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 u vertically into the sky. The astronaut knows that the Moon has a density of 3400 kg/m^3 and a radius R of 1800 km. (a) Show with (1) that the potential energy of the rock at height h above the surface is given by: E=-(4 pie G)/3 mp*(R^3)/(R+H) (2) (b) Next, show that the gravitational constant can be determined by: G=(3)/(8 pie)*(v^2)/(pR^2)[1-(R)/(R+H)]^-1 (3) (c)What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?

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 u vertically into the sky. The astronaut knows that the Moon has a density of 3400 kg/m^3 and a radius R of 1800 km. (a) Show with (1) that the potential energy of the rock at height h above the surface is given by: E=-(4 pie G)/3 mp(R^3)/(R+H) (2) (b) Next, show that the gravitational constant can be determined by: G=(3)/(8 pie)(v^2)/(pR^2)[1-(R)/(R+H)]^-1 (3) (c)What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?