Question

Derive expression for total energy of orbiting satellite

Answer 1

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

We know that,

The Centripetal force on a satellite of mass 'm' moving at velocity ' v ' in an orbit of radius r is

F = mv^2/r  

But this is equal to the gravitational force ' F ' between the planet mass of M and the satellite. So, we get,

F =GMm/r^2 and

mv^2= GMm/r

But,

kinetic energy = ½mv^2

So,

Satellite's kinetic energy = ½ GMm/r

Orbit's kinetic energy = ½ mv^2 = + ½GMm/r

All satellites have to be given a tangential velocity ' v ' to maintain their orbit position by the process that is called orbit injection.  

 

Total energy of satellite in orbit = -GMm/2r

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Answer 2

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