To Orbit (Continued) To Orbit (Continued) and Spacecraft Systems and Spacecraft Systems

EngineeringEngineering

Scott SchonemanScott Schoneman

13 November 0313 November 03

AgendaAgenda Some brief history - a clockwork universe?Some brief history - a clockwork universe? The BasicsThe Basics

What is really going on in orbit - the popular myth of zero-GWhat is really going on in orbit - the popular myth of zero-G Motion around a single bodyMotion around a single body Orbital elementsOrbital elements Ground tracksGround tracks

PerturbationsPerturbations J2 and gravity modelsJ2 and gravity models DragDrag ““Third bodies”Third bodies”

Orbit PropagationOrbit Propagation

Basic Orbit EquationsBasic Orbit Equations

Circular Orbit Velocity:Circular Orbit Velocity:

Circular Orbit Period:Circular Orbit Period:

Escape Velocity:Escape Velocity:

rvc

rvc

rve

2

3rt

Perturbations: Reality is More Complicated Perturbations: Reality is More Complicated Than Two Body MotionThan Two Body Motion

Orbit PerturbationsOrbit Perturbations

Non-spherical Earth gravity effects (i.e Non-spherical Earth gravity effects (i.e “J-2 Effects”)“J-2 Effects”)Earth is an “Oblate Spheriod” Not a SphereEarth is an “Oblate Spheriod” Not a Sphere

Atmospheric Drag: Even in Space!Atmospheric Drag: Even in Space!““Third” bodiesThird” bodiesOther effectsOther effects

Solar Radiation pressureSolar Radiation pressureRelativistic EffectsRelativistic Effects

J2 Effects - PlotsJ2 Effects - Plots J2-orbit rotation rates are a function of:J2-orbit rotation rates are a function of:

semi-major axissemi-major axis inclinationinclinationeccentricityeccentricity

(Regresses West)(Regresses East)

Applications of J2 EffectsApplications of J2 Effects

Sun-synchronous OrbitsSun-synchronous OrbitsThe regression of nodes matches the Sun’s longitude The regression of nodes matches the Sun’s longitude

motion (360 deg/365 days = 0.9863 deg/day)motion (360 deg/365 days = 0.9863 deg/day)Keep passing over locations at same time of day, same Keep passing over locations at same time of day, same

lighting conditionslighting conditionsUseful for Earth observationUseful for Earth observation

““Frozen Orbits”Frozen Orbits”At the right inclination, the Rotation of Apsides is zeroAt the right inclination, the Rotation of Apsides is zeroUsed for Molniya high-eccentricity communications Used for Molniya high-eccentricity communications

satellitessatellites

Third-Body EffectsThird-Body EffectsGravity from additional objects complicates matters greatlyGravity from additional objects complicates matters greatly

No explicit solution exists like the ellipse does for the 2-body problemNo explicit solution exists like the ellipse does for the 2-body problemThird body effects for Earth-orbiters are primarily due to the Sun and MoonThird body effects for Earth-orbiters are primarily due to the Sun and Moon

Affects GEOs more than LEOsAffects GEOs more than LEOsPoints where the gravity and orbital motion “cancel” each other are called the Points where the gravity and orbital motion “cancel” each other are called the

Lagrange pointsLagrange pointsSun-Earth L1 has been the destination for several Sun-science missions Sun-Earth L1 has been the destination for several Sun-science missions

(ISEE-3 (1980s), SOHO, Genesis, others planned)(ISEE-3 (1980s), SOHO, Genesis, others planned)

Lagrange Points ApplicationLagrange Points ApplicationGenesis Mission:Genesis Mission:

NASA/JPL Mission to collect solar wind samples from outside NASA/JPL Mission to collect solar wind samples from outside Earth’s magnetosphere (Earth’s magnetosphere (http://http://genesismission.jpl.nasa.govgenesismission.jpl.nasa.gov//))

Launched: 8 August 2001Launched: 8 August 2001Returning: Sept 2004Returning: Sept 2004

