Gravitational Potential Energy Near Earth

When you lift a book, your hand does work against gravity, and that work doesn't vanish. It gets stored as potential energy, ready to turn back into kinetic energy the instant you let go. That's the whole point of potential energy: it's a way of bookkeeping work you've already done, so you don't have to track every force again later. The book falling back down just converts the stored energy back into motion.

Here's the mechanism. The force of gravity on a mass m is m g, pointing down. To lift the object a height h at constant speed, you push up with a force of m g over that distance, doing work W = m g h. Since energy isn't created or destroyed, that work is stored as gravitational potential energy: U = m g h, measured from whatever height you've decided to call h = 0. That zero point is just a reference, like choosing where a ruler starts. It never shows up in a real answer, because physics only cares about changes in U — the energy released or absorbed when height changes — and any constant offset cancels when you subtract. This is why the problem collapses nicely: instead of tracking a changing force through an integral, you just compute m g times a height difference.

This simple form only works because g is treated as constant, which is excellent near Earth's surface but fails for large altitude changes, like sending a rocket far from Earth. There, g weakens with distance, and the true potential energy becomes U = -G M m / r, the antiderivative of the real, distance-dependent gravitational force. mgh is just the local, flat-Earth approximation of that deeper law.