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

We know,

F = G $\dfrac{\text{m}$1\text{m}2}{\text{d}^2}

Where,

F = force of attraction

G = constant of proportionality

m₁ = mass of first object

m₂ = mass of second object

d = distance between the two objects.

When distance is reduced to half then, d' = $\dfrac{\text{d}}{2}$

So, substituting we get,

F' = G $\dfrac{\text{m}$1\text{m}2}{\Big(\dfrac{\text{d}}{2}\Big)^2} = G $\dfrac{\text{m}$1\text{m}2}{\dfrac{\text{d}^2}{4}} = 4G $\dfrac{\text{m}$1\text{m}2}{\text{d}^2} = 4F

Hence, when the distance between the objects is reduced to half, the gravitational force increases four times.