The average distance between the centers of the Moon and the Earth is approximately 60 Earth radii. How many times will the force of the gravitational interaction of an object weighing 1 kg and the Earth decrease if the object is first on the surface of the Earth, and then in the lunar orbit?
m = 1 kilogram is the mass of the object;
M is the mass of the Earth;
r2 = 60 * r1 – the distance between the Earth and the Moon is equal to 60 Earth radii;
G is the gravitational constant.
It is required to determine F1 / F2 – how many times the force of attraction between the body and the Earth will decrease if first the object is on the surface of the Earth, and then on the Moon.
On the surface of the earth, the force of attraction will be equal to:
F1 = G * m * M / r1 ^ 2.
In lunar orbit, the force of attraction between the object and the Earth will be equal to:
F2 = G * m * M / r2 ^ 2 = G * m * M / (60 * r1) ^ 2 = G * m * M / (3600 * r1 ^ 2).
F1 / F2 = (G * m * M / r1 ^ 2) / (G * m * M / (3600 * r1 ^ 2)) = 3600, that is, it will decrease 3600 times.
Answer: the force of gravitational interaction will decrease 3600 times.
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