Answer:
One-fourth of the original gravitational force.
Explanation:
The gravitational force between two objects of masses [tex]m\textrm{ and }M[/tex] is given as:
[tex]F_{g}=\frac{GmM}{r^2}[/tex]
Where,
[tex]G\rightarrow \textrm{gravitational constant}\\r\rightarrow \textrm{distance between the masses}[/tex]
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 [tex]r = 2r[/tex], then new gravitational force is,
[tex]F_{g,new}=\frac{GmM}{(2r)^2}=\frac{GmM}{4r^2}=\frac{1}{4}\frac{GmM}{r^2}[/tex]
As seen above, new gravitational force is one-fourth of the original gravitational force between moon and Earth.
