Astronomia nova

Johannes Kepler's Astronomia nova, published in 1609, contains the results of the astronomer's ten year long investigation of the motion of Mars. The full title of his work, in English, is New Astronomy, Based upon Causes, or Celestial Physics, Treated by means of Commentaries on the Motions of the Star Mars, from the Observations of Tycho Brahe, Gent. Where previous astronomers had relied on geometric models to explain the observed positions of the planets, Kepler sought for and discovered physical causes for planetary motion. He based his work on the observations of Danish astronomer Tycho Brahe.

The Astronomia nova also relates Kepler's discovery of first two of his three laws of planetary motion

These are:

That the planets move in elliptical orbits with the sun at one focus, and
That the speed of the planet changes at each moment such that the time between two positions is always proportional to the area swept out on the orbit between these positions.

Kepler discovered the second law before the first. He noticed that the speed of the planet varied inversely based upon its distance from the Sun, and therefore he could measure changes in position of the planet by adding up all the distance measures, or looking at the area along an orbital arc.

Kepler did not accept the observations by Tycho as facts but rather vigorously investigated them for embedded errors. He discovered that the assumption that the Sun or Earth (depending on whether a heliocentric or geocentric model is used) skewed the results of critical measurements. In Part II of the Astronomia nova he also demonstrated conclusively that the prevailing models of planetary motion could not be made to work by simply revising them, and the new systems and causes needed to be sought.

Part III of Kepler's work contains his discussion of gravitation, and in Part IV he discovers that the orbit of Mars can not be circular, but must rather describe some sort of oval shape. He subsequently recounts his realization that the shape of the orbit conformed to one of the four conic sections, the ellipse.

Kepler discovered his "third law" a decade after the publication of the Astronomia nova, shortly after his work Harmonices Mundi (Harmonies of the world) was sent to the printer. In the process of his investigation of harmonic relationships in the Solar System he found that the ratio of the length of the semi-major axis of each planet's orbit (squared), to the time of its orbital period (cubed), is the same for all planets.