SNAP Spacecraft Orbit DesignSNAP Spacecraft Orbit Design

Stanford University

Matthew Peet

Presentation LayoutPresentation Layout

Mission requirementsThe use of swingby trajectoriesPrevious researchResearch goalsStatus of current workPlans for future work

SNAP Mission RequirementsSNAP Mission Requirements

Minimize Accelerations– Improves target tracking

Minimize length of eclipse duration– Reduces onboard battery requirements

• Weight(~1kg/kW-hr)• complexity

– Heating and standby power reduced Maximum contact with Berkeley

– Allows increased data download– Improves control ability and reaction time

Avoid radiation belts

Candidate Orbit TypesCandidate Orbit Types

Low Earth Orbit Geostationary Orbit

High Earth Orbit Lagrange Orbit

Preferred Orbit DesignPreferred Orbit Design

High earth orbit High inclination to

avoid eclipse– >35 degrees required to

avoid moon, but higher is better

Moderate eccentricity– Rp > 8 Re to avoid

radiation– Ra < Rm to reduce

antenna power Apogee over northern

hemisphere

Launch RequirementsLaunch Requirements

For direct injection three burns required

for a total delta-v of 12 km/s– 1.75 km/s worth of fuel

onboard for final burn– 2200 lbs of fuel for a

2000 lb spacecraft Delta II Class Launch

Vehicle Needed– Upper Stage Required– Cost: 80M-100M

Gravity AssistsGravity Assists

Uses the gravitational attraction of a planetary body to alter the motion of a satellite.

Rotates relative spacecraft velocity in the planet-fixed reference frame about axes fixed to the planet.– Satellite energy is conserved within the planetary reference

frame.

Planet-fixed frame is in motion with respect to the inertial space– A rotation in planetary system may not result in satellite

energy conservation in inertial space

Swingby trajectoriesSwingby trajectories

Path of the spacecraft in planetary reference frame is rotated by angle delta– Sin(/2) = 1/e– e = 1 - Rp/a– a = 2*/v2

Previous ResearchPrevious Research

History of swingby trajectories in interplanetary mission design– Voyager, Pioneer, Magellan, Galileo, Cassini

Prometheus mission concept development– Long term observation strategy

Communications satellite rescue mission– Provided inclination change for stranded

geostationary satellite

Interplanetary Mission DesignInterplanetary Mission Design

First uses of Swingby concept

Restricted to in-plane maneuvers– No inclination

changes– Allows for

simplification Voyager and Apollo

through Cassini

Prometheus Mission ConceptPrometheus Mission Concept

1985 - current First exploration of

swingby trajectories for near-earth applications– Inclination changing– Perigee raising

Utilized a Monte-Carlo style technique

Never launched

Satellite Rescue Mission AnalysisSatellite Rescue Mission Analysis

1998 - current Development of

technique for multiple passes– Insufficient fuel

resources for direct encounter

Derivative based solution developed by Cesar Ocampo et al.

Goals of Current ResearchGoals of Current Research

1. Reduce launch costs by minimizing the delta-v required to place the SNAP satellite in its optimal orbit

2. Facilitate mission planning by developing an analytic process that will produce an optimal lunar assist trajectory given launch date and desired orbit

3. Improve the analytical process to provide long-term orbit stability

Status of Current ResearchStatus of Current Research

Developed baseline trajectory based on adaptations of historical mission plans

Developed first order method for prediction and control of lunar encounter

Improved baseline trajectory based on analytical predictions

Baseline TrajectoryBaseline Trajectory

Launch: October 20, 2007

Based on Prometheus mission design– Earth observation

satellite mission Lunar intersection

occurs at descending node– Eases adaptation of

orbit

Development of TrajectoryDevelopment of Trajectory

Used STK with Astrogator to propagate orbit– Used 12th order earth

model with perturbations out to 1/3 lunar distance• Runge-Kutta variable

step propagator

– Used 4th order selenocentric model with earth point mass and perturbations during lunar encounter• CisLunar variable step

propagator

Used Initial trajectory identical to Prometheus mission

Calculated relative phase of moon in orbit at intersection during old mission

Calculated next occurrence for this phase starting in October, 2007

Determined launch date and time to intercept moon at this point in time

Baseline TrajectoryBaseline Trajectory

Final Orbital Elements:– Rp = 11 Re– e = .696– i = 55.3 deg– RAAN= 354.3 deg– AOP = 22.3

