let the mass of the two objects be m₁ and m₂ respectively and the distance between the two objects be "r₁" initially.
the gravitational force between the two objects initially is then given as
F₁ = G m₁ m₂ /r₁² eq-1
where G = universal gravitational constant
when the objects are moved closer and the distance between the objects become one third of the original distance, hence
r₂ = distance after objects moved closer = r₁/3
new gravitational force between the objects after they are moved closed is given as
F₂ = G m₁ m₂ /r₂² eq-2
dividing eq-2 by eq-1
F₂/F₁ = (G m₁ m₂ /r₂² )/(G m₁ m₂ /r₁²)
F₂/F₁ = r₁²/r₂²
we know that , r₂ = r₁/3
hence
F₂/F₁ = r₁²/(r₁/3)²
F₂/F₁ = 9
F₂ = 9 F₁
hence the gravitational force becomes nine times its initial value
