The energy required to shift a satellite from orbital radius r to orbital radius 2r is E. What energy will be required to shift the satellite from orbital radius 2r to orbital radius 3r?

Options

A. E
B. `(E )/(2)`
C. `(E )/(4)`
D. `(E )/(3)`.

Answer

D

Explanation

`E=(-GMm)/(2r)-((-GMm)/(2))=(GMm)/(r )[1-(1)/(2)]`
`E=(GMm)/(2r)`
Also `E.=(-GMm)/(3r)-((-GMm)/(2r))=(GMm)/(r )[(1)/(2)-(1)/(3)]`
`E.=(GMm)/(6r)`
Thus `E.=(E )/(3)`
So the correct choice is (d).