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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 ...
Here we show that a necessary condition for stable, exactly closed non-circular orbits is an inverse-square force or radial harmonic oscillator potential. In the following sections, we show that those two force laws produce stable, exactly closed orbits .
Informally, the case of a point charge in an arbitrary static electric field is a simple consequence of Gauss's law.For a particle to be in a stable equilibrium, small perturbations ("pushes") on the particle in any direction should not break the equilibrium; the particle should "fall back" to its previous position.
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.
Inductionism is the scientific philosophy where laws are "induced" from sets of data.As an example, one might measure the strength of electrical forces at varying distances from charges and induce the inverse square law of electrostatics.
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 ...
Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity. 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 the Coulomb's law, and Gauss's law for ...