2(c))^2+(x1(c))^2)*sin(sangle);

end

plot(relstate(:,1),relstate(:,2),’r-’)

figure(2) plot(x1,y1,’b-’);hold on; plot(x3,y3,’r-’)

% function used to plot time vs. p(max) and p(min)% in order to pick a p of the plot related to the% transfer time

111

function[] = pplot(r1v,r2v,mu,dt)

r1m = sqrt(dot(r1v,r1v)); r2m = sqrt(dot(r2v,r2v));

df = acos(dot(r1v,r2v)/(r1m*r2m)); k = r1m*r2m*(1-cos(df)); l =r1m+r2m; m = r1m*r2m*(1+cos(df));

pi = k/(l+sqrt(2*m)); pii = k/(l-sqrt(2*m));

pp = pi:100000:pii; for i = 1:length(pp)ao(i) = (m*k*pp(i))/((2*m-l^2)*pp(i)^2+(2*k*l*pp(i))-k^2);fo(i) = 1-(r2m/pp(i))*(1-cos(df));fdoto(i) = sqrt(mu/pp(i))*tan(df/2)*((1-cos(df))/pp(i)-1/r1m-1/r2m);go(i) = (r1m*r2m)/(mu*pp(i))*sin(df);sindEo(i) = -(r1m*r2m*fdoto)/sqrt(mu*ao);cosdEo(i) = 1-(1-fo(i))*(r1m/ao(i));dEo(i) = atan2(sindEo(i),cosdEo(i));dtgo(i) = -(go(i)+sqrt(ao(i)^3/mu)*(dEo(i)-sin(dEo(i))));tdiff(i) = dtgo(i)-dt;

end

plot(pp,tdiff)

% this function is simply a Newtons method function% which takes e, Mo, and a tolerance(tol) and% converges to find and Eccentricic anomaly angle

function[res]=newtorb_ell(e,Mo,tol)

E=Mo; dE=(Mo-((E-e*sin(E))))/(e*cos(E)-1);

while abs(dE)>tolE1=E-(Mo-((E-e*sin(E))))/(-1+e*cos(E));E=E1;dE=(Mo-((E-e*sin(E))))/(e*cos(E)-1);

112

end

res=E;

Power

clear all; clc; close all;

timespan=24/24*86400; %time span in seconds

initialbatteryenergy=600000; %initial energy stored in battery, joules

adcspower=5; %ADCS nominal power consumption, wattscommpower=20; %Communication system nominal power consumption, wattsproppower=0; %Propulsion system nomimal power consumption, watts

solararrayoutput=80; %nominal power production of solar panels, watts

adcson=1; %switch for adcs system operationcommon=1; %switch for communication system operationpropon=1; %switch for propulsion system operation

powergenhistory=zeros(timespan,1);powerusehistory=zeros(timespan,1);acceptablepowerhistory=zeros(timespan,1);batteryenergyhistory=zeros(timespan,1);

batteryenergy=initialbatteryenergy; time=1; while time<=timespanpowerstep=0;if adcson==1

powerstep=powerstep+adcspower;endif common==1

powerstep=powerstep+commpower;endif propon==1

113

powerstep=powerstep+proppower;endpowerusehistory(time)=powerstep;powergenhistory(time)=solararrayoutput;

commdumptime=7200;commdumpduration=14400;if time==commdumptime

[powerusehistory,powergenhistory,acceptablepowerhistory,batteryenergyhistory,batteryenergy]=commdump(commdumptime,commdumpduration,powerusehistory,powergenhistory,acceptablepowerhistory,adcspower,2,commpower,80,proppower,0,solararrayoutput,batteryenergyhistory,batteryenergy);time=time+commdumpduration-1;

endstationkeepingtime=30000;stationkeepingduration=50;if time==stationkeepingtime

[powerusehistory,powergenhistory,acceptablepowerhistory,batteryenergyhistory,batteryenergy]=stationkeeping(stationkeepingtime,stationkeepingduration,powerusehistory,powergenhistory,acceptablepowerhistory,adcspower,3,commpower,0,proppower,10,solararrayoutput,batteryenergyhistory,batteryenergy);time=time+stationkeepingduration-1;

endif powerusehistory(time)>powergenhistory(time)

acceptablepowerhistory(time)=1;endif powerusehistory(time)<powergenhistory(time) & batteryenergy<initialbatteryenergy

batteryenergy=batteryenergy+(powergenhistory(time)-powerusehistory(time));

endbatteryenergyhistory(time)=batteryenergy;time=time+1;

end

subplot(2,1,1) plot(1:1:timespan,powerusehistory,’r-’); hold on;plot(1:1:timespan,powergenhistory,’b-’); ylabel(’Power, watts’)

