What will happen to the gravitational force experienced by two objects if the distance between them doubles, according to Newton's law of gravitation?

According to Newton's law of gravitation, the gravitational force between two objects is inversely proportional to the square of the distance between their centers. This can be expressed mathematically with the formula:

[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} ]

where ( F ) is the gravitational force, ( G ) is the gravitational constant, ( m_1 ) and ( m_2 ) are the masses of the two objects, and ( r ) is the distance between their centers.

When the distance between the two objects is doubled (( r) changes to ( 2r)), the equation for gravitational force becomes:

[ F' = \frac{G \cdot m_1 \cdot m_2}{(2r)^2} = \frac{G \cdot m_1 \cdot m_2}{4r^2} ]

This shows that the new force ( F' ) is one-fourth of the original force ( F ). Therefore, when the distance is doubled, the gravitational force experienced by the objects actually reduces to a quarter of its original value. In the context of