If the distance between two objects is doubled while their masses stay the same, the gravitational force between them becomes:

1. The force is inversely proportional to the square of the distance, $F \propto \dfrac{1}{d^2}$. 2. If distance doubles, $d \to 2d$, then $d^2 \to 4d^2$. 3. So the force changes by a factor $\dfrac{1}{4}$, decreasing to one-fourth. 4. Doubling distance does not halve the force (that would need $F \propto 1/d$), so 'half' is the trap. _Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.13_