Development of Analytic MethodDevelopment of Analytic Method

Consists of 3 stages

–Intercept stage

–Swingby stage

–Return stage

–Intercept stage

–Swingby stage

–Return stage

Intercept StageIntercept Stage

Relate launch conditions to arrival conditions at moon

Find launch conditions for a given set of arrival conditions

Include effects of phasing loops and determine launch windows for desired conditions

Development of Intercept StageDevelopment of Intercept Stage

Calculate launch conditions given launch date and azimuth

Calculate lunar position given intercept time

Apply phasing loops, if any

Propagate to lunar sphere of influence– Uses proportional error

control to converge on solution

– yields time of arrival and lunar position at arrival

Calculate relative position and velocity of the craft with respect to the moon at arrival

Given desired arrival conditions,relate back to specified launch conditions– Assumes constant arrival

time at sphere of influence

– work in progress

Swingby StageSwingby Stage

Within sphere of influence, use simplified 2 body orbital motion

Relate exit conditions to arrival conditions

Development of Swingby StageDevelopment of Swingby Stage

Translate relative position and velocity into Keplerian elements describing the lunar encounter

Propagate orbit through to edge of sphere of influence

Transform relative position and velocity to the inertial frame

Given beta-plane targeting parameters, calculate position and velocity at entrance to sphere of influence

Given exit position and velocity, determine beta-plane targeting parameters

The beta-plane parameters are used as outputs when the scenario is run through STK to ensure the values are roughly accurate

Return StageReturn Stage

Relate elements of final orbit to sphere of influence exit conditions

Assume an apogee lowering burn at perigee to provide orbital stability

Development of Return StageDevelopment of Return Stage

Given position and velocity at edge of lunar sphere of influence, calculate new orbital element

Given new set of orbital elements, calculate apogee lowering burn for desired stability period– ¼, ½, 2/3 lunar period, etc.

Find the final orbital elements following final burn– i and RAAN do not change– e can be related directly to

elements at exit• efinal = 1-afinal(1-e)/a

Given desired Earth-Vehicle-Moon(EVM) angle and orbital parameters, determine initial AOP– not yet complete

Verify that desired orbital parameters meet Tisserand Criterion

Find exit position and velocity given desired orbital elements– entirely analytic solution– does not include mean or

true anomaly

Improved Baseline TrajectoryImproved Baseline Trajectory

Improved orbital characteristicsRp = 20 Ree = .399i = 73 degRAAN = 351 degAOP = 221.5 deg

High InclinationHigh Inclination

Inclination of 73 degrees– Reduced eclipse time to 5.6 hours– Only 82 minutes in the umbra

Orbital StabilityOrbital Stability

Three year nominal stability

Intrinsic stability of semi-major axis due to lunar influence

Slight reduction of inclination over lifetime of spacecraft– Increase in eclipse time

is small– This stability issue will

be explored in future work

Orbit StabilityOrbit Stability

Coverage TimeCoverage Time

Over the course of the three year lifetime– 60% is spent in

Northern Hemisphere

– 55.2% is spent in LOS contact with Bay Area

Launch CostsLaunch Costs

On-board fuel reserves require only 90 m/s– only 78 lb of fuel

required

Launch Vehicle requirements reduced– C3 of –2 km^2/s^2

Plans for Future WorkPlans for Future Work

Orbital Stability InvestigationImprove Matlab modelsDesign semi-analytic tools similar to

the Ocampo research