114

set(gcf,’Color’,[1 1 1]) axis([0 timespan 01.25*max(powergenhistory)]); legend(’Power Usage’,’PowerGeneration’,0)

plot(1:1:timespan,0,’g-’) for j=1:1:timespanif acceptablepowerhistory(j)==1

plot(j,0,’r-’)end

end

subplot(2,1,2) plot(1:1:timespan,batteryenergyhistory/1000,’b-’)axis([0 timespan 0 .00125*max(batteryenergyhistory)]);legend(’Battery Energy Stored’,0) ylabel(’Battery Energy, kJ’)xlabel(’Time, t, seconds’)

function[powerusehistory,powergenhistory,acceptablepowerhistory,batteryenergyhistory,batteryenergy]=commdump(starttime,duration,powerusehistory,powergenhistory,acceptablepowerhistory,adcspower,adcsboostamp,commpower,commboostamp,proppower,propboostamp,solararrayoutput,batteryenergyhistory,batteryenergy)

for i=starttime:1:(starttime+duration)

%Additional power required by ADCS during communications dumpif i<(starttime+duration/100)

adcspowerterm=adcspower+adcsboostamp;

elseif i>(starttime+duration*99/100)adcspowerterm=adcspower+adcsboostamp;

elseadcspowerterm=adcspower;

end%Additional power required by communication system during dumpcommpowerterm=commpower+commboostamp;%Additional power required by propulsion system during dumpproppowerterm=proppower+propboostamp;

115

powerusehistory(i)=adcspowerterm+commpowerterm+proppowerterm;powergenhistory(i)=solararrayoutput-10+10*abs(((i-1-starttime)/(duration-1)-.5)^2.5);if powerusehistory(i)>powergenhistory(i)

deficit=powerusehistory(i)-powergenhistory(i);if deficit<batteryenergy

batteryenergy=batteryenergy-deficit;powergenhistory(i)=powergenhistory(i)+deficit;

endendif powerusehistory(i)>powergenhistory(i)

acceptablepowerhistory(i)=1;endbatteryenergyhistory(i)=batteryenergy;

end

function[powerusehistory,powergenhistory,acceptablepowerhistory,batteryenergyhistory,batteryenergy]=stationkeeping(starttime,duration,powerusehistory,powergenhistory,acceptablepowerhistory,adcspower,adcsboostamp,commpower,commboostamp,proppower,propboostamp,solararrayoutput,batteryenergyhistory,batteryenergy)

for i=starttime:1:(starttime+duration)%Additional power required by ADCS during communications burnif i<(starttime+duration/6)

adcspowerterm=adcspower+adcsboostamp;

elseif i>(starttime+duration*5/6)adcspowerterm=adcspower+adcsboostamp;

elseadcspowerterm=adcspower;

end%Additional power required by communication system during burncommpowerterm=commpower+commboostamp;%Additional power required by propulsion system during burnproppowerterm=proppower+propboostamp;powerusehistory(i)=adcspowerterm+commpowerterm+proppowerterm;

116

powergenhistory(i)=solararrayoutput;if powerusehistory(i)>powergenhistory(i)

acceptablepowerhistory(i)=1;endif powerusehistory(i)>powergenhistory(i)

deficit=powerusehistory(i)-powergenhistory(i);if deficit<batteryenergy

batteryenergy=batteryenergy-deficit;powergenhistory(i)=powergenhistory(i)+deficit;

endendif powerusehistory(i)>powergenhistory(i)

acceptablepowerhistory(i)=1;endbatteryenergyhistory(i)=batteryenergy;

end

Thermal

% This segment will calculate the thermal properties of% SIRA main bus using a spherical satellite assumption.

Gs = 1418; % Solar Constant (W/m^2)D = 0:0.01:1; % Diameter of spacecraft (m)Ac = (pi.*D.^2)./4; % Cross sectional area of the spacecraft (m^2)alpha = 0.6; % Solar absorptivityA = 4*pi.*(D/2).^2; % Surface area of the sphere (m^2)sigma = 5.67051e-8; % Stefan-Boltzmann’s constant (W/(m^2*K^4))e = 0.8; % Infared emissivityQw = 50:150; % Electrical Power Dissipation (W)T = (((Ac.*Gs.*alpha)+Qw)./(A*sigma.*e)).^0.25;% Temperature of the spacecraft (K)

plot(D,T) title(’Spacecraft Diameter vs. Temperature’);xlabel(’Spacecraft Diameter, m’); ylabel(’Temperature, K’);

% This segment computes the size of the body-mounted radiator.

