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For two pairwise interacting point particles, the gravitational potential energy is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): = = where is the displacement vector of the mass, is gravitational force acting on it and denotes scalar product.
The following is a list of notable unsolved problems grouped into broad areas of physics. [1]Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result.
[7] [8] [9] The Watt–Misner theory (1999) is a recent example of a scalar theory of gravitation. It is not intended as a viable theory of gravitation (since, as Watt and Misner point out, it is not consistent with observation), but as a toy theory which can be useful in testing numerical relativity schemes. It also has pedagogical value. [10]
The equivalence between mass and energy, as expressed by the formula E = mc 2, is the most famous consequence of special relativity. In relativity, mass and energy are two different ways of describing one physical quantity. If a physical system has energy, it also has the corresponding mass, and vice versa.
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.
In classical mechanics, a gravitational field is a physical quantity. [5] A gravitational field can be defined using Newton's law of universal gravitation.Determined in this way, the gravitational field g around a single particle of mass M is a vector field consisting at every point of a vector pointing directly towards the particle.
The first test of Newton's law of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798. [5] It took place 111 years after the publication of Newton's Principia and approximately 71 years after his death.
"Exact solutions of the gravitational field equations". In Witten, L. (ed.). Gravitation: An Introduction to Current Research. Wiley. pp. 49– 101. hdl:11858/00-001M-0000-0013-5F17-4. OCLC 504779224. A classic survey, including important original work such as the symmetry classification of vacuum pp-wave spacetimes.