In 1609 Kepler published his first two laws of planetary motion deduced from his studies of Tycho Brahe's data on Mars.  This appeared in his book Astronomia nova .

(1) The planets move in elliptical orbits about the sun, with the sun at one of the foci of the ellipse.

(2) The radius vector from the sun to the planet sweeps out equal areas for equal times.


(3) The third law appeared in 1619 in his book Harmonices mundi .
This states that the square of the period of a planet's motion divided by the semi major axis cubed is a constant.


Kepler himself did not know why the constant k has this value. This came out only after Newton's discovery of universal gravitation.