And the potential is determined by the surrounding mass distribution by Poisson's partial differential equation
This formulation is entirely equivalent to Newton's law of gravitation. Because a test particle's acceleration depends only on the potential generated by matter in the surroundings, the theory respects the weak equivalence principle: the motion of a particle is independent of its internal structure or composition. As the subject of Galileo Galilei's apocryphal experiment at the tower of Pisa, this principle is supported by a series of high precision experiments culminating in those directed by Baron Lorand von Eötvos in Budapest in 1922, Robert Dicke at Princeton in 1964, and Vladimir Braginsky in Moscow in 1972.
Highly successful in everyday applications, newtonian gravitation has also proved accurate in describing motions in the solar system (except for tiny relativistic effects), the internal structure of planets, the sun and other stars, orbits in binary and multiple stellar systems, the structure of molecular clouds, and, in a rough way, the structure of galaxies and clusters of galaxies (but see below).
THE GENERAL THEORY OF RELATIVITY
According to newtonian theory, gravitational effects propagate from place to place instantaneously. With the advent of Einstein's special theory of relativity in 1905, a theory uniting the concepts of space and time into that of four dimensional flat space-time (named Minkowski space-time after the mathematician Hermann Minkowski), a problem became discernible with newtonian theory. According to special relativity, which is the current guideline to the form of all physical theory, the speed of light, = 3 x 1010 cm s-1, is the top speed allowed to physical particles or forces: There can be no instantaneous propagation. After a decade of search for new concepts to make gravitational theory compatible with the spirit of special relativity, Einstein came up with the theory of general relativity (1915), the prototype of all modern gravitational theories. Its crucial ingredient, involving a colossal intellectual jump, is the concept of gravitation, not as a force, but as a manifestation of the curvature of space-time, an idea first mentioned in rudimentary form by the mathematician Ceorg Bernhard Riemann in 1854. In Einstein's hands gravitation theory was thus transformed from a theory of forces into the first dynamical theory of geometry, the geometry of four dimensional curved space-time.