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Concept
Gravitational energy
Summary
Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (converted into kinetic energy) when the objects fall towards each other. Gravitational potential energy increases when two objects are brought further apart.
For two pairwise interacting point particles, the gravitational potential energy is given by
where and are the masses of the two particles, is the distance between them, and is the gravitational constant.
Close to the Earth's surface, the gravitational field is approximately constant, and the gravitational potential energy of an object reduces to
where is the object's mass, is the gravity of Earth, and is the height of the object's center of mass above a chosen reference level.
In classical mechanics, two or more masses always have a gravitational potential. Conservation of energy requires that this gravitational field energy is always negative, so that it is zero when the objects are infinitely far apart. The gravitational potential energy is the potential energy an object has because it is within a gravitational field.
The force between a point mass, , and another point mass, , is given by Newton's law of gravitation:
To get the total work done by an external force to bring point mass from infinity to the final distance (for example the radius of Earth) of the two mass points, the force is integrated with respect to displacement:
Because , the total work done on the object can be written as:
In the common situation where a much smaller mass is moving near the surface of a much larger object with mass , the gravitational field is nearly constant and so the expression for gravitational energy can be considerably simplified.
Official source
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