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The inverse-square law, fundamental in Euclidean spaces, also applies to non-Euclidean geometries, including hyperbolic space. The curvature present in these spaces alters physical laws, influencing a variety of fields such as cosmology, general relativity, and string theory.
Newton, faced in May 1686 with Hooke's claim on the inverse square law, denied that Hooke was to be credited as author of the idea. Among the reasons, Newton recalled that the idea had been discussed with Sir Christopher Wren previous to Hooke's 1679 letter. [ 12 ] Newton also pointed out and acknowledged prior work of others, [ 13 ] including ...
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law [ 1 ] of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called the electrostatic force or Coulomb force. [ 2 ] Although the law was known earlier, it was first published in 1785 by ...
Square–cube law. The square–cube law was first mentioned in Two New Sciences (1638). The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases.
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Coulomb's law has charge in place of mass and a ...
According to this equation, the second force F 2 (r) is obtained by scaling the first force and changing its argument, as well as by adding inverse-square and inverse-cube central forces. For comparison, Newton's theorem of revolving orbits corresponds to the case a = 1 and b = 0, so that r 1 = r 2. In this case, the original force is not ...
A recent assessment about the early history of the inverse square law is that "by the late 1660s", the assumption of an "inverse proportion between gravity and the square of distance was rather common and had been advanced by a number of different people for different reasons". [86]
In classical physics, many important forces follow an inverse-square law, such as gravity or electrostatics. The general mathematical form of such inverse-square central forces is F = α r 2 = α u 2 {\displaystyle F={\frac {\alpha }{r^{2}}}=\alpha u^{2}} for a constant α {\displaystyle \alpha } , which is negative for an attractive force and ...