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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 m {\displaystyle m} , due to the presence of another point mass M {\displaystyle M} at a distance r {\displaystyle r} , is given by Newton's law of ...
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.
Conversely, as two massive objects move towards each other, the motion accelerates under gravity causing an increase in the (positive) kinetic energy of the system and, in order to conserve the total sum of energy, the increase of the same amount in the gravitational potential energy of the object is treated as negative. [1]
In general relativity, the metric tensor plays the role of the gravitational potential in the classical theory of gravitation, although the physical content of the associated equations is entirely different. [1] Gutfreund and Renn say "that in general relativity the gravitational potential is represented by the metric tensor." [2]
Gravitational energy is the potential energy associated with gravitational force, as work is required to elevate objects against Earth's gravity. The potential energy due to elevated positions is called gravitational potential energy, and is evidenced by water in an elevated reservoir or kept behind a dam.
Geopotential is the gravitational potential energy per unit mass at elevation : = (,) where (,) ... because then it has the properties of a conservative force.
However, the total energy of the Earth orbiting the Sun (kinetic energy + gravitational potential energy) is about 1.14 × 10 36 joules of which only 200 watts (joules per second) is lost through gravitational radiation, leading to a decay in the orbit by about 1 × 10 −15 meters per day or roughly the diameter of a proton.
Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object. If the object falls to the ground, gravity does mechanical work on the object which transforms the potential energy in the gravitational field to the kinetic energy released as heat on impact with the ground.