Gravitational Force between two bodies of masses M and m separated by a distance d = Fg = G M m / d²
Force is proportional inversely to the square of distance d between objects.
F = K / d² , where K is a constant
Originally, F₁ = K/ d₁²
when distance is doubled, d₂ = 2*d₁ ==> F₂ = K/d₂²
F₂ / F₁ = d₁² / d₂² = d₁² / 4d₁² = 1/4 So force becomes 1/4th.
Force is proportional directly to the (product of) masses of the objects.
F = K M m , K = a constant
F₂ / F₁ = K M₂ m₂ / K M₁ m₁ = 2 M₁ 2 m₁ / M₁ m₁ = 4
So force becomes 4 times.