orbital mechanics by viasbirs

7/29/2019 Orbital Mechanics by Viasbirs

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www.stk.com SSMD-1102-366 [1]

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Understanding Orbital Mechanics Through a Step-by-Step

Examination of the Space-Based Infrared System (SBIRS)

Denny Sissom Elmco, Inc.

May 2003
http://www.stk.com/http://www.stk.com/


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Radars

IFICS (In-Flight Interceptor Communications System)

Ground-Based Interceptors Battle Management (BMC3)

Space-Based Infrared System (SBIRS)

SBIRS High GEO (Geo-Stationary Orbits)

SBIRS High HEO (Highly-Elliptical Orbits) SBIRS Low (Low-Altitude Orbits)

SBIRS Ground Station Processing (MCS)

The Ground-Based MidcourseDefense Architecture (2004)

The Ground-Based MidcourseDefense Architecture (2004)


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SBIRS Low

DSP/GEO

SBIRS High

MissionControl

Station(MCS)

Mission Control Station

One Central CONUS Location Boost and Coast Tracking Booster Typing Launch Point Estimation Impact Point Prediction

Mission Control Station

One Central CONUS Location Boost and Coast Tracking Booster Typing Launch Point Estimation Impact Point Prediction

Launch DetectionBoost Tracking

SBIRS Comm unicat ion

GEO Satellites Rotating Platform Provides 2D

Detection Reports toMCS

Scanner Only- SWIR Band

- Periodic Revisit

DSP Payload

2D Detection

Report

Highly EllipticalOrbit (HEO)

Scanner Only- SWIR, MWIR

Bands- Taskable Scan

Rate and Revisit

HEO Payload

ScannerRapid Global

CoverageSWIR, MWIR

BandsTaskable Scan

Rate and Revisit StarerSWIR, MWIR

BandsTaskable Revisit

Follow-on andreplacement forDSP

GEO

Payload

LEO Payload

Acquisition Sensor- Wide FOV (WFOV)- SWIR Band- Boost Detection

Track Sensor- Narrow FOV(NFOV)

- Multiple Wavebands- 2-Axis GimbalControl- Precise MidcourseAcquisition,Tracking, &Discrimination

SBIRS Archi tecture

Four Satellites in Geo-stationary Orbits (GEO)

Two Satellites in HighlyElliptical Orbits (HEO)

Twenty or moreSatellites in Low EarthOrbit (LEO)

Ground-Based MissionControl Station (MCS)



Mid-CourseTracking

Discrimination

SBIRS Model Overview


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SBIRS Concept of Operations

SBIRS High (GEO and/or HEO)Acquire Target (SBIRS Low Can

Also Acquire Target)

Data Transmitted From SBIRSHigh To Mission Control Station

(MCS) Track Data Is Transmitted From

MCS To SBIRS Low

SBIRS Low Acquires And HandsData Over From Acquisition

Sensor To Track Sensor

Data Handed Over To Other SBIRSLow Spacecraft and MCS

Track Data Sent FromMCS To Battle Manager

Animation Showing Concept of OperationsFrom www.stk.com
http://www.stk.com/http://www.stk.com/http://www.stk.com/http://www.stk.com/


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Keplers Laws

Keplers First Law: The Orbits of Planets (or Satellites) are Ellipses with the Sun at a Focus

Keplers Second Law: The Orbits of the Planets Sweep Out Equal Areas in Equal Time

Keplers Third Law: The Square of the Orbit Period (The Time it Takes to Go Around Once)

is Proportional to the Cube of the Average Distance to the SunWhere:

P = Period (sec)

a = Semi-Major Axis (km)

= Gravitational Parameter (km3/s2) = GMearthG = Universal Gravitational Constant (Nm2/kg2)

Mearth = Mass of the Earth (kg)

a2P

3

=

Area 2Area 1Planetary

Motion over

30 Days

Planetary

Motion over

30 Days

Area 1 = Area 2

Average Distance


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Newtons Law and the Restricted Two-Body Equation of Motion

amF =

2

21mGm

Fg =

R

R

mF Egr

2

=

RmamRmE &&vv==

2

02

=+R

RR&&v

Newtons Second Law

Newtons Law of Universal Gravitation

Newtons Law of Universal Gravitation inVector Form with Earth as Central Body

(E = GMearth = 3.986 x1014 m3/s2)

Combining Newtons Two Laws, assuming:(1) No perturbations (drag, earths oblateness, other planets, etc.)

(2) Bodies are spherically symmetric

(3) m1 >> m2

We Get the Restricted Two-Body Equation of

Motion Which is a Second-Order, Non-Linear,

Vector Differential Equation YUK!

This Equation Represents a Conic Section (Circle, Ellipse, Parabola, or Hyperbola)


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A Few More Useful Equations forOrbital Mechanics

VmRH = Angular Momentum

Specific Angular Momentum, whereVRh =

R

mmVE

= 2

2

1

V =

2

2

a2

=

m

Hhv

Total Mechanical Energy for Orbiting Spacecraft

(Must remain constant!)

