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An inverse square law is a scientific law (i.e., well-established model) asserting that some value depends upon the distance from something, more specifically, proportional to the reciprocal ("inverse") of the square of that distance (1/d²). If that something is a point or spherically symmetric body, then given any distance (i.e., the radius of a sphere centered on the point), the sum (integral) of the value across all points at any such given distance is the same. An inverse square law generally implies three-dimensional Euclidean space, and serves as an approximation if the space is close to that, such as are current models of the universe. Some common physical phenomena adhering to inverse square laws:
These all fall off with the square of the distance from the source, but it still may be the case that the amount also depends upon the direction from the source: for example, the source of the recently detected gravitational waves produces the strongest waves out over a plane. However, once produced, their energy density falls off by an inverse square law in any specific direction.
An example of something that is not an inverse square law is something spreading across a surface, such as the energy carried by a fixed-arclength portion of a spreading circular ripple from something dropped in a pond, such as the energy per inch-length portion of the circle. The ripple spreads over just 2 dimensions instead of 3 and the energy carried by such a portion of the ripple is related to 1/radius rather than 1/radius². After the circular ripple has increased to twice some particular radius, each inch of the circle then carries half the energy analogously carried by an inch of the circle when it had the earlier radius.