On the dynamical derivation of the Titius-Bode law

Abstract

The Principle of Least Action Interaction, developed by the dynamical astronomer Michael W. Ovenden, is tested using a new algorithm based on the ergodic hypothesis that the time mean of the disturbing function is equal to the space mean. This algorithm is an improvement over the one that Ovenden (1972) used in testing his principle, i.e. it can be applied to systems having more than three satellites without violating the conservation law of angular momentum and these satellites may have significant inclinations. This algorithm treats the problem of finding the configuration of least action interaction as a Lagrange multiplier problem. Renormalization group techniques and existing non-gradient optimization algorithms are incorporated into this new algorithm to reduce some of the numerical complexities.