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?

Options

A. `5/3mgR`
B. `4/3mgR`
C. `5/6mgR`
D. `5/4mgR`

Answer

C

Explanation

Total energy `E=1/2mv^(2)-(GmM)/r`
`=(GmM)/(2r)-(GMm)/r=-G(mM)/(2r)`
`r=2R=R=3R`
`E=(GmM)/(6R)`
Potential energy `=-(GMm)/R`
Minimum energy required `=1/6(GMm)/R-((-GMm)/R)=5/6(GMm)/R`