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Newton's law of gravity says that the gravitational force felt on mass m i by a single mass m j is given by [15] = ‖ ‖ ‖ ‖ = ‖ ‖, where G is the gravitational constant and ‖ q j − q i ‖ is the magnitude of the distance between q i and q j (metric induced by the l 2 norm).
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun
Gravity field surrounding Earth from a macroscopic perspective. Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors.
Bentley's paradox (named after Richard Bentley) is a cosmological paradox pointing to a problem occurring when Newton's theory of gravitation is applied to cosmology. Namely, if all the stars are drawn to each other by gravitation, they should collapse into a single point.
It is an attribute of matter, radiation, and non-gravitational force fields. The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity. Because this tensor has 2 indices (see next section) the Riemann ...
The Cauchy problem (sometimes called the initial value problem) is the attempt at finding a solution to a differential equation given initial conditions. In the context of general relativity , it means the problem of finding solutions to Einstein's field equations - a system of hyperbolic partial differential equations - given some initial data ...
The gravitational force exerted on a body at radius r will be proportional to / (the inverse square law), so the overall gravitational effect is proportional to / =, so is linear in . These results were important to Newton's analysis of planetary motion; they are not immediately obvious, but they can be proven with calculus .
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.