Third-Body Effects: SlingshotThird-Body Effects: SlingshotA way of taking orbital energy from one body ( a planet ) and giving it to A way of taking orbital energy from one body ( a planet ) and giving it to

another ( a spacecraft )another ( a spacecraft )Used extensively for outer planet missions (Pioneer 10/11, Voyager, Used extensively for outer planet missions (Pioneer 10/11, Voyager,

Galileo, Cassini)Galileo, Cassini)Analogous to Hitting a Baseball: Same Speed, Different DirectionAnalogous to Hitting a Baseball: Same Speed, Different Direction

planet’s orbit velocity

spacecraft incomingto planet

hyperbolic flyby(relative to planet)

spacecraft departing planet

departing sun-centric velocity

incoming sun-centric velocity

Hohmann TransferHohmann Transfer

Hohmann transfer is the most efficient Hohmann transfer is the most efficient transfer (requires the least transfer (requires the least V) between V) between 2 orbit assuming:2 orbit assuming: Only 2 burns allowedOnly 2 burns allowed Circular initial and final orbitsCircular initial and final orbits

Perform first burn to transferPerform first burn to transfer

to an elliptical orbit which just touchesto an elliptical orbit which just touches

both circular orbitsboth circular orbits

Perform second burn to transferPerform second burn to transfer

to final circular GEO orbitto final circular GEO orbit

GEO orbit

GTO orbit

Initial CircularParking

Orbit

Earth-Mars TransferEarth-Mars Transfer

Mars at Spacecraft Arrival

Mars at Spacecraft Departure

• A (nearly) Hohmann transfer to Mars

Atmospheric DragAtmospheric Drag

Along with J2, dominant perturbation for LEO satellitesAlong with J2, dominant perturbation for LEO satellitesCan usually be completely neglected for anything higher Can usually be completely neglected for anything higher

than LEOthan LEOPrimary effects:Primary effects:

Lowering semi-major axisLowering semi-major axisDecreasing eccentricity, if orbit is ellipticalDecreasing eccentricity, if orbit is elliptical

In other words, apogee is decreased much more than In other words, apogee is decreased much more than perigee, though both are affected to some extentperigee, though both are affected to some extent

For circular orbits, it’s an evenly-distributed spiralFor circular orbits, it’s an evenly-distributed spiral

Atmospheric DragAtmospheric Drag Effects are calculated using the same equation used for aircraft:Effects are calculated using the same equation used for aircraft:

To find acceleration, divide by mTo find acceleration, divide by m m / Cm / CDDA : “Ballistic Coefficient”A : “Ballistic Coefficient”

For circular orbits, rate of decay can be expressed simply as:For circular orbits, rate of decay can be expressed simply as:

As with aircraft, determining CAs with aircraft, determining CDD to high accuracy can be tricky to high accuracy can be tricky Unlike aircraft, determining Unlike aircraft, determining is even trickier is even trickier

ACVF D2

2

1

m

ACaa DREV

22

Dragging Down the ISSDragging Down the ISS

Applications of DragApplications of DragAerobraking / aerocaptureAerobraking / aerocapture

Instead of using a rocket, dip into the Instead of using a rocket, dip into the atmosphereatmosphereLower existing orbit: aerobrakingLower existing orbit: aerobrakingBrake into orbit: aerocaptureBrake into orbit: aerocapture

Aerobraking to control orbit first Aerobraking to control orbit first demonstrated with Magellan mission to demonstrated with Magellan mission to VenusVenus

Used extensively by Mars Global Used extensively by Mars Global SurveyorSurveyor

Of course, all landing missions to bodies Of course, all landing missions to bodies with an atmosphere use drag to slow down with an atmosphere use drag to slow down from orbital speed (Shuttle, Apollo return to from orbital speed (Shuttle, Apollo return to Earth, Mars/Venus landers)Earth, Mars/Venus landers)

Reentry Dynamics: Reentry Dynamics: Coming Back to EarthComing Back to Earth

Ballistic ReentryBallistic Reentry SuborbitalSuborbital

Reentry VehiclesReentry Vehicles

OrbitalOrbital Mercury and GeminiMercury and Gemini

Skip EntrySkip Entry ApolloApollo

Gliding EntryGliding Entry ShuttleShuttle

““Systems” EngineeringSystems” Engineering Looking at the “Big” PictureLooking at the “Big” Picture Requirements: What Does the Satellite Need to Do? Requirements: What Does the Satellite Need to Do?

