The planets keep a secret pact: square a planet’s YEAR and it always equals the cube of its DISTANCE from the sun. Mercury races; Neptune crawls; and the ratio between them was fixed before anyone measured it. Kepler found it in Tycho’s data; Newton later showed it falls out of gravity. Slide the distance and read the year.
Kepler’s third law: for anything orbiting the sun, T² = a³ when the period T is in years and the semi-major axis a in astronomical units — the square of the year equals the cube of the distance. Newton generalised it to T² = 4π²a³/(GM), revealing it as a consequence of gravity and a way to WEIGH the central body. A fail-loud self-check throws unless T²/a³ stays ~1 across the real planets (Mars 1.881² ≈ 1.524³), the constant Kepler saw.
T²=a³ in solar units assumes the sun’s mass dominates (the exact law carries 1/M); eccentric orbits use the semi-major axis, which this treats as the radius. The relation is exact for two-body Keplerian motion.