Answer to Question #96638 in Mechanics | Relativity for abru

Question

The Chandrayaan-2 orbiter is orbiting the moon in a circular polar orbit at a height of 1.00×105 m
above the surface. It has a mass of 2379 kg. What is the change of momentum in the orbiter
from when it passes over the North Pole compared to when it passes over the South Pole?

Answer 1

Assume that the axis of direction reference is directed to the right and the satellite goes right above the North pole and goes left below the South pole.

Thus, the initial momentum is $p_1$ and the final momentum is $p_2=-p_1.$

The change in momentum is

$$∆p=p_1-p_2=2p_1,\\ ∆p=mv.$$

The escape velocity for the Moon at that height is:

$$v=\sqrt{\frac{GM}{r}}=\sqrt{\frac{6.673\cdot10^{-11}\cdot7.348\cdot10^{22}}{1\cdot10^5}}=7002\text{ m/s}.$$

Then

$$\Delta p=2379\cdot7002=16\space657\space758\text{ kg}\cdot\text{ m/s}^2.$$