When? Where? How?When? Where? How? Juggling All The PiecesJuggling All The Pieces

Mission Design: Orbits, etc.Mission Design: Orbits, etc. Instruments and PayloadsInstruments and Payloads Electronics and PowerElectronics and Power CommunicationsCommunications MassMass Attitude ControlAttitude Control PropulsionPropulsion Cost and ScheduleCost and Schedule

Mission DesignMission Design Low Earth Orbit (LEO)Low Earth Orbit (LEO)

Earth or Space ObservationEarth or Space Observation International Space Station SupportInternational Space Station Support Rendezvous and ServicingRendezvous and Servicing

Geosynchronous Orbit (GEO)Geosynchronous Orbit (GEO) Communication SatellitesCommunication Satellites Weather SatellitesWeather Satellites Earth and Space ObservationEarth and Space Observation

Lunar and Deep SpaceLunar and Deep Space LunarLunar Inner and Outer PlanetaryInner and Outer Planetary Sun ObservingSun Observing

Spacecraft Design ConsiderationsSpacecraft Design Considerations

Instruments and PayloadsInstruments and Payloads Optical InstrumentsOptical Instruments RF Transponders (Comm. Sats)RF Transponders (Comm. Sats) ExperimentsExperiments

Electronics and PowerElectronics and Power Solar Panels and BatteriesSolar Panels and Batteries Nuclear PowerNuclear Power

CommunicationsCommunications Uplink/DownlinkUplink/Downlink Ground Station LocationsGround Station Locations Frequencies and Transmitter PowerFrequencies and Transmitter Power

Spacecraft Design ConsiderationsSpacecraft Design Considerations(Cont’d)(Cont’d)

Mass PropertiesMass Properties Total MassTotal Mass Distribution of Mass (Moments of Inertia)Distribution of Mass (Moments of Inertia)

Attitude ControlAttitude Control Thrusters: Cold Gas and/or Chemical PropulsionThrusters: Cold Gas and/or Chemical Propulsion Gravity Gradient (Non-Spherical Earth Effect)Gravity Gradient (Non-Spherical Earth Effect) Spin StablizedSpin Stablized Magnetic TorquersMagnetic Torquers

PropulsionPropulsion Orbit Maneuvering and/or Station KeepingOrbit Maneuvering and/or Station Keeping Chemical or ‘Exotic’Chemical or ‘Exotic’ Propellant SupplyPropellant Supply

Spacecraft Design ConsiderationsSpacecraft Design Considerations(Cont’d)(Cont’d)

Cost and ScheduleCost and ScheduleDevelopmentDevelopmentLaunchLaunchMission LifetimeMission Lifetime

1 Month, 1 Year, 1 Decade?1 Month, 1 Year, 1 Decade?

Spacecraft Integration and TestSpacecraft Integration and Test

GPS SatellitesGPS Satellites

Constellation of 24 satellites in Constellation of 24 satellites in 12,000 nm orbits 12,000 nm orbits First GPS satellite launched in 1978First GPS satellite launched in 1978 Full constellation achieved in 1994. Full constellation achieved in 1994.

10 Year Liftetime 10 Year Liftetime Replacements are constantly being Replacements are constantly being

built and launched into orbit. built and launched into orbit.

Weight: ~2,000 pounds Weight: ~2,000 pounds Size: ~17 feet across with the Size: ~17 feet across with the

solar panels extended. solar panels extended. Transmitter power is only 50 Transmitter power is only 50

watts or less. watts or less.

