Question

how to calculate the kinetic energy of a satellite with altitude?

Answer 1

Answer:

The kinetic energy of an object in orbit can easily be found from the following equations:

Centripetal force on a satellite of mass m moving at velocity v in an orbit of radius r = mv2/r

But this is equal to the gravitational force (F) between the planet (mass M) and the satellite:

F =GMm/r2 and so mv2 = GMm/r

But kinetic energy = ½mv2 and so:

kinetic energy of the satellite = ½ GMm/r

All satellites have to be given a tangential velocity (v) to maintain their orbit position and this process is called orbit injection.

However the total energy INPUT required to put a satellite into an orbit of radius r around a planet of mass M and radius R is therefore the sum of the gravitational potential energy (GMm[1/R-1/r]) and the kinetic energy of the satellite ( ½GMm/r).

Energy of launch = GMm[1/R – 1/2r]

Answer 2

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