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 on the reciprocal 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 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 inverse-square examples:

• The density of things, e.g., particles, sprayed in all directions (or covering 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.

Phenomena that are not inverse square:

• 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.
• gravitational waves, also 1/d, more like ripples in a pond than like EMR or sound waves.