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In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal gravitation. It is named after Carl Friedrich Gauss. It states that the flux (surface integral) of the gravitational field over any closed surface is proportional to the mass enclosed. Gauss's ...
Gauss's law for gravity – Restatement of Newton's law of universal gravitation Jordan and Einstein frames – different conventions for the metric tensor, in a theory of a dilaton coupled to gravity Pages displaying wikidata descriptions as a fallback
The standard gravitational parameter GM appears as above in Newton's law of universal gravitation, as well as in formulas for the deflection of light caused by gravitational lensing, in Kepler's laws of planetary motion, and in the formula for escape velocity. This quantity gives a convenient simplification of various gravity-related formulas.
The equivalent field equation in terms of mass density ρ of the attracting mass is: = = which contains Gauss's law for gravity, and Poisson's equation for gravity. Newton's law implies Gauss's law, but not vice versa; see Relation between Gauss's and Newton's laws .
The inertial trajectories of particles and radiation in the resulting geometry are then calculated using the geodesic equation. As well as implying local energy–momentum conservation, the EFE reduce to Newton's law of gravitation in the limit of a weak gravitational field and velocities that are much less than the speed of light. [4]
As a consequence of the law of gravitation and Kepler's third law, k is directly proportional to the square root of the standard gravitational parameter of the Sun, and its value in radians per day follows by setting Earth's semi-major axis (the astronomical unit, au) to unity, k:(rad/d) = (G M ☉) 0.5 ·au −1.5.
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.
In fact, any inverse-square law can be formulated in a way similar to Gauss's law: for example, Gauss's law itself is essentially equivalent to Coulomb's law, and Gauss's law for gravity is essentially equivalent to Newton's law of gravity, both of which are inverse-square laws.