Satellite Physics

Satellite Physics Newton, orbits and DIY Spaceflight January 2009 Morten Jagd Christensen

Rocket Science

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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Rocket Science vx(t), vy(t)

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 Science

Rocket Thrust m

V T

F

F

mve ( pe

T

m F

V

p0 ) Ae

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Rocket Science

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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Rocket Science

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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