According to the universal law of gravitation, gravitational force (F) acting between two objects is inversely proportional to the square of the distance (r) between them, i.e.,
F ∝ {1\over \text{r}^2}
If distance r becomes r/2, then the gravitational force will be proportional to
\text{F}_2\over \text{F}_1 = {{1\over \text{r}^2}\over {1\over({\text{r} \over2})^2}}
or, \text{F}_2\over \text{F}_1 = {4\text{r}^2\over \text{r}^2}
or, F2 = 4F1
Hence, if the distance is reduced to half, then the gravitational force becomes four times larger than the previous value.
