structural:scholar_edition
Astronomia Nova

The extended line of research that culminated in Astronomia Nova (A New Astronomy)—including the first two laws of planetary motion —began with the analysis, under Tycho's direction, of the orbit of Mars. In this work Kepler introduced the revolutionary concept of planetary orbit, a path of a planet in space resulting from the action of physical causes, distinct from previously held notion of planetary orb (a spherical shell to which planet is attached). As a result of this breakthrough astronomical phenomena came to be seen as being governed by physical laws. Kepler calculated and recalculated various approximations of Mars's orbit using an equant (the mathematical tool that Copernicus had eliminated with his system), eventually creating a model that generally agreed with Tycho's observations to within two arcminutes (the average measurement error). But he was not satisfied with the complex and still slightly inaccurate result; at certain points the model differed from the data by up to eight arcminutes. The wide array of traditional mathematical astronomy methods having failed him, Kepler set about trying to fit an ovoid orbit to the data.

In Kepler's religious view of the cosmos, the Sun (a symbol of God the Father) was the source of motive force in the Solar System. As a physical basis, Kepler drew by analogy on William Gilbert 's theory of the magnetic soul of the Earth from De Magnete (1600) and on his own work on optics. Kepler supposed that the motive power (or motive species) radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it. Perhaps this assumption entailed a mathematical relationship that would restore astronomical order. Based on measurements of the aphelion and perihelion of the Earth and Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun. Verifying this relationship throughout the orbital cycle required very extensive calculation; to simplify this task, by late 1602 Kepler reformulated the proportion in terms of geometry: planets sweep out equal areas in equal times —his second law of planetary motion.

He then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped ovoid orbit. After approximately 40 failed attempts, in late 1604 he at last hit upon the idea of an ellipse, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. Finding that an elliptical orbit fit the Mars data (the Vicarious Hypothesis), Kepler immediately concluded that all planets move in ellipses, with the Sun at one focus —his first law of planetary motion. Because he employed no calculating assistants, he did not extend the mathematical analysis beyond Mars. By the end of the year, he completed the manuscript for Astronomia nova, though it would not be published until 1609 due to legal disputes over the use of Tycho's observations, the property of his heirs.