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What is the minimum energy required to l...

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

A

`(5Gm M)/(6R)`

B

`(2Gm M)/(3R)`

C

`(Gm M)/(2R)`

D

`(Gm M)/(3R)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `K` be the `KE` given to the satellite on the surface if earth to take it to the desired location. Following the law of conservation of total energy, we have
`-(G mM)/(R ) + K = - (G mM)/((2R +R)) + (1)/(2)m((GM)/(3R))`
`= - (GM m)/(3R) + (GM m)/(6R) = - (GM m)/(6R)`
or `K = (GM m)/(R ) - (GM m)/(6R) = (5GM m)/(6R)`
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