Question

if there are two bodies and we decrease mass of any one body by 9 times. how much should the distance between them be increased to keep force of gravity between them constant.

Answer 1

According to the Newton's gravity law, the initial force between two masses is the following:

$$F_1 = G\dfrac{m_1m_2}{r^2}$$

If we increase one of the masses by a factor of 9 ($m_1 \to9m_1$ ), then we should increase the distance by a factor of 3 ($r \to 3r$) in order to keep the force the same. Let's check:

$$F_2 = G\dfrac{(9m_1)m_2}{(3r)^2} = G\dfrac{9m_1m_2}{9r^2} = G\dfrac{m_1m_2}{r^2} = F_1$$

Indeen, $F_2 = F_1$.

Answer. The distance between masses should be increased by 3 times.