Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's center. Satellite A is to orbit at an altitude of 5580 km. Satellite B is to orbit at an altitude of 21000 km. The radius of Earth REis 6370 km. (a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit

=0.43

Explanation:

Given

mv^2/R=GMm/R^2

Make V the subject

V^2 = (GM/R)

For satellite A

Va^2 = (GM/R) = (GM / (5580+6370) * 10^3)

Vb^2 = (GM / (21000+6370) * 10^3)

Va^2 = (GM/11950*10^3)

Vb^2 = (GM/27370*10^3)

But kinetic Energy Ek of orbiting object is MV^2/2=GMm/2R

Hence EkA = GMm/2*11950*10^3)

EkB = GMm (2*27370*10^3)

EkB/EkA = 2*11950*10^3/2*27370*10^3

=0.43