Kepler's Laws

Kepler's three laws (1609, 1619) describe planetary motion — empirical, derived from Tycho Brahe's data; later explained by Newton's gravity.

1st law (LAW OF ORBITS): each planet moves in an ELLIPSE with the Sun at one FOCUS.

2nd law (LAW OF AREAS): the line joining planet to Sun sweeps out equal AREAS in equal times. Consequence of conservation of angular momentum (no torque from a central force).

3rd law (LAW OF PERIODS): square of orbital period ∝ cube of semi-major axis. T² = (4π²/GM)·a³.

Applies to any small body orbiting a much larger one (planets/Sun, moons/planet, satellites/Earth).

2nd law implies planets move FASTER at PERIHELION (closest to Sun) and SLOWER at APHELION.

Newton showed Kepler's laws follow from the inverse-square attractive force.

Bonus: Kepler's 3rd law lets us measure the mass of the central body if T and a are known.