Inverse Square Law

Search for ‘cause and effect of an action’ often leads to an evidence that two variables are causally related or not. Observation and measurement of actions may indicate a definite pattern by which an increase in one variable always causes another measurable quantity to increase. This is a ‘direct’ relationship. Observation might also indicate that an increase in one variable always causes another measurable quantity to decrease. This is an ‘inverse’ relationship. In physics, an ‘inverse-square law’ generally states that a specified physical parameter is inversely proportional to the square of the distance from its source. It is generally applied when some conserved quantity is radiated outward radially in three-dimensional space from a point source. Since the surface area of a sphere is proportional to the square of its radius, as the radiated parameter gets farther from its source, it is spread out over an area that is increasing in proportion to the square of the distance from the source. Hence, the intensity of radiation passing through any unit area (directly facing the point source) is inversely proportional to the square of the distance from the point source. Thus any law in which a physical quantity varies with distance from a point, inversely as the square of that distance, is called an ‘inverse square law’. As gravitational attraction is considered as an ‘attractive force’, inverse square law was adopted to determine its magnitude. Magnitude of gravitational attraction between two point-matter-bodies (masses) is directly proportional to the product of their masses (representing their 3D matter-contents) and inversely proportional to square of their separation distance. Gravitational attraction is assumed always as attractive and acting along the straight line, joining centers of two macro bodies. If distribution of 3D matter in each body is spherically symmetric, then these objects can be treated as point masses, whose whole 3D matter-contents are concentrated at their centers. To calculate magnitude of gravitational attraction between large macro bodies, we need to add all point-to-point attractions vectorially and this magnitude of net attraction might not show exact inverse square relationship. However, if distance between the macro bodies is much larger compared to their sizes, then it is reasonable to treat their 3D matter-contents (masses) as point mass while calculating (approximate) magnitude of gravitational attraction. It is evident that the magnitude of gravitational attraction between two 3D matter-bodies is in proportion to their 3D matter-contents and in inverse proportion to the distance between them. On this basis, an empirical formula is devised and used to determine magnitude of gravitational attraction between two 3D matter-bodies. As there are no references available, magnitudes of gravitational attractions are determined on empirical basis and with the help of inverse square law. Gravitational attraction is measured in terms of rate of work that can be done on a (macro) body. Rate of work-done on a physical body is the ‘force’. Hence, gravitational attraction is defined as a ‘force’ of attraction between 3D matter-bodies. Equal magnitude of ‘force’ is presumed to act on both bodies, towards each other. However, they are never taken in combination. Gravitational attraction on any one body and its effect are usually taken in isolation and the same on other body are ignored. Additional work, done on a body, changes its state (of motion). Change in the state of motion is the acceleration of the matter-body. Thus, magnitude of gravitational attraction is measured in terms of rate of additional work (force) that can change the state of motion at certain rate. Force of gravitational attraction; , where m1 and m2 are rest masses of two bodies, equivalent to their 3D matter-contents, d is the distance between their centers of gravity and G is a constant, empirically determined from experiments. Inverse square law for force of gravitational attraction is scaled by the use of a constant, G, determined by measuring inertial (that causes motion) actions of bodies due gravitational attraction between them, as it is done in the cases of various occasions, where this law is applicable. Since G is determined experimentally, no theoretical determination is attempted on logical reasons behind magnitude of this constant.