Kepler's Third Law

Kepler's Third Law links an orbit's size to its period (the time for one lap):

T² ∝ a³

The period squared is proportional to the semi-major axis cubed. Bigger orbits take disproportionately longer — double the size and the period grows by 2^1.5 ≈ 2.83×.

This one law lets astronomers weigh the cosmos. Measure a moon's orbital size and period, and the same relationship (with the full constant, T² = 4π²a³/μ) hands you the mass of the planet it circles. It is how we know the mass of the Sun, of Jupiter, even of black holes.