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User avatar #121 - SuitUp (03/18/2013) [-]
Here you go:

First two lines is deriving the escape velocity from kinetic energy and gravitational field equations.

Lines 3 - 6 is working out the characteristics of the orbit of the satellite.
- 3rd: Orbit velocity
- 4th: Application of kepler's laws to work out the perigee radius (Closest distance during orbit. As opposed to apogee which is the furthest.)
- 5th: 'e' is the eccentricity of the orbit, how much it deviates from a perfect circle.
- 6th: theta is the angle between the point the satellite is launched from and the point on the planet that corresponds to the perigee point. This angle finishes characterising the orbit.

7th Line is just the drag force on it.
8th is standard formula for mach number = speed of object/speed of sound in the same medium.
9th Calculating the speed of sound from specific heat, gas constant and temperature. (Satellites usually aren't in absolute space so it isn't in a vacuum.)
10th line is the thrust that needs to be produced.
11th gives the momentum of the satellite.
Lastly is Newtons 2nd law, aka F=ma=dp/dt the rate of change of momentum.

SCIENCE!

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