Question

A satellite of mass 400 kg is in a circular orbit of radius 2R about the earth, where R is radius of the earth. How much energy is required to transfer it to a circular orbit of radius 4R? Find the changes in the kinetic and potential energies? (R = 637 x 106m)

Answer 1

$E_i=\frac{-G{M}_e.m}{4R_e}$

$E_f=\frac{-G{M}_{e}m}{8R_e}$

Energy required $=\frac{-G{M}_{e}m}{8R_e}+\frac{G{M}_{e}m}{4R_e}$

$=\frac{g.m{R}_e}{8}=3.13\times {10}^{9}J$

$K.E$ will become half & $P.E$ will become twice.