Lumina

Meet Lumina, a star whose light spreads thinner the farther it travels.

A star sends out power L in all directions. At a distance d, that power is spread over the surface of a sphere of area 4πd². The flux you receive, the power falling on each square metre, is therefore F = L/(4πd²). Nothing is lost on the way; the same light is simply covering more area.

Double the distance and the area grows four times, so the star looks a quarter as bright. At ten times the distance, it is a hundred times fainter. At Earth, the Sun delivers about 1,361 watts per square metre above the atmosphere. At Mars, about 1.52 times farther, the flux is around 1/1.52² ≈ 0.43 of that.

The same law, for the same geometric reason, governs sound from a point source, radiation doses from a small source, and gravity. Astronomers use it backwards: knowing how bright a type of star really is, its measured flux gives its distance.

The law assumes a point source in empty space. Dust that absorbs light, or a beam that is not spreading evenly, breaks it.