How does the force of gravitation between two objects change when the distance between them is reduced to half?

When considering the force of gravitation between two objects, Newton’s law of universal gravitation provides insight into how this force changes concerning the distance between the objects.

1. Inverse Square Law: Newton’s law of universal gravitation states that the force of attraction between two objects is inversely proportional to the square of the distance between their centers. The formula is F = ((G.m₁.m₂)/(r²)) where F is the gravitational force, G is the gravitational constant, m₁ and m₂ are the masses of the objects, and r is the distance between their centers.

2. Impact of Halving the Distance: If the distance between the objects is reduced to half, according to the formula, this new distance r will be one-half of the original distance. When substituted into the formula, r² decreases to one-fourth of its initial value.

3. Effect on Gravitational Force: As per the inverse square law, halving the distance means r² becomes one-fourth of its initial value. Therefore, the gravitational force increases proportionally, becoming four times stronger than it was at the original distance.

In essence, when the distance between two objects is reduced to half, the force of gravitation between them intensifies significantly, becoming four times stronger. This demonstrates the substantial impact of distance on gravitational force according to Newton’s law of universal gravitation, where closer proximity results in a much stronger gravitational pull between objects.