Question

A satellite of mass `m` is in a circular orbit of radius `2R_(E)` about the earth. The energy required to transfer it to a circular orbit of radius `4R_(E)` is (where `M_(E)` and `R_(E)` is the mass and radius of the earth respectively)
A. `1.65 xx 10^(9)J`
B. `3.13 xx 10^(9)J`
C. `6.26 xx 10^(9)J`
D. `4.80 xx 10^(9)J`

Answer 1

Correct Answer - B
Total energy of satellite in circular orbit of radius `2R`
`E_(1) = PE + KE = - (GM m)/(2R) + (1)/(2)m [sqrt((GM)/(2R))]^(2)`
`= -(GM m)/(4R)`
Total energy of satellite in circular orbit of radius `4R`
`E_(2) = -(GM m)/(4R) + (1)/(2)m [sqrt((GM)/(4R))]^(2) = -(GM m)/(8R)`
Energy spent `= E_(2) -E_(1) = -(GM m)/(8R) + (GM m)/(4R)`
`=(GM m)/(8R)=(gR^(2) m)/(8R) = (mg R)/(8)`
`= (400 xx 9.80 xx (6.4 xx 10^(6)))/(8) = 3.13 xx 10^(9)J`