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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; Kepler orbit – Celestial orbit whose trajectory is a conic section in the orbital plane
Examples include gravity and electromagnetism as described by Newton's law of universal gravitation and Coulomb's law, respectively. The problem is also important because some more complicated problems in classical physics (such as the two-body problem with forces along the line connecting the two bodies) can be reduced to a central-force problem.
In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses that orbit each other in space and calculate their subsequent trajectories using Newton's laws of motion and Newton's law of universal gravitation.
Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitation in classical physics.
Coulomb's law and Newton's law of universal gravitation are based on action at a distance. Historically, action at a distance was the earliest scientific model for gravity and electricity and it continues to be useful in many practical cases. In the 19th and 20th centuries, field models arose to explain these phenomena with more precision.
Both Robert Hooke and Newton were well aware that Newton's Law of Universal Gravitation did not hold for the forces associated with elliptical orbits. [10] In fact, Newton's Universal Law does not account for the orbit of Mercury, the asteroid belt's gravitational behavior, or Saturn's rings. [27]
For an inverse-square law such as Newton's law of universal gravitation, where n equals 1, there is no angular scaling (k = 1), the apsidal angle α is 180°, and the elliptical orbit is stationary (Ω = β = 0). As a final illustration, Newton considers a sum of two power laws +
Ultimately, this led to the development of the parametrized post-Newtonian formalism by Nordtvedt and Will, which parametrizes, in terms of ten adjustable parameters, all the possible departures from Newton's law of universal gravitation to first order in the velocity of moving objects (i.e. to first order in /, where v is the velocity of an ...
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