inverse square law

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:

• The density of things, e.g., particles, sprayed equally in all directions (or throughout some specific solid angle) from a point.
• Electromagnetic radiation (EMR), similarly, from a point source.
• Sound waves from a point source.
• Gravity.
• Electric force, e.g., associated with an electron or proton.
• Gravitational waves.

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 amplitude falls off by an inverse square law in any specific direction.

An example of something that is not an inverse square law is the height of spreading ripples in a pond, e.g., from where something dropped into it. The ripples spread over just 2 dimensions instead of 3 and the height is related to 1/d rather than 1/d².