For centuries scholars such as Tycho Brahe, Johannes Kepler, and Isaac Newton have studied celestial mechanics (the motion of astronomical bodies as they move under the influence of their mutual gravitation). They analyzed the orbital motions of planets, comets, and asteroids. In fact, Newton's laws of motion and his theory of universal gravitation are the basis for celestial mechanics. Kepler's laws (first two published in 1609, the third in 1919) give a close approximation to planetary motion.
Kepler's Laws of Planetary Motion
The orbits of planets are ellipses, with the Sun at one focus.
The line joining the planet to the Sun sweeps out equal areas in equal times.
The square of the period of a planet's orbit is proportional to the cube of the semi-major axis of its orbit.
How did Kepler do it? He found his laws through observation and a detailed study of Tycho Brahe's cataloged observations. Mr. Brahe was probably the most precise observational astronomer who has ever lived. The planets obeyed the laws Kepler discovered, but he didn't know why they did...until Newton provided the explanation 40 years later...GRAVITY!