Question

A satellite of mass $m_1$is launched from the surface of the Earth into an orbit of radius $2r_e$, where $r_e$is the radius of the Earth. How much work is done to get it into orbit?

Answer 1

The potential energy of a satellite is due to its position w.r.t. earth , and in its orbit of radius $2r_e$ it is given by , $U=-G{M}_E{m}_1/2r_e$ ,

where $M_E=$ mass of earth ,

$m_1=$ mass of satellite ,

and potential energy of a satellite on earth is given by ,

$U=-G{M}_E{m}_1/2r_e$ ,

therefore work done will be change in the potential energy of satellite from earth's surface to its orbit

$W=-G{M}_E{m}_1/2r_e-(-G{M}_E{m}_1/r_e)$ ,

or $W=G{M}_E{m}_1/2r_e$