Kepler's laws of planetary motion accurately explain and predict the motion of the planets. He made observations over many years, and was able two deduce three mathematical laws.
1.
The orbit of each planet about the Sun is an ellipse with the Sun at one focus.
2.
A line connecting the Sun and a particular planet sweeps out equal areas in equal time, or equivalently the rate at which the line sweeps out the area,
is constant. This is equivalent to the conservation of angular momentum of the planet around the Sun. Mathematically,
where
but
so if
is constant, so is
3. The square of the orbital period of the planet about the Sun is proportional to the cube of the average distance from the Sun. This was an empirical observation and was not understood theoretically until Newton's Law of Gravity was known.