Question

Two objects have a force of gravity of 100 N. If the distance between both objects decreases by a factor of 7, while the masses both decrease by a factor of 8. What is the new Fg?

Answer 1

The gravitational force F between two masses M and m a distance r apart is

F = G M m / r ²

Decrease the distance by a factor of 7 by replacing r with r / 7, and decrease both masses by a factor of 8 by replacing M and m with M / 8 and m / 8, respectively. Then the new force F* is

F* = G (M / 8) (m / 8) / (r / 7)²

F* = (1/64 × G M m) / (1/49 × r ²)

F* = 49/64 × G M m / r ²

In other words, the new force is scaled down by a factor of 49/64 ≈ 0.7656, so the new force has magnitude approx. 76.56 N.