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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 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 ...
where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant. The first test of Newton's law of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry ...
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
The singularity at = in the formula for gravitational potential energy means that the only other apparently reasonable alternative choice of convention, with = for =, would result in potential energy being positive, but infinitely large for all nonzero values of r, and would make calculations involving sums or differences of potential energies ...
where = is the gravitational redshift, is the optical clock transition frequency, = is the difference in gravitational potential, and denotes the violation from general relativity. By Ramsey spectroscopy of the strontium-87 optical clock transition (429 THz, 698 nm) the group determined the gravitational redshift between the two optical clocks ...
The measured elapsed time of a light signal in a gravitational field is longer than it would be without the field, and for moderate-strength nearly static fields the difference is directly proportional to the classical gravitational potential, precisely as given by standard gravitational time dilation formulas.
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]