When the Moon is a distance of 0.25 D from the Earth, the gravitational force on the Moon from Earth is 16.00 Fm. At what distance with the force on the Moon be 4.00 Fm?

When the gravitational force on the Moon from the Earth = 4.00 Fm, the distance of the Moon from the Earth is 0.5·D

Explanation:

The given information includes;

The distance of the moon from the Earth = 0.25·D

The gravitational force, F, on the Moon from the Earth = 16.00 Fm

When the gravitational force on the Moon from the Earth = 4.00 Fm, the distance of the Moon from the Earth is found as follows;

From Newton's law of gravitation;

At r = 0.25·D, F = 16.00 Fm

Therefore;

G×m₁×m₂ = (0.25·D)²×16.00 Fm = D²×Fm = Constant

When, the gravitational force of the Moon from the Earth = 4.00 Fm, we have;

Therefore;

r₂ = 0.5·D

Where;

r₂ = The new distance of the Moon from the Earth

Therefore the distance of the Moon from the Earth when the gravitational force on the Moon from the Earth = 4.00 Fm is r₂ = 0.5·D.

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