Specific Mechanical Energy, where

m

E

Shows We can Easily Find Specific Mechanical Energy Just

Knowing the Semi-Major Axis

Apogee:

High PE = -m/RLow KE = mV2

Perigee:

Low PE = -m/RHigh KE = mV2

Earth

- is negative for circles and ellipses

- is zero for parabolas

- is positive for hyperbolas

E


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Geocentric EquatorialCoordinate System

Origin Center of Earth

Fundamental Plane Earths Equator

Principle Direction (I-Axis) Vernal Equinox Direction Found by Drawing a Line from the Earth to the

Sun on the First Day of Spring Points at First Star in Aries Constellation (First Point of Aries) Denoted by Rams Head Symbol Wanders Due to Earth Spin-Axis Wobble Because of the Wobble, Sometimes the Vernal Equinox Direction is

Specified at a Certain Time or Epoch Fixed at Vernal Equinox direction at Noon on January 1, 2000 at

Greenwich Meridian by International Astronomical Union (More TrulyInertial)

K-Axis North Pole


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circle

Semi-Major Axis and EccentricityThe Size and Shape of a Orbit

Size Determination: Semi-Major Axis

Shape Determination: Eccentricity

Apogee radius

Apogee Altitude

Apogee Perigee

Perigee Altitude

Perigee radius

Semi-Major Axis

CCenter ofEllipse

C = distance from center of Earth to centerof ellipse = eccentricity * semi major axis

e = 1

e > 1

0 < e < 1

ellipse

e = 0


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InclinationThe Orientation of an Orbit

Tilt of Orbital Plane with Respect to Fundamental Plane (of Geocentric-Equatorial Coordinate System)

Angle Between Specific Angular Momentum Vector ( ) and theVector Perpendicular to the Fundamental Plane Pointing Through theNorth Pole (K-axis)

Ranges from 0 to 180

VRh =

Indirect or Retrograde(Moves Against the

Direction of Earths

Rotation)

90 < i 180

Direct or Prograde (Moves

in the Direction of Earths

Rotation)

0 i < 90

Polar90

Equatorial0 or 180

DiagramOrbital TypeInclination

i =90

Ascendingnode

Ascendingnode

J

I

Kh i


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Right Ascension of Ascending Node (RAAN or)The Swivel of an Orbit

Angle, Along the Equator, Between Principle Direction (i.e., First Pointof Aries) and the Point Where the Orbital Plane Crosses the Equator,from South to North (The Ascending Node), Measured Eastward

Not the Same As the Longitude of the Ascending Node RAAN Relative to Inertial Frame (Geocentric-Equatorial) Longitude of Ascending Node Relative to Rotating Earth

Ranges from 0 to 360

J

I

K

Ascending

Node

Equatorial

Plane


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Argument of Perigee ()The Orientation of the Orbit within the Orbital Plane

Angle Along Orbital Path Between the Ascending Node and the Perigee

Always measured Along the Orbital Path in Direction of SpacecraftMotion

Perigee Closest Approach to Earth Ranges from 0 to 360

J

I

K

Perigee


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True Anomaly at EpochThe Spacecrafts Location within an Orbit

Angle Along Orbital Path from Perigee to Spacecrafts Position

Always Measured Along Orbital Path in Direction of Spacecraft Motion

The Only Orbital Element Set Parameter That Varies with Time as the

Spacecraft Travels Around its Fixed Orbit, Assuming a Spherically-Symmetric Earth (A So-So Assumption)

R Perigee

V


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Summary of Orbital Elements

When e = 0 (circular orbit)0 360Angle from perigee to

the spacecrafts position

True anomaly

When i = 0 or 180(equatorial orbit) or e = 0(circular orbit)

0 360Angle from ascending

node to perigee

Argument of

perigee

Swivel, angle from

vernal equinox to

ascending node

Tilt, angle from unit

vector to specificangular momentum

vector

Shape

Size

Description

0 360

0 i 180

e = 0: Circle0 < e < 1: ellipse

Depends on the

Conic Section

Range of Values

When i = 0 or 180(equatorial orbit)

Right ascension

of the ascending

node

NeverInclinationi

NeverEccentricitye

NeverSemimajor Axisa

UndefinedNameElement

K

h


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Alternate Orbital Elements

A Circular Orbit? No Argument of Perigee No True Anomaly

An Equatorial Orbit? No RAAN

No Argument of Perigee

A Circular Equatorial Orbit? No RAAN No Argument of Perigee No True Anomaly

Angle from the principaldirection to the spacecrafts

position

Angle from the principaldirection to perigee

Angle from ascending node

to the spacecrafts position

Description

0 l 360

0 360

0 u 360

Range of Values

Use when there is no perigee andascending node (e = 0 and i = 0or 180)

True longitudel

Use when equatorial (i = 0 or180) because there is noascending node

Longitude ofperigee

Use when there is no perigee (e =

0)

Argument of

latitude

u

UndefinedNameElement

What Do We Do With:


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SBIRS High Scenario

SBIRS High is a Molniya Type Orbit Russian word for Zipper or Lightning Large Dwell Time over Northern Hemisphere Usually a 12-Hour Orbit with High Eccentricity (0.7)

and Perigee in Southern Hemisphere

Has Inclination of 63.4 (No Rotation of Perigee)

