Question

When the distance between two interacting objects becomes one third, the gravitational force becomes 9 times. Why 1/3 and gravitational force becomes 9 times?

Answer 1

I tried this:

Explanation:

Consider the force between our objects of masses `m_1` and `m_2` at distance `r` as:

`F=G(m_1m_2)/r^2`

now let us shorten the distance to `r'=1/3r`; we get:

`F'=G(m_1m_2)/((r')^2)`

but: `r'=1/3r`
so we get:

`F'=G(m_1m_2)/(1/3r)^2=G(m_1m_2)/(1/9r^2)`

rearranging:

`F'=9*G(m_1m_2)/r^2`

but: `G(m_1m_2)/r^2=F`

and so:

`F'=9F`