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THE ENERGY OF GRAVITY: THE GRAVITATIONAL POTENTIAL
E = -GMm/r (potential energy = negative-one * Mass * mass / distance dE = mgh (change in potential energy = mass of small object * gravitational acceleration of large object * height of small object) The gravitational potential energy equation describes the amount of energy an object must have to stay at a particular location in the gravity field of another object. (An example might be the amount of energy a brick must have to stay 6500 km away from Earth's center without falling inward.) To determine the amount of gravitational potential energy released when an object moves in a gravity field, we (1) compute the potential energy it had at its previous location before it moved, then (2) compute the potential energy it has now at its current location, then (3) take the difference between the two energies. Usually, the direction an object must move to release potential energy is toward the center of the gravity field - on the surface of a planet, for example, that usually means falling downward toward the planet's center. Conveniently, this gravitational potential energy equation reverts to the second, simpler version when the height (or distance to be traveled) is so small that the gravitational acceleration on the object doesn't change much. This would be the case, for example, when dropping a brick from shoulder height to the floor, or even from a skyscraper to street level. This approximation fails for objects moving large distances, such as planets, stars and satellites. Interestingly, the potential energy of an object in a gravitational potential field is "sort of" the gravitational force of the object integrated over the distance. What does this mean to you? |