The Orbital Distances Law in Planetary Systems

A new approach is proposed for the old problem of the planetary orbital distances in the Solar System. The solution is a simple exponential formula of the type: an= C e 2n/k. The same formula with different parameters could be used also for a large number of satellites of the giant planets Jupiter, Saturn, Uranus, and Neptune. The inner and the most massive satellites follow the respective exponential law, but the less massive outer satellites generally do not. The same exponential law, with different parameters, seems to apply also to the extra-solar planetary systems of 55 Cancri and HD 160691. The general conclusion is that orbital distances in planetary systems are not completely at random: The most massive bodies around stars and planets follow an exponential rule. This is a severe constrain on any theory of the origin of the Solar System. The inclusion of two extra-solar planetary systems (55 Cancri and HD 160691) seems to corroborate this approach also for other planetary systems. The solution for 55 Cancri, however, implies a “missing” planet at n=5. The solution for HD 160691 implies a missing “planet” at n=2. The exponential orbital distances law in planetary systems casts serious doubts on existing theories of the origin of the Solar System, which are based on gravitational collapse. Radically new ideas may be necessary to deal with the problem of the origin of planetary systems.