The Earth has a mass of 5.97x10^24 kg and the Moon has a mass of 7.36x10^22 kg.

Question

The Earth has a mass of 5.97x10^24 kg and the Moon has a mass of 7.36x10^22 kg. The average distance between the center of the Earth and the center of the Moon is 3.84x10^8 m.

a) What is the gravitational force acting on the Moon due to the Earth?
b) What is the gravitational force acting on the Earth due to the Moon?
c) How far away would the Moon need to be for the magnitude of the gravitational force acting on it due to the Earth be the same as the magnitude of the gravitational force of a 72 kg student sitting at their desk on the surface of the earth?

d) A supermassive black hole passes through the edge of the solar system 1.20 x 10^13 m away. The gravitational force between an observant 79 kg astronomer and the black hole is 1N. What is the mass of the black hole?

Explanation / Answer

Force = Gm1m2/r^2

Therefore

F = (6.674*10^-11*5.97*10^24*7.36*10^22)/(3.84*10^8)^2

= 1.988*10^20 N

Same Force occur in Case 2 because Action = Reaction(Newton Third Law)

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