Question

A satellite of mass m is revolving at a height r from earth surface. Here r is the radius of earth. The gravitational potential energy of the satellite is

Answer 1

Let the position vector of the first object be r1 and the position vector of the second object be r2 . So here the work done in bringing the object from one position to another is:

W = ∫r2r1Fdr

where, F = GMemr2

W = ∫r2r1GMemdr

= – GMem[ 1r2 – 1r1 ]WBA = mg ( h2– h1) = mg h2 – mg h1WBA = Force × displacementThe height of point A from the surface of the earth is h2 and that of point B is h1Assume an object at point A and later it moves to point B. So, in this case, the work done is force × displacement.W = ∫r2r1Fdr

where, F = GMemr2

W = ∫r2r1GMemdr

= – GMem[ 1r2 – 1r1 ]