Consider a pair of planets for which the distance between them decreases by a factor of 5. Demonstrate that the force between them becomes 25 times greater

Answer 1

Gravitational Force = (G(m1)(m2))/(r)^2

Here, m1 and m2 are the masses of the planets, and r is the distance between them.

From the formula, we see that if the masses are kept constant, gravitational force is inversely proportional to the distance squared.

F = k/r^2

F' = k/(r/5)^2
= k/(r/25)
= 25(k/r)
= 25F

Hence, if the distance decreases by a factor of 5, the force is 25 times greater.