According to Newton's Law of Universal Gravitation, what happens to the force of attraction between two objects if the distance between them is doubled?

According to Newton's Law of Universal Gravitation, the force of attraction between two objects is inversely proportional to the square of the distance between their centers. This means that if the distance between the two objects is doubled, the influence of that distance on the gravitational force is calculated by squaring the change in distance.

When the distance is doubled, the new distance is 2d, and the gravitational force can be expressed as ( F' = G \frac{m_1 m_2}{(2d)^2} = G \frac{m_1 m_2}{4d^2} ). Here, ( G ) is the gravitational constant, and ( m_1 ) and ( m_2 ) are the masses of the two objects. The factor of ( 4 ) indicates that the force of attraction is reduced to one-fourth of the original amount, as the original force would be ( F = G \frac{m_1 m_2}{d^2} ).

This mathematical relationship illustrates the principle that as the distance between two objects increases, the gravitational force decreases significantly, leading to the conclusion that doubling the distance results in the gravitational force being reduced to one-fourth