117

theta = 0:(0.05*pi)/180:(5*pi)/180; % Worst case sun angle (radians)Qw_over_Ar = ((sigma*e.*T.^4)-(Gs*alpha.*cos(theta)));% Waste Heat per Radiator Area (W/m^2)

figure plot(Qw_over_Ar,T) title(’Waste Heat per Radiator Area vs.Temperature’); xlabel(’Waste Heat per Radiator Area, W/m^2’);ylabel(’Temperature, K’);

% This segment computes the body-mounted solar cell thermal characteristics.

Asolar = A./4; % Solar cells take up 1/4 of surface area (m^2).alpha_solar = 0.77; % EOL solar array absorptivity.e_solar = 0.76; % Emissivity of solar cells.Qsa = Gs.*Asolar*alpha_solar; % Direct solar energy absorbed be cells (W).eta = 0.07:0.0015:0.22; % Solar cell efficiency.Tequil = (((Gs*alpha_solar)+eta.*Gs)/(2*e_solar*sigma)).^(1/4);% Equilibrium temperature of the solar array (K).Qe = (2*sigma*e_solar.*Asolar.*Tequil.^4);% Emitted radiation energy from solar array.

plot(Asolar,Qsa) %title(’Solar Array Area vs. Absorbed Solar Energy’); %xlabel(’Solar Array Area, m^2’); %ylabel(’Absorbed Solar Energy, W’);%figure%plot(Asolar,Qe)%title(’Solar Array Area vs. Emitted Radiation Energy’);%xlabel(’Solar Array Area, m^2’);%ylabel(’Emitted Radiation Energy, W’);%figure%plot(Asolar,Tequil)%title(’Solar Array Area vs. Solar Array Temperature’);%xlabel(’Solar Array Area, m^2’);%ylabel(’Solar Array Temperature,K’);%

Communications

clear; clc;

118

for s = [1000000000:100000000:3000000000];

watts = 30; %trans power%s = 3000000000; %distance in (kilo?)meters from earthd =0.5; %SIRA high gain dishD = 70; %DSN 70m dishGHz = 8.5; %trans freqHz = GHz * 1000000000;theta = 21/(GHz*d); %half-power beamwidth (deg)e = theta; %pointing error

P = 10*log10(watts); %transmitter powerLl = -5; %tran/ant lossLs = 147.55 - 20*log10(s) - 20*log10(Hz); %space lossLa = -10; %trans lossGt = 17.8 + 20*log10(d) + 20*log10(GHz); %trans gainGr = 17.8 + 20*log10(D) + 20*log10(GHz); %recieve gainTs = 300 ; %system noise temp (Earth)Ltheta = -12*(e/theta)^2 ; %pointing error loss

R = [10000:1000:100000]; %data rate (bps)

EbNo = P + Ll + Gt + Ls + La + Ltheta + Gr + 228.6 - 10*log10(Ts)- 10*log10(R);

plot(EbNo,R,’r’); xlabel(’E_b/N_o’); ylabel(’Date Rate, R (10,000sbits/sec’); hold on;

end

clear; clc;

for L = [0.05:0.05:0.5]; d = 0.002;

watts = 300; %trans powers = 1500000000; %distance in (kilo?)meters b/t satsD = 70; %DSN 70m dish

119

GHz = 8.5; %trans freqHz = GHz * 1000000000;

C = pi.*d; lam = (3*10^8)/Hz; Clam = C./lam;

theta = 52./((C.^2*L)./lam^3).^.5;thetaD = 21/(GHz*D); %half-power beamwidth (deg)e = theta; %pointing error

Gr = 10.3 + 10*log10((C.^2*L)/lam^3); %Gr = Gt;

P = 10*log10(watts); %transmitter powerLl = -5; %tran/ant lossLs = 147.55 - 20*log10(s) - 20*log10(Hz); %space lossLa = -10; %trans lossGt = 17.8 + 20*log10(D) + 20*log10(GHz); %trans gainTs = 300 ; %system noise temp (space)Ltheta = -12*(e/theta)^2 ; %pointing error loss

R = [1:1000:300000]; data rate (bps)

EbNo = P + Ll + Gt + Ls + La + Ltheta + Gr + 228.6 - 10*log10(Ts)- 10*log10(R);

plot(EbNo,R); xlabel(’E_b/N_o’); ylabel(’Date Rate, R (10,000sbits/sec’); hold on;

% plot(d,theta);% xlabel(’diameter’); ylabel(’Beamwidth, theta’);% hold on;

end

120