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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 ...
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 observational result of Hubble's law, the proportional relationship between distance and the speed with which a galaxy is moving away from us, usually referred to as redshift, is a product of the cosmic distance ladder. Edwin Hubble observed that fainter galaxies are more redshifted. Finding the value of the Hubble constant was the result ...
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 ...
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 ...
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 ...
Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account. The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance.
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 .