Question

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?

Answer 1

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

Step-by-step 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;

`F_(1) = F_(2) =G(m_(1)m_(2))/(r^(2))`

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;

`F = 4.00 \ Fm =(D^2 * Fm)/(r_2^(2))`

Therefore;

`r_2^(2) =(D^2 * Fm)/(4.00 \ Fm) = (D^2)/(4)`

`r_2 =\sqrt{(D^2)/(4)} = (D)/(2) = 0.5 \cdot D`

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.