Kepler, Newton and numerical analysis

Numerical methods are usually constructed for solving mathematical problems such as differential equations or optimization problems. In this contribution we discuss the fact that numerical methods, applied inversely, were also important in establishing these models. We show in detail the discovery of the laws of planetary motion by Kepler and Newton, which stood at the beginning of modern science. The 400th anniversary of the publication of Kepler's laws (1609) is a good occasion for this investigation.