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Question

Energy of a satellite in circular orbit is E0. The energy required to move the satellite to a circular orbit of 3 times the radius of the initial orbit is

A
23E0
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B
2E0
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C
E03
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D
32E0
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Solution

The correct option is A 23E0
For a satellite of mass m revolving around a planet of mass M in a circular orbit of radius r. So the total mechanical energy of a satellite is given by

E=GMm2r

Total mechanical energy at radius r will be

E1=GMm2r=E0

Total mechanical energy at radius 3r is

E2=GMm2(3r)=E03

Energy required is given by

E2E1=E03E0=2E03

Therefore, option (a) is correct.
Key Concept : The work done energy required to shift a satellite from one configuration to the other is equal to the difference between the total mechanical energy of the two configurations.

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