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)/(2R)`

Answer

A

Explanation

(a) Applying energy conservation
`k+((-GMm)/(R )) = (1)/(2)mv_0^2 + (-(GMm)/(R +h))`
`k-(GMm)/(R ) = (1)/(2) m ((Gm)/(R + 2R)) - (GMm)/(R +2R))`
`:. K = (5GMm)/(6r)`