CBSE Class 11-science Answered
Derive an expression for total energy of a satellite orbiting the earth.
Asked by Abhishika John | 01 Oct, 2013, 04:16: PM
Expert Answer
he 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
Kinetic energy in orbit = ½ mv2 = + ½GMm/r
All satellites have to be given a tangential velocity (v) to maintain their orbit position and this process is called orbit injection.
Total energy of satellite in orbit = -GMm/2r
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]
Answered by | 02 Oct, 2013, 10:49: PM
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