This should be more widely known, as it gives some insight into the nature of scientific truth. I understand that the explanation of this surprising result is

This should be more widely known, as it gives some insight into the nature of scientific truth. I understand that the explanation of this surprising result is related to harmonic analysis, such as Fourier series - the evolution of any periodic process in time can be just as correctly represented by a collection of harmonics of the correct amplitude and phase. This does not, however, seem to lead one to gravity, while Kepler's laws do. One thing that Newton showed is that epicycles are unnecessary as part of an explanation of planetary motion. If you were to apply the epicyclic model with sufficient precision to show the gravitational effects between the planets, I would guess you would have to include, for any one planet, epicycles with frequencies that are harmonics of the other planets' orbits. Without a theory of gravity, there is no obvious reason why that should be so.