§ DICTIONARY · CONCEPT
inverse-square law
Force or intensity that falls as 1/r² with distance; the form of Newton's gravity and Coulomb's law.
§ 01
Definition
An inverse-square law is any relationship in which a quantity decreases with the square of the distance from its source. Double the distance, one-quarter the strength. Triple it, one-ninth. The form shows up whenever something — force, light, sound — spreads out uniformly from a point over the surface of a sphere, because the area of that sphere grows as r².
Newton's law of universal gravitation and Coulomb's law of electrostatics are both inverse-square laws. It is specifically the inverse-square form of gravity that makes Kepler's laws geometrically exact: any other power would give open, non-closing orbits.