To Orbit (Continued) and Spacecraft Systems Engineering

1. To Orbit (Continued) and Spacecraft Systems Engineering Scott Schoneman 13 November 03

2. Agenda • Some brief history - a clockwork universe? • The Basics • What is really going on in orbit - the popular myth of zero-G • Motion around a single body • Orbital elements • Ground tracks • Perturbations • J2 and gravity models • Drag • “Third bodies” • Orbit Propagation

3. Basic Orbit Equations • Circular Orbit Velocity: • Circular Orbit Period: • Escape Velocity:

4. Perturbations: Reality is More Complicated Than Two Body Motion

5. Orbit Perturbations • Non-spherical Earth gravity effects (i.e “J-2 Effects”) • Earth is an “Oblate Spheriod” Not a Sphere • Atmospheric Drag: Even in Space! • “Third” bodies • Other effects • Solar Radiation pressure • Relativistic Effects

6. (Regresses West) (Regresses East) J2 Effects - Plots • J2-orbit rotation rates are a function of: • semi-major axis • inclination • eccentricity

7. Applications of J2 Effects • Sun-synchronous Orbits • The regression of nodes matches the Sun’s longitude motion (360 deg/365 days = 0.9863 deg/day) • Keep passing over locations at same time of day, same lighting conditions • Useful for Earth observation • “Frozen Orbits” • At the right inclination, the Rotation of Apsides is zero • Used for Molniya high-eccentricity communications satellites

8. Third-Body Effects • Gravity from additional objects complicates matters greatly • No explicit solution exists like the ellipse does for the 2-body problem • Third body effects for Earth-orbiters are primarily due to the Sun and Moon • Affects GEOs more than LEOs • Points where the gravity and orbital motion “cancel” each other are called the Lagrange points • Sun-Earth L1 has been the destination for several Sun-science missions (ISEE-3 (1980s), SOHO, Genesis, others planned)

9. Lagrange Points Application • Genesis Mission: • NASA/JPL Mission to collect solar wind samples from outside Earth’s magnetosphere (http://genesismission.jpl.nasa.gov/) • Launched: 8 August 2001 • Returning: Sept 2004

10. spacecraft departing planet departing sun-centric velocity hyperbolic flyby (relative to planet) planet’s orbit velocity spacecraft incoming to planet incoming sun-centric velocity Third-Body Effects: Slingshot • A way of taking orbital energy from one body ( a planet ) and giving it to another ( a spacecraft ) • Used extensively for outer planet missions (Pioneer 10/11, Voyager, Galileo, Cassini) • Analogous to Hitting a Baseball: Same Speed, Different Direction

11. GTO orbit GEO orbit Hohmann Transfer • Hohmann transfer is the most efficient transfer (requires the least DV) between 2 orbit assuming: • Only 2 burns allowed • Circular initial and final orbits • Perform first burn to transfer to an elliptical orbit which just touches both circular orbits • Perform second burn to transfer to final circular GEO orbit Initial Circular Parking Orbit

12. Earth-Mars Transfer • A (nearly) Hohmann transfer to Mars Mars at Spacecraft Arrival Mars at Spacecraft Departure

13. Atmospheric Drag • Along with J2, dominant perturbation for LEO satellites • Can usually be completely neglected for anything higher than LEO • Primary effects: • Lowering semi-major axis • Decreasing eccentricity, if orbit is elliptical • In other words, apogee is decreased much more than perigee, though both are affected to some extent • For circular orbits, it’s an evenly-distributed spiral

14. Atmospheric Drag • Effects are calculated using the same equation used for aircraft: • To find acceleration, divide by m • m / CDA : “Ballistic Coefficient” • For circular orbits, rate of decay can be expressed simply as: • As with aircraft, determining CD to high accuracy can be tricky • Unlike aircraft, determining r is even trickier

15. Dragging Down the ISS

16. Applications of Drag • Aerobraking / aerocapture • Instead of using a rocket, dip into the atmosphere • Lower existing orbit: aerobraking • Brake into orbit: aerocapture • Aerobraking to control orbit first demonstrated with Magellan mission to Venus • Used extensively by Mars Global Surveyor • Of course, all landing missions to bodies with an atmosphere use drag to slow down from orbital speed (Shuttle, Apollo return to Earth, Mars/Venus landers)

