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  2. Inverse-square law - Wikipedia

    en.wikipedia.org/wiki/Inverse-square_law

    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 ...

  3. Newton-Hooke priority controversy for the inverse square law

    en.wikipedia.org/wiki/Newton-Hooke_priority...

    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 ...

  4. De motu corporum in gyrum - Wikipedia

    en.wikipedia.org/wiki/De_motu_corporum_in_gyrum

    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 ...

  5. Kepler problem - Wikipedia

    en.wikipedia.org/wiki/Kepler_problem

    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.

  6. Leibniz–Newton calculus controversy - Wikipedia

    en.wikipedia.org/wiki/Leibniz–Newton_calculus...

    Newton's approach to the priority problem can be illustrated by the example of the discovery of the inverse-square law as applied to the dynamics of bodies moving under the influence of gravity. Based on an analysis of Kepler's laws and his own calculations, Robert Hooke made the assumption that motion under such conditions should occur along ...

  7. Distance decay - Wikipedia

    en.wikipedia.org/wiki/Distance_decay

    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.

  8. Binet equation - Wikipedia

    en.wikipedia.org/wiki/Binet_equation

    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 ...

  9. Earnshaw's theorem - Wikipedia

    en.wikipedia.org/wiki/Earnshaw's_theorem

    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).