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

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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 Suns
  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 Earths magnetosphere
  (http//genesismission.jpl.nasa.gov/)
• Launched 8 August 2001
• 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
  )
• Used extensively for outer planet missions
  (Pioneer 10/11, Voyager, Galileo, Cassini)
• Analogous to Hitting a Baseball Same Speed,
  Different Direction

11
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
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Earth-Mars Transfer

• A (nearly) Hohmann transfer to Mars

Mars at Spacecraft Arrival
Mars at Spacecraft Departure
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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, its an evenly-distributed
  spiral

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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
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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)

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Reentry Dynamics Coming Back to Earth

• Ballistic Reentry
• Suborbital
• Reentry Vehicles
• Orbital
• Mercury and Gemini
• Skip Entry
• Apollo
• Gliding Entry
• Shuttle

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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

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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

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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

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Spacecraft Design Considerations(Contd)

• 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

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Spacecraft Design Considerations(Contd)

• Cost and Schedule
• Development
• Launch
• Mission Lifetime
• 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
• 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.

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References

• Orbit simulation tools http//www.colorado.edu/p
  hysics/2000/applets/satellites.html
• http//home.wanadoo.nl/dms/video/orbit.html
• Current satellites in their orbits
• NASA JTRACK http//liftoff.msfc.nasa.gov/Real
  Time/Jtrack/3d/JTrack3D.html
• Heavens Above web page http//www.heavens-ab
  ove.com/
• Satellite Tool Kit Astronautics Primer
  http//www.stk.com/resources/help/help/stk43/prime
  r/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/ptolem
  aic_system.html
• http//es.rice.edu/ES/humsoc/Galileo/Things/copern
  ican_system.html
• http//www-gap.dcs.st-and.ac.uk/history/Mathemati
  cians/Kepler.html
• http//www-gap.dcs.st-and.ac.uk/history/Mathemati
  cians/Brahe.html
• http//www-gap.dcs.st-and.ac.uk/history/Mathemati
  cians/Halley.html
• http//www-gap.dcs.st-and.ac.uk/history/Mathemati
  cians/Newton.html

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References

• Third-Body Effects
• Interplanetary Superhighway Description
  http//www.cds.caltech.edu/shane/superhighway/des
  cription.html
• http//www.wired.com/wired/archive/7.12/farquhar_p
  r.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