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

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

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Basic Orbit Equations Circular Orbit Velocity: Circular Orbit Velocity: Circular Orbit Period: Circular Orbit Period: Escape Velocity: Escape Velocity:

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Perturbations: Reality is More Complicated Than Two Body Motion

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

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

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

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

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

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

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

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

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

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Atmospheric 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 m To find acceleration, divide by m m / C D A : “Ballistic Coefficient” m / C D 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 C D to high accuracy can be tricky As with aircraft, determining C D to high accuracy can be tricky Unlike aircraft, determining is even trickier Unlike aircraft, determining is even trickier

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Dragging Down the ISS

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Applications of Drag Aerobraking / aerocapture Aerobraking / aerocapture Instead of using a rocket, dip into the atmosphere Instead of using a rocket, dip into the atmosphere Lower existing orbit: aerobraking Lower existing orbit: aerobraking Brake into orbit: aerocapture Brake into orbit: aerocapture Aerobraking to control orbit first demonstrated with Magellan mission to Venus Aerobraking to control orbit first demonstrated with Magellan mission to Venus Used extensively by Mars Global Surveyor 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) 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)

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

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

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

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

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

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

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Spacecraft Integration and Test

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

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References Orbit simulation tools: http://www.colorado.edu/physics/2000/applets/satellites.html Orbit simulation tools: http://www.colorado.edu/physics/2000/applets/satellites.html http://home.wanadoo.nl/dms/video/orbit.html http://home.wanadoo.nl/dms/video/orbit.html Current satellites in their orbits: Current satellites in their orbits: NASA “JTRACK”: http://liftoff.msfc.nasa.gov/RealTime/Jtrack/3d/JTrack3D.html 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 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 Other orbital mechanics primers: http://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.html http://es.rice.edu/ES/humsoc/Galileo/Things/ptolemaic_system.html http://es.rice.edu/ES/humsoc/Galileo/Things/copernican_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/Kepler.html http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brahe.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/Halley.html http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Newton.html http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Newton.html

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References Third-Body Effects Third-Body Effects Interplanetary Superhighway Description: http://www.cds.caltech.edu/~shane/superhighway/description.html 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 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 Genesis mission trajectory: http://cfa- www.harvard.edu/~hrs/ay45/2001/2and3BodyOrbits.html Texts Texts Spacecraft Mission Design, Brown, Charles, (AIAA): a good, compact introduction, with lots of handy formula pages 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 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 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 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 Chobotov, Vladimir: Orbital Mechanics (2nd edition) (AIAA series): Classic, but dry and detailed text on many orbital mechanics topics

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