Question

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:

4πG R3

E = −

3 mρ · R + h (2)

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

3 v2 .

R Σ−1


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

Answer 1

Answer:

An astronaut on the moon measures the acceleration due to gravity to be

. He known that the radius of the moon is about

times that of the earth . Find the ratio of the mass of the earth to that of the moon , if the value of g on the earth's surface is

answer =79