Constraints on Newtonian Interplanetary Point-Mass