Satellite Physics Newton, orbits and DIY Spaceflight January 2009 Morten Jagd Christensen
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Agenda Law 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
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Newtons laws of motion
dV F m a m dt GMm F r 2 r d 2 r (t ) GM r (t ) 2 2 dt r (t )
r
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Differential equations (2D) d GM v x (t ) x(t ) 3 dt r (t ) d GM v y (t ) y (t ) 3 dt r (t ) d x(t ) v x (t ) dt d y (t ) v y (t ) dt r (t )
x ( t ), y ( t )
r (t )
x 2 (t )
F
x(t), y(t)
y
x
y 2 (t ) 13-05-2009
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Solution: Ellipse Can be done in Excel
v x1
vx 0
ax0
x1
x0 v x 0
t t
etc.
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Runge-Kutta method Adaptive step size Gnuplot
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From low Earth orbit to GEO
r b
a v2
GM
2 r
1 a
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Rocket Thrust m
V T
F
F
mve ( pe
T
m F
V
p0 ) Ae
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Burn times Centaur rocket GTO Delta V for orbit insertion is ~ 2.4 km/s Engines deliver ~147kN Mass: 15000kg prop + 6000kg sat Burn time: ~343s
GTO to GEO Delta V for circular orbit is ~1.5 km/s Mass: 6000kg Thrust data for I4 unavailable
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Re-clocking I4 satellites I4 F2 moves from 53W Distance travelled: L
25E 78 2 R 460
Time: 30days*86.400s/day Velocity ~23m/s (80km/h) New orbit is 650m lower
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Re-clocking - finally
78
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Three-body problem
F (r )
res
M e ms G res 3 | res |
M e ms rms 3 | rms |
rms
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Chaotic orbits
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Chaotic orbits?
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Yes really! y0 = 0.4 y0 = 0.4 + Mass
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Non sperical mass distribution
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Non-spherical gravitational field U (r , )
GM 1 r
Jn n 2
Earth Earthdata data -6-6 JJ2 ==1082.63 10 2 1082.63 10 -6-6 JJ3 ==-2.51 10 -2.51 10 3
R r
n
Pn sin
P0 ( x) 1 P1 ( x) P2 ( x)
-6-6 JJ4 ==-1.60 10 -1.60 10 4
P3 ( x)
-6-6 JJ5 ==-0.15 10 -0.15 10 5
...
x 1 3x 1 2 1 3 5 x 3x 2
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And it gets worse! Relativistic spacetime effects Earth geometry corrections Tides Plate techtonics Pole movements Internal mass shifts
Pico second time resolution
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Satellite tracking - Pioneer 10 First probe to visit outer planets Tracking data from 1972 to 2002 Anomalous acceleration 8x10-8G
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Space travel with Orbiter
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Orbiter features Full solar system dynamics simulation Including non spherical gravitational fields Sun, all planets, moons, and other orbiting objects Timewarp for interplanetary cruises Broad range of spacecraft
Realism settings Atmospheric haze, clouds Aerodynamics in earths atmosphere Rocket engine exhaust
Launch from Earth, land on moon base Realistic on board flight software Star constellation overlay 13-05-2009
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Orbiter Demo
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References J.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 Rockets http://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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