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The divergence of a vector field which is the resultant of radial inverse-square law fields with respect to one or more sources is proportional to the strength of the local sources, and hence zero outside sources. Newton's law of universal gravitation follows an inverse-square law, as do the effects of electric, light, sound, and radiation ...
In addition, Newton had formulated, in Propositions 43–45 of Book 1 [16] and associated sections of Book 3, a sensitive test of the accuracy of the inverse square law, in which he showed that only where the law of force is calculated as the inverse square of the distance will the directions of orientation of the planets' orbital ellipses stay ...
Later, in 1686, when Newton's Principia had been presented to the Royal Society, Hooke claimed from this correspondence the credit for some of Newton's content in the Principia, and said Newton owed the idea of an inverse-square law of attraction to him – although at the same time, Hooke disclaimed any credit for the curves and trajectories ...
Distance decay is a geographical term which describes the effect of distance on cultural or spatial interactions. [1] The distance decay effect states that the interaction between two locales declines as the distance between them increases.
The inverse square law behind the Kepler problem is the most important central force law. [1]: 92 The Kepler problem is important in celestial mechanics, since Newtonian gravity obeys an inverse square law. Examples include a satellite moving about a planet, a planet about its sun, or two binary stars about each other.
This statement was later condensed into the following inverse-square law: F = G m 1 m 2 r 2 , {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},} where F is the force, m 1 and m 2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant 6.674 × 10 −11 m 3 ⋅kg −1 ⋅s ...
Earnshaw's theorem applies to classical inverse-square law forces (electric and gravitational) and also to the magnetic forces of permanent magnets, if the magnets are hard (the magnets do not vary in strength with external fields).
The traditional Kepler problem of calculating the orbit of an inverse square law may be read off from the Binet equation as the solution to the differential equation = (+) + = > If the angle θ {\displaystyle \theta } is measured from the periapsis , then the general solution for the orbit expressed in (reciprocal) polar coordinates is l u = 1 ...