Question

Find the ratio of the gravitational force between two planets if the masses of both planets are quadrupled but the distance between them stays the same.

Answer 1

Answer:

The ratio of the new force over the original force is 16

Explanation:

Recall the formula for the gravitational force between two masses M1 and M2 separated a distance D:

$F_G=G\,\frac{M_1\,\,M_2}{D^2}$

So now, if the masses M1 and M2 are quadrupled and the distance stays the same, the new force becomes:

$F'_G=G\,\frac{4M_1\,\,4M_2}{D^2}=G\,\frac{16\,\,M_1\,\,M_2}{D^2}=16\,\,G\,\frac{M_1\,\,M_2}{D^2}= 16\,\,F_G$

which is 16 times the original force.

So the ratio of the new force over the original force is 16