The first law states that every planet follows an elliptical orbit with the Sun at a focus. The second law concerns the speed of a planet around its orbit, and notes that an imaginary line bet ween the planet and the Sun would sweep out the same area in the same given time (shown above).
Both these laws were published in Astronomia Nova, 1609. His third law was in the last chapter of De Harmonices Mundi, 1619. It states that the square of the time a planet takes to go round its orbit is proportional to the cube of the orbit's semi-major axis (half the diameter of the planet's orbit). But not all of Kepler's ideas were correct. One of his theories stated that planets were swept along by radiated magnetic influence from the Sun: later disproved by the Newtonian theory of gravitation (see pp.106-107).
Kepler's third law revealed the
relative sizes of the planetary orbits but not their absolute sizes. The ancient Greeks had estimated that the Sun was 1150 Earth-radii away, but Kepler's Mars calculations convinced him that the real value was far greater. There was much confusion in the 17th century - the 1687 and 1713 editions of Newton's Principia show a doubling of his estimate. Newton increased the estimated mass of the Sun by an astonishing factor of eight.
In 1716 Edmond Halley suggested a way of measuring the distance from the Earth to the Sun, using the timing of the transits of either Mercury or Venus, measured by observers over a wide range of latitudes. This method was used in 1769 to observe the Venus transit. Today we know that the Sun is about 150,000,000km (93,000,000 miles), or 23,455 Earth-radii, away.
Kepler's calculations in Astronomia Nova
This book demonstrates Kepler's mathematical workings, as he abandoned the Copernican and Ptolemaic views on the circularity of planetary orbits.