Question

Explain how the gravitational force between two objects depends on the distance between them?

Answer 1

Step 1: The gravitational force ‘F’ between two bodies of masses $m_1$and $m_2$is given as

$F=\frac{G{m}_1{m}_2}{r^2}$

$m_1,m_2=$masses of two bodies

$r=$distance between centers of masses.

$G=$gravitational constant.

Step 2: Finding force and distance between centers of masses relation

The force between two bodies is inversely proportional to the square of the distance.

$F\propto \frac{1}{r^2}$

Since ‘F’ is inverse to the square of the r. Therefore, when the distance is doubled, the gravitational force becomes one-fourth and when the distance is halved, the gravitational force between two bodies becomes four times