To Orbit 2

To Orbit (Continued) and Spacecraft Systems Engineering: 

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

Agenda: 

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

Basic Orbit Equations: 

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

Slide4: 

Perturbations: Reality is More Complicated Than Two Body Motion

Orbit Perturbations: 

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

J2 Effects - Plots: 

J2 Effects - Plots J2-orbit rotation rates are a function of: semi-major axis inclination eccentricity

Applications of J2 Effects: 

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

Third-Body Effects: 

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)

Lagrange Points Application: 

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

Third-Body Effects: Slingshot: 

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

Hohmann Transfer: 

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

Earth-Mars Transfer: 

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

Atmospheric Drag: 

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

Atmospheric Drag: 

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

Dragging Down the ISS: 

Dragging Down the ISS

Applications of Drag: 

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)

Reentry Dynamics: Coming Back to Earth: 

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

“Systems” Engineering: 

“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

Mission Design: 

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

Spacecraft Design Considerations: 

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

Spacecraft Design Considerations(Cont’d): 

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

Spacecraft Design Considerations(Cont’d): 

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

Spacecraft Integration and Test: 

Spacecraft Integration and Test

GPS Satellites: 

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.

References: 

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

References: 

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