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.

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