How much work is required to lift a 700kg satellite to an altitude of 1x10^6m above the surface of the earth? The gravitation force is F=GMm/r^2, where M is the mass of the earth, m is the mass of the satellite, and r is the distance between them. The radius of the earth is 6.4x10^6m, its mass is 6x10^24 kg, and in these units the gravitational constant, G, is 6.67x10^-11.

Question

Steve · Answer

To lift the mass a distance of dr, the work involved is

F dr = 700GM/r^2 dr
= (700 * 6.67*10^-11 * 6*10^24)/r^2
= 2.8*10^17/r^2 dr

So, the work is

∫[6.4*10^6,7.4*10^6] 2.8*10^17/r^2 dr = 5.9*10^9 Joules