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 2 R is

Step-by-step solution

Orbital energy, E ₀= - GMm 2( R + h ) E ₀= - GMm 2( R +2 R ) = - GMm 6 R ( ~h =2 R ) Energy at surface E= - GMm R aligned Min. energy required & = E ₀- E & = - GMm 6 R - ( - GMm R ) & = 5 GMm 6 R aligned