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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.
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.
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.
There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is ...
Every mass has an associated gravitational potential. The gradient of this potential is a force. A gravimeter measures this gravitational force. For a small body, general relativity predicts gravitational effects indistinguishable from the effects of acceleration by the equivalence principle.
However, the predictions of Newtonian gravity do not match the observations, as discovered in 1859 from observations of Mercury. If the potential energy between the two bodies is not exactly the 1/r potential of Newton's gravitational law but differs only slightly, then the ellipse of the orbit gradually rotates (among other possible effects).
In general relativity, the effective gravitational potential energy of an object of mass m revolving around a massive central body M is given by [43] [44] = + A conservative total force can then be obtained as its negative gradient