Physics

Gravitational potential energy depends on the inverse distance between masses, not linear distance—this is the key difference from everyday potential energy like $mgh$. When you move a mass in a gravitational field, you're not just multiplying force by displacement; you need to integrate the varying gravitational force $F = \frac{GMm}{r^2}$ over the path. The work done equals the change in potential energy, which you find by evaluating the potential energy function at both positions and taking the difference.

Gravitational potential energy depends on the inverse distance between masses, not linear distance—this is the key difference from everyday potential energy like $mgh$. When you move a mass in a gravitational field, you're not just multiplying force by displacement; you need to integrate the varying gravitational force $F = \frac{GMm}{r^2}$ over the path. The work done equals the change in potential energy, which you find by evaluating the potential energy function at both positions and taking the difference.