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. `(5GmM)/(6R)`
B. `(2GmM)/(3R)`
C. `(GmM)/(2R)`
D. `(GmM)/(3R)`

Answer

a

Explanation

`r=2R+R=3R`
`E_(2)=-(GmM)/(6R) " and "E_(1)=-(GmM)/(R)`
`therefore" Minimum energy required is ,"`
`E_(2)-E_(1)=-(GmM)/(6R)-(-(GmM)/(R))`
`=(5GmM)/(6R)`