It fell to Kepler to provide the final piece of the puzzle: after a long struggle, in which he tried mightily to avoid his eventual conclusion, Kepler was forced finally to the realization that the orbits of the planets were not the circles demanded by Aristotle and assumed implicitly by Copernicus, but were instead the "flattened circles" …show more content…
For simplicity, we'll consider the motion of the planets in our solar system around the Sun, with gravity as the central force. Among other things, Kepler's laws allow one to predict the position and velocity of the planets at any given time, the time for a satellite to collapse into the surface of a planet, and the period of a planet's orbit as a function of its orbits' geometry. Though the laws were originally obtained by Kepler after careful analysis of empirical data, the complete understanding was missing until Newton derived each law as pieces of his orbital mechanics. In his footsteps we will obtain each law in turn, as we consider the orbit of a planet in the gravity of a massive