♞ Kepler's Three Fundamental Laws of Planetary Motion

Tycho Brahe’s accurate observations of planetary positions provided the data used by Johannes Kepler to derive his three fundamental laws of planetary motion.
Kepler’s laws describe the behavior of planets in their orbits as follows:

(1) planetary orbits are ellipses with the Sun at one focus;

(2) in equal intervals, a planet’s orbit sweeps out equal areas; and

(3) the relationship between the orbital period (P) and the semimajor axis (a) of an orbit is given by 

P² = a³ 

(when a is in units of AU and P is in units of Earth years).