Consider the gravitational force between two masses. What happens to this force if each mass is tripled while the distance the mass is halved?

Question

Consider the gravitational force between two masses. What happens to this force if each mass is tripled while the distance the mass is halved?

Answer 1

F = Gm₁m₂ / d²

Replace m₁ with 3m₁, m₂ with 3m₂, and d with d/2.

F₁ = G(3m₁)(3m₂) / (d/2)² = 36 Gm₁m₂ / d² = 36F

The force increases from F to 36F.