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

Answer

D

Explanation

Energy of the satellite on the surface of the planet
`E_1=KE+PE=0+(-"GMm"/R)=-(GMm)/R`
Energy of the satellite in the circular orbit of radius (R + 2R) is
`therefore` Minimum energy required to launch the satellite is :
`DeltaE=E_f-E_i=-(GMm)/(6R)-(-"GMm"/R)=-"GMm"/(6R)+"GMm"/R="5GMm"/"6R"`