Why does gravity get weaker with distance according to the inverse-square law?

Gravity follows an inverse-square law because the influence from a point-like mass spreads outward in all directions through three-dimensional space. At twice the distance, that influence is spread over a sphere with four times the surface area, so the intensity is one-fourth as strong. Isaac Newton described this in 1687 in Principia, and it applies not only to gravity but also to light and other spreading fields. This is why Earth’s gravity is much weaker at the distance of the Moon than at the surface, even though it still keeps the Moon in orbit. The same geometry also helps explain why satellites must move fast enough to stay aloft.