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The gravitational potential energy is the potential energy an object has because it is within a gravitational field. The magnitude & direction of gravitational force experienced by a point mass , due to the presence of another point mass at a distance , is given by Newton's law of gravitation. [2]
The gravitational potential (V) at a location is the gravitational potential energy (U) at that location per unit mass: =, where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.
The product of force and displacement gives the work done, which is equal to the gravitational potential energy, thus =. The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position.
Gravitational energy, or gravitational potential energy, is the potential energy a massive object has because it is within a gravitational field. In classical mechanics , two or more masses always have a gravitational potential .
The potential energy, U, depends on the position of an object subjected to gravity or some other conservative force. The gravitational potential energy of an object is equal to the weight W of the object multiplied by the height h of the object's center of gravity relative to an arbitrary datum: =
The potential has units of energy per mass, e.g., J/kg in the MKS system. By convention, it is always negative where it is defined, and as x tends to infinity, it approaches zero. The gravitational field, and thus the acceleration of a small body in the space around the massive object, is the negative gradient of the gravitational potential ...
For convenience it is often defined as the negative of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of the geopotential, without the negation. In addition to the actual potential (the geopotential), a theoretical normal potential and their difference, the disturbing potential, can also be defined.
In the case of the gravitational field g, which can be shown to be conservative, [3] it is equal to the gradient in gravitational potential Φ: =. There are opposite signs between gravitational field and potential, because the potential gradient and field are opposite in direction: as the potential increases, the gravitational field strength decreases and vice versa.