Question

If the distance between two object in increase two times, they by how many times will the mass of one of the object be change to maintain the same gravitational force?

Answer 1

Given,

Distance increased twice.

Gravitational force,$F=GM\frac{m}{r^2}$ where m and r is variable.

If $r$ increase to twice, keeping $F=$ constant.

$F=GM\frac{m^{\prime }}{{\left(2r\right)}^2}$

$GM\frac{m}{r^2}=GM\frac{m^{\prime }}{4r^2}$

$m^{\prime }=4m$

Hence, one mass increase to four times.