Question

If the moon were twice as far from the earth as it is now, the gravitational force it

Answer 1

Answer:

One-fourth of the original gravitational force.

Explanation:

The gravitational force between two objects of masses $m\textrm{ and }M$ is given as:

$F_{g}=\frac{GmM}{r^2}$

Where,

$G\rightarrow \textrm{gravitational constant}\\r\rightarrow \textrm{distance between the masses}$

Therefore, the gravitational force is inversely proportional to the square of the distance between the masses.

Now, if the distance is doubled, then the force has to be reduced by a factor of one by four or gravitational force will one-fourth of the original.

Let us verify it.

If $r = 2r$, then new gravitational force is,

$F_{g,new}=\frac{GmM}{(2r)^2}=\frac{GmM}{4r^2}=\frac{1}{4}\frac{GmM}{r^2}$

As seen above, new gravitational force is one-fourth of the original gravitational force between moon and Earth.