17. Reentry Dynamics: Coming Back to Earth • Ballistic Reentry • Suborbital • Reentry Vehicles • Orbital • Mercury and Gemini • Skip Entry • Apollo • Gliding Entry • Shuttle

18. “Systems” Engineering • Looking at the “Big” Picture • Requirements: What Does the Satellite Need to Do? When? Where? How? • Juggling All The Pieces • Mission Design: Orbits, etc. • Instruments and Payloads • Electronics and Power • Communications • Mass • Attitude Control • Propulsion • Cost and Schedule

19. Mission Design • Low Earth Orbit (LEO) • Earth or Space Observation • International Space Station Support • Rendezvous and Servicing • Geosynchronous Orbit (GEO) • Communication Satellites • Weather Satellites • Earth and Space Observation • Lunar and Deep Space • Lunar • Inner and Outer Planetary • Sun Observing

20. Spacecraft Design Considerations • Instruments and Payloads • Optical Instruments • RF Transponders (Comm. Sats) • Experiments • Electronics and Power • Solar Panels and Batteries • Nuclear Power • Communications • Uplink/Downlink • Ground Station Locations • Frequencies and Transmitter Power

21. Spacecraft Design Considerations(Cont’d) • Mass Properties • Total Mass • Distribution of Mass (Moments of Inertia) • Attitude Control • Thrusters: Cold Gas and/or Chemical Propulsion • Gravity Gradient (Non-Spherical Earth Effect) • Spin Stablized • Magnetic Torquers • Propulsion • Orbit Maneuvering and/or Station Keeping • Chemical or ‘Exotic’ • Propellant Supply

22. Spacecraft Design Considerations(Cont’d) • Cost and Schedule • Development • Launch • Mission Lifetime • 1 Month, 1 Year, 1 Decade?

23. Spacecraft Integration and Test

24. GPS Satellites • Constellation of 24 satellites in 12,000 nm orbits • First GPS satellite launched in 1978 • Full constellation achieved in 1994. • 10 Year Liftetime • Replacements are constantly being built and launched into orbit. • Weight: ~2,000 pounds • Size: ~17 feet across with the solar panels extended. • Transmitter power is only 50 watts or less.

25. References • Orbit simulation tools: http://www.colorado.edu/physics/2000/applets/satellites.html http://home.wanadoo.nl/dms/video/orbit.html Current satellites in their orbits: NASA “JTRACK”: http://liftoff.msfc.nasa.gov/RealTime/Jtrack/3d/JTrack3D.html “Heavens Above” web page: http://www.heavens-above.com/ • Satellite Tool Kit Astronautics Primer: http://www.stk.com/resources/help/help/stk43/primer/primer.htm • Other orbital mechanics primers: http://aerospacescholars.jsc.nasa.gov/HAS/Cirr/SS/L2/orb1.htm • http://www.heavens-above.com/ • History of Orbital Mechanics: • http://es.rice.edu/ES/humsoc/Galileo/Things/ptolemaic_system.html • http://es.rice.edu/ES/humsoc/Galileo/Things/copernican_system.html • http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Kepler.html • http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brahe.html • http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Halley.html • http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Newton.html

26. References • Third-Body Effects • Interplanetary Superhighway Description: http://www.cds.caltech.edu/~shane/superhighway/description.html • 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 trajectory • Genesis mission trajectory: http://cfa-www.harvard.edu/~hrs/ay45/2001/2and3BodyOrbits.html • Texts • Spacecraft Mission Design, Brown, Charles, (AIAA): a good, compact introduction, with lots of handy formula pages • Space Mission Analysis & Design, Larson & Wertz : a good techincal introduction with lots of practical formulas, charts, and tables • Space Vehicle Design, Griffin and French, (AIAA): Good overview of all facets of space vehicles • Spaceflight Dynamics, Wiesel, W., (McGraw-Hill): Good, readable coverage of spacecraft design • Chobotov, Vladimir: Orbital Mechanics (2nd edition) (AIAA series): Classic, but dry and detailed text on many orbital mechanics topics