Satellite Physics
24
Satellite Physics Newton, orbits and DIY Spaceflight January 2009 Morten Jagd Christensen
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A talk on Satellite orbits and DIY space travel with Orbiter space flight simulator
Transcript of Satellite Physics
Satellite PhysicsNewton, orbits and DIY Spaceflight
January 2009
Morten Jagd Christensen
213-05-2009
Rocket Science
AgendaLaw of gravitation and of motion
Geometry and dynamics of circular orbits
Elliptical orbits
Geosynchronous orbits
Launching a sattelite Hohmann transfer
Re-clocking
Non-spherical mass distribution
Deep space tracking and further complications
Orbit adjustments
DIY space travel with Orbiter
313-05-2009
Rocket Science
Newtons laws of motion
)()(
)(22
2
2
trtr
GM
dt
trd
rr
GMmF
dt
VdmamF r
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Differential equations (2D)
)(2)(2)(
)(),()(
)()(
)()(
)()(
)(
)()(
)(
3
3
tytxtr
tytxtr
tvtydt
d
tvtxdt
d
tytr
GMtv
dt
d
txtr
GMtv
dt
d
y
x
y
x
x
yF x(t), y(t)
vx(t), vy(t)
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Solution: EllipseCan be done in Excel
.001
001
etc
tvxx
tavv
x
xxx
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Runge-Kutta method
Adaptive step size
Gnuplot
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From low Earth orbit to GEO
a b
r
arGMv
122
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Rocket Thrust
eee AppvmF )( 0
VF
mTF
T
Vm
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Burn times
Centaur rocket GTODelta V for orbit insertion is ~ 2.4 km/sEngines deliver ~147kNMass: 15000kg prop + 6000kg satBurn time: ~343s
GTO to GEODelta V for circular orbit is ~1.5 km/sMass: 6000kgThrust data for I4 unavailable
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Re-clocking I4 satellitesI4 F2 moves from 53W 25E
Distance travelled:
Time: 30days*86.400s/day
Velocity ~23m/s (80km/h)
New orbit is 650m lower
RL 2460
78
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Re-clocking - finally
78
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Three-body problem
rmsres
msms
sees
es
se rr
mMr
r
mMGrF
33 ||||)(
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Chaotic orbits
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Chaotic orbits?
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Yes really!
y0 = 0.4y0 = 0.4 + Mass
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Non sperical mass distribution
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Non-spherical gravitational field
2
sin1),(n
n
n
n Pr
RJ
r
GMrU
Earth data
J2 = 1082.63 10-6
J3 = -2.51 10-6
J4 = -1.60 10-6
J5 = -0.15 10-6
Earth data
J2 = 1082.63 10-6
J3 = -2.51 10-6
J4 = -1.60 10-6
J5 = -0.15 10-6
...
352
1)(
132
1)(
)(
1)(
33
2
1
0
xxxP
xxP
xxP
xP
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And it gets worse!Relativistic spacetime effects
Earth geometry correctionsTidesPlate techtonicsPole movementsInternal mass shifts
Pico second time resolution
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Satellite tracking - Pioneer 10First probe to visit outer planets
Tracking data from1972 to 2002
Anomalous acceleration8x10-8G
2013-05-2009
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Space travel with Orbiter
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Orbiter featuresFull solar system dynamics simulation
Including non spherical gravitational fieldsSun, all planets, moons, and other orbiting objectsTimewarp for interplanetary cruisesBroad range of spacecraft
Realism settingsAtmospheric haze, cloudsAerodynamics in earths atmosphereRocket engine exhaust
Launch from Earth, land on moon base
Realistic on board flight software
Star constellation overlay
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Orbiter Demo
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ReferencesJ.D. Anderson, et.al. Study of the anomalous acceleration of
Pioneer 10 and 11
A. Celetti et. al. The Celestial Waltz
Inmarsat
H.Kartunen, et. al. Fundamental Astronomy
NASA Basics of Space Flight , http://www.jpl.nasa.gov/basics
NASA Beginner s Guide to Rocketshttp://exploration.grc.nasa.gov/education/rocket/bgmr.html
M.Schweiger Orbiter - Space Flight Simulator , http://www.orbitersim.com
W.H.Press, et. al. Numerical Recipes in C , http://www.nr.com
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