$$\LaTeX$$ Formula Editor for Blogger

Saturday, January 4, 2014

On the Principle of Least Action Interaction (Ovenden)


The history of the Titius-Bode Law is summarized, and possible explanations for the law are examined. Numerical integrations confirm the intuition that any N-body point-mass planetary system spends most of its time in configurations where the planetary interactions are least. This result is formalized into the Principle of Least Interaction Action, viz. that such a system will most often be found in a configuration where the time-mean of the action associated with the mutual interactions of the planets is a local minimum. It is shown that this principle leads to the resonant structures predicted (by a complementary argument) by Roy and Ovenden (1955), and found in the satellite systems of Jupiter and Saturn. Time-scale estimates show that the time of relaxation from an arbitrary configuration is short compared with the time spent near such a minimum interaction configuration. These results suggest that the present distribution of planetary and satellite orbits is the result of mutual perturbations, that tidal forces need not be invoked, and that the present distribution gives no information concerning the origin of the solar system.

However, if it can be shown that processes operate within the solar system that can rearrange the planetary orbits on a su~iciently short time-scale then we must conclude that the present distribution of planetary and satellite orbits contains no information about conditions at the time of formation of the solar system. The rest of this paper will be devoted to providing evidence that such a process does exist, in the mutual gravitational perturbations of one planet or satellite upon another.

From all these integrations a general characteristic stands out clearly. A system spends a short time with the planets close together and interacting violently, and spends most of its time with the planets far apart and interacting mildly, as is indeed to be expected from the most elementary consideration. We now formalize this elementary consideration into The Principle of Planetary Claustrophobia, namely that, in any system, the planets will spend most of their time as far away from each other as possible.

No comments:

Post a Comment