Copernicus' Theorem

Copernicus' Theorem states that if an object moves in a circular path under the influence of a force directed toward the center (like gravity), the period of its orbit squared is proportional to the radius of that path cubed. Mathematically, \( T^2 \propto R^3 \). This relation helps explain planetary motions: planets farther from the Sun take longer to orbit, following this precise mathematical relationship. The theorem was crucial in developing the heliocentric model, showing that planetary orbits follow predictable patterns consistent with circular motion under central forces.