Physics Review Question

Question

A 100 kg satellite is in orbit around the earth at a height of 10,000 km above the ground.

how much additional kinetic energy would be required for the satellite to escape from earth completely? IE: What is the gravitational potential energy of the satellite?

Answer 1

F = GmM/(R + x)²; Elementary work dW = GmMdx/(R + x)²; W = ∫_d^∞GmMdx/(R + x)² =

-GmM/(R + x)_d∞ = GmM/(R + d);

On surface of Eaeth mg = GMm/R². So, GM = gR² . So, additional work W = gR²m/(R + h);

g = 9.8 m/s², R = 6.371·10⁶m; m = 100 kg; d = 10⁷m

W = 9.8·(6.371·10⁶)·100/(6.371·10⁶ + 10⁷) =2.43·10⁷ J

Potential energy U = - GmM/(R + d) = - 2.43·10^{7 J}