Covers High Latitudes and Polar Regions Very Well


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SBIRS Low Coverage Studies

SBIRS Low Constellation Showing Threat Object Coverage

(Sensor Footprints in Green, Sensor Acquisitions in Yellow)

SBIRS Low Constellation As Implemented In TESS

Coverage Almost Complete Utilizing 24 Satellites

Orbital Element Set Propagation Within TESS


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SBIRS DSP (GEO)

Geostationary Orbits (Fixed ECR) Above and Below-the-Horizon Viewing Ability

From www.stk.com


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In Summary

Excellent References Expensive: Understanding Space An Introduction to Astronautics, Jerry

Jon Sellers$66.00 at www.walmart.com

Cheap: Fundamentals of Astrodynamics, Roger R. Bate$9.00 at www.walmart.com

Introduction to Space Dynamics, William Tyrrell Thomson$9.00 at www.walmart.com Free: TRW Space Data, Neville J. Barter, editor

Free from TRW Space and Electronics Group

Excellent Web Site www.heavens-above.com

Iridium Flares, ISS, HST, etc. Excellent Software

Satellite Tool Kitfrom Analytical Graphics, Inc. (www.stk.com) Price: Free to Over $100,000

Training Available for Basic Orbital Mechanics
http://www.stk.com/http://www.walmart.com/http://www.walmart.com/http://www.walmart.com/http://www.heavens-above.com/http://www.stk.com/http://www.stk.com/http://www.heavens-above.com/http://www.walmart.com/http://www.walmart.com/http://www.walmart.com/http://www.stk.com/


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Supplemental Charts


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GBIs

IFICS

BMC3

GBR-P

IFICS

UEWR

Cobra Dane

IFICS

GBIs

IFICS

GBIs

IFICS

BMC3

GBIs

BMC3

SBIRS MCSAEGIS

Ground-Based MidcourseDefense Architecture (2004)


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From www.stk.com

GMD with SBIRS High and DSP


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SBIRS Waveband Utilization

SBIRS DSP, High, and LowUtilize Different SensorWavebands

Different Target Types are Visible

in Different Wavelengths Synergy Between Satellites Allow

Full Tracking of Threat Objectsfrom Initial Launch Through Mid-Course

Provides Extended Capability for

Strategic and Theater MissileDefense

SBIRS Low

LWIR (8-14 m) MWIR (3-8 m)

SWIR (1-3 m)

Visible (0.4-0.7 m)

30201510864321.510.80.60.4

Visible Near Infrar ed Middle Infrar ed Far Infr ar ed Extr eme Infrar ed

V B G Y O R

Upper

Stage

Boost

Phase

Low-

Altitude

Boost

Phase

PBV

Plumes

DSP/GEO

SBIRS High

MWIR (3-8 m)

SWIR (1-3 m) SWIR (1-3 m)

Mid-

Course

Tracking

PBVs


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Effects of Earths Oblatenesson Orbiting Spacecraft

Equatorial Bulge Causes Slight Shift in Direction

Gravity Pulls Spacecraft Modeled by Complex Mathematics Referred to asthe J2 Effect

Earth is 22 km Bigger (radius) at Equator

Causes Nodal Regression Rate (Movement of theRAAN, ) and a Perigee Rotation Rate ()

R

22 km

22 km

2JF

Nodal Regression RateNodal Regression Rate

Perigee Rotation RatePerigee Rotation Rate

.

.

Graphs from Understanding Space by Jerry Jon Sellers


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Sun Synchronous OrbitsIf Someone Gives You Lemons, Make Lemonade! (Part 1)

Despite the Complexities That the J2 Effect Cause, There are Advantages

Sun-Synchronous Orbits Take Advantage of the Rate of Change of the RAAN

Inclination is Set to Give Approximately a One-Degree Nodal Regression Eastward per day (Note that theEarth Moves 0.9863 Degrees per day in its Orbit Around the Sun (i.e., 360 /365 days)

Spacecrafts Orbital Plane Always Maintains Same Orientation to Sun Spacecraft Always Sees Same Sun Angle When It Passes Over a Particular Point on Earth Suns Shadows Cast by Objects on Earths Surface Will Not Change When Pictures are Taken Days or Weeks Apart Good for Remote Sensing, Reconnaissance, Weather, etc.

Inclination = 97.03

Earth movesaround the Sun at

1 /dayOrbital plane

rotates at ~1 /daydue to earths

oblateness

Orbital plane

Sun lineSun angle


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Molniya OrbitsIf Someone Gives You Lemons, Make Lemonade! (Part 2)

Another Advantage of the J2 Effect

Molniya Russian word for Zipperor Lightning

Large Dwell Time over Northern

Hemisphere Usually a 12-Hour Orbit with High

Eccentricity (0.7) and Perigee inSouthern Hemisphere

Has Inclination of 63.4 (No Rotation

of Perigee) Covers High Latitudes and Polar

Regions Very Well


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Geosynchronous OrbitNo Perigee Rotation

Orbits Every 24 Hours Inclination of 63.4 degrees No Perigee Rotation

orbital mechanics by viasbirs

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