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 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: 4тG R3 E = - -тр: (2) 3 R+h (b) Next, show that the gravitational constant can be determined by: -1 3 v2 G = 87 pR² R (3) R+h (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 v vertically into the sky. The astronaut knows that the Moon 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: 4тG R3 E = - -тр: (2) 3 R+h (b) Next, show that the gravitational constant can be determined by: -1 3 v2 G = 87 pR² R (3) R+h (c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?
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Transcribed Image Text: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 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:
4тG
R3
E = -
тр.
(2)
3
R+h
(b) Next, show that the gravitational constant can be determined by:
-1
3 v2
R
G =
(3)
87 pR²
R+h
(c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?
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