Question

One of your summer lunar space camp activities is to launch a 1210-kg rocket from the surface of the Moon. You are a serious space camper and you launch a serious rocket: it reaches an altitude of 229 km. What gain in gravitational potential energy does the launch accomplish? The mass and radius of the Moon are 7.36 × 1022 kg and 1740 km, respectively.

Answer 1

change in p.e = -GM1M2/r
M1 = mass of moon = 7.36*10^22 kg
M2 = mass of rocket = 1210 kg
r1 = 1740,000m when rocket is at surface
r2 = 1740,000+229,000 m = 1969,000 m

Δ P.E = - GM1M2(1/r2) - (-GM1M2(1/r1))

= GM1M2(1/r1-1/r2)

= 394877877 J