If the distance between two masses is halved, the gravitational force between them increases by a factor of four. According to Newton's law of universal gravitation, the gravitational force ( F ) between two masses ( m_1 ) and ( m_2 ) is inversely proportional to the square of the distance ( r ) between them:

[ F = G \frac{{m_1 \cdot m_2}}{{r^2}} ]

So if ( r ) is halved (i.e., replaced by ( \frac{r}{2} )), the force becomes:

[ F' = G \frac{{m_1 \cdot m_2}}{{\left(\frac{r}{2}\right)^2}} = G \frac{{m_1 \cdot m_2}}{{\frac{r^2}{4}}} = 4 \cdot G \frac{{m_1 \cdot m_2}}{{r^2}} = 4F ]

Thus, the gravitational force becomes four times stronger.