ReferencesReferences Orbit simulation tools: http://www.colorado.edu/physics/2000/applets/satellites.htmlOrbit simulation tools: http://www.colorado.edu/physics/2000/applets/satellites.html

http://home.wanadoo.nl/dms/video/orbit.htmlhttp://home.wanadoo.nl/dms/video/orbit.html

Current satellites in their orbits: Current satellites in their orbits:

NASA “JTRACK”: NASA “JTRACK”: http://liftoff.msfc.nasa.gov/RealTime/Jtrack/3d/JTrack3D.htmlhttp://liftoff.msfc.nasa.gov/RealTime/Jtrack/3d/JTrack3D.html

““Heavens Above” web page: http://www.heavens-above.com/Heavens Above” web page: http://www.heavens-above.com/ Satellite Tool Kit Astronautics Primer: Satellite Tool Kit Astronautics Primer:

http://www.stk.com/resources/help/help/stk43/primer/primer.htmhttp://www.stk.com/resources/help/help/stk43/primer/primer.htm Other orbital mechanics primers: Other orbital mechanics primers:

http://aerospacescholars.jsc.nasa.gov/HAS/Cirr/SS/L2/orb1.htmhttp://aerospacescholars.jsc.nasa.gov/HAS/Cirr/SS/L2/orb1.htm http://www.heavens-above.com/http://www.heavens-above.com/ History of Orbital Mechanics:History of Orbital Mechanics:

http://es.rice.edu/ES/humsoc/Galileo/Things/ptolemaic_system.htmlhttp://es.rice.edu/ES/humsoc/Galileo/Things/ptolemaic_system.html http://es.rice.edu/ES/humsoc/Galileo/Things/copernican_system.htmlhttp://es.rice.edu/ES/humsoc/Galileo/Things/copernican_system.html http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Kepler.htmlhttp://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Kepler.html http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brahe.htmlhttp://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brahe.html http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Halley.htmlhttp://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Halley.html http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Newton.htmlhttp://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Newton.html

ReferencesReferences Third-Body EffectsThird-Body Effects

Interplanetary Superhighway Description: Interplanetary Superhighway Description: http://www.cds.caltech.edu/~shane/superhighway/description.htmlhttp://www.cds.caltech.edu/~shane/superhighway/description.html

http://www.wired.com/wired/archive/7.12/farquhar_pr.html "The Art of Falling" - http://www.wired.com/wired/archive/7.12/farquhar_pr.html "The Art of Falling" - about Robert Farquhar, the ISEE-3/ICE trajectory, the NEAR trajectoryabout Robert Farquhar, the ISEE-3/ICE trajectory, the NEAR trajectory

Genesis mission trajectory: Genesis mission trajectory: http://cfa-www.harvard.edu/~hrs/ay45/2001/2and3BodyOrbits.htmlhttp://cfa-www.harvard.edu/~hrs/ay45/2001/2and3BodyOrbits.html

TextsTexts Spacecraft Mission Design, Brown, Charles, (AIAA): a good, compact Spacecraft Mission Design, Brown, Charles, (AIAA): a good, compact

introduction, with lots of handy formula pagesintroduction, with lots of handy formula pages Space Mission Analysis & Design, Larson & Wertz : a good techincal Space Mission Analysis & Design, Larson & Wertz : a good techincal

introduction with lots of practical formulas, charts, and tables introduction with lots of practical formulas, charts, and tables Space Vehicle Design, Griffin and French, (AIAA): Good overview of all facets of Space Vehicle Design, Griffin and French, (AIAA): Good overview of all facets of

space vehiclesspace vehicles Spaceflight Dynamics, Wiesel, W., (McGraw-Hill): Good, readable coverage of Spaceflight Dynamics, Wiesel, W., (McGraw-Hill): Good, readable coverage of

spacecraft designspacecraft design Chobotov, Vladimir: Orbital Mechanics (2nd edition) (AIAA series): Classic, but Chobotov, Vladimir: Orbital Mechanics (2nd edition) (AIAA series): Classic, but

dry and detailed text on many orbital mechanics topicsdry and detailed text on many orbital mechanics topics