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A satellite of mass m is in circular orb...

A satellite of mass m is in circular orbit of radius `3R_E` about earth (mass of earth `M_E` , radius of earth `R_E`).
How much additional energy is required to transfer the satellite to an orbit of radius `9R_E` ?

A

`(GM_Em)/(3R_E)`

B

`(GM_Em)/(18 R_E)`

C

`(3GM _Em)/(2R_E)`

D

`(GM_Em)/(9R_E)`

Text Solution

Verified by Experts

The correct Answer is:
D
Total energy of the satellite in orbit of radius r is given by,
`E=-(GMm)/(2r)`
Therefore, `E_1=-(GM_Em)/(2xx3R_E) and E_2=-(GM_Em)/(2xx9R_E)`
`therefore` additional energy required,
`E_2-E_1=-(GM_Em)/(6R_E)(1/3-1)=(GM_Em)/(6R_E)xx2/3`
`=(GM_Em)/(9R_E)`
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