TABLE OF CONTENTS Among the most important developments in the history of the scientific method is Newton's analytical solution of the two-body problem. In Astronomia Nova (1609), Kepler published the first essentially correct solution for the motion of planets around the sun, where the solution was obtained by solving the inverse problem of "given the observed (measured) right ascension and declination history of a planet, determine a mathematical model which captures the behavior with sufficient rigor that predictions as accurate as the measurements can be made." Kepler was seeking to modify the historical work of Copernicus, who modeled the planet paths as circular orbits about the sun. Kepler was intrigued by Tycho Brahe's observations of the orbit of Mars which appeared to deviate significantly from the Copernican circular model, and in the course of developing a model that fit the data for Mars and all of the other more circular planetary orbits, he conjectured that the motion was actually an ellipse with the sun at a focus. Kepler's elegant geometric analysis amounted to an insightful, sophisticated curve-fitting operation, but was found to be in such excellent agreement with the measurements of the day, that his laws of planetary motion were considered exact.
Newton, in his quest to develop calculus, differential equations, and his famous laws of motion, was fascinated...
