A satellite of mass m revolving in a circular orbit of radius `3 R_E` around the earth (mass of earth is Me and radius is `R_E` ). How much excess energy be spent to bring it to orbit of radius `9 R_E` ?

Options

A. `(GM_Em)/(3R_E)`
B. `(GM_Em)/(18R_E)`
C. `(3GM_Em)/(2R_E)`
D. `(GM_Em)/(9R_E)`

Answer

D

Explanation

`implies` Total energy of satellite `|E| = (GM_Em)/r`
`:.` Energy at `r = 3R_E`
`|E_1|=(GM_Em)/(2(3R_E))=(GM_Em)/(6R_E)`
and Energy at `r = 9R_E`
`|E_2|=(GM_Em)/(2(9R_E))=(GM_Em)/(18R_E)`
`:.` Excess energy from going `3R_E " to " 9R_E`
`DeltaE=E_1 -E_2`
`= (GM_Em)/(6R_E) - (GM_Em)/(18R_E)`
`= (2GM_Em)/(18R_E)`
`= (GM_Em)/(9R_E)`