Physics, 02.03.2021 04:00 ameliaduxha7
Nesseccery
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?
Answers: 2
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