An astronaut working on the Moon tries to determine the gravitational constant G by throwinga Moon rock of mass m with a velocity of v vertically into the sky. The astronaut knows that theMoon has a density p 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:4тGR3E = -тр.(2)3R+h(b) Next, show that the gravitational constant can be determined by:-13 v2RG =(3)87 pR²R+h(c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?

(a) Using Work-Energy theorem, ∆E=∫∞hFdrEh-E∞=∫∞hGMmR+r2drEh-0=GMm∫∞hdrR+r2Eh=-GMmR+h=-GmR+h43πR3ρ…

Answered: An astronaut working on the Moon tries…

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