Please answer this necessarily with an explanation and I will mark the brilliant An astronaut working on the Moon tries to determine the gravitational constant G by throwing

a Moon rock of mass m with a velocity of v vertically into the sky. The astronaut knows that the

Moon has a density ρ of 3340 kg/m3 and a radius R of 1740 km.

(a) Show with (1) that the potential energy of the rock at height h above the surface is given by:

E = −4πG

3

mρ ·

R3

R + h (2)

(b) Next, show that the gravitational constant can be determined by:

G = 3

8π

v2

ρR2 1 − RR+ h−1 (3)

(c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?