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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 ...
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 ...
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 ...
Newton's tract De motu corporum in gyrum, which he sent to Halley in late 1684, derived what is now known as the three laws of Kepler, assuming an inverse square law of force, and generalised the result to conic sections. It also extended the methodology by adding the solution of a problem on the motion of a body through a resisting medium.
Two types of central forces—those that increase linearly with distance, F = Cr, such as Hooke's law, and inverse-square forces, F = C/r 2, such as Newton's law of universal gravitation and Coulomb's law—have a very unusual property. A particle moving under either type of force always returns to its starting place with its initial velocity ...
1684 – Isaac Newton proves that planets moving under an inverse-square force law will obey Kepler's laws in a letter to Edmond Halley. [7] 1686 – Isaac Newton uses a fixed length pendulum with weights of varying composition to test the weak equivalence principle to 1 part in 1000. [9] [10]
Discovered and stated by Isaac Newton (1643–1727), they can be formulated, in modern terms, as follows: First law: A body remains at rest, or keeps moving in a straight line (at a constant velocity), unless acted upon by a net outside force. Second law: The acceleration of an object of constant mass is proportional to the net force acting ...
After these explanations were discounted, some physicists were driven to the more radical hypothesis that Newton's inverse-square law of gravitation was incorrect. For example, some physicists proposed a power law with an exponent that was slightly different from 2.