Question

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 6240 km. Satellite B is to orbit at an altitude of 20400 km. The radius of Earth R_E is 6370 km. a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit? b) What is the ratio of the kinetic energy of satellite B to that of satellite A, in orbit? c) Which satellite (answer A or B) has the greater total energy if each has a mass of 35.0 kg? d) By how much?

Answer 1

A] Ratio of potential energy = PE_B/PE_A = [-GMm/rB]/[-GMm/rA]

= rA/rB = (6370+6240)/(6370+20400) = 0.471

B] Ratio of KE = [GMm/2rB]/[-GMm/2rA] = rA/rB = (6370+6240)/(6370+20400) = 0.471

c] Total energy =   -GMm/2r

B has larger r, so less negative total energy , so greater energy

d] Difference =  -GMm/2rB - -GMm/2rA = -6.67e-11*5.972e24*35/2 *(1/(6370e3+20400e3) - 1/(6370e3+6240e3))

= 2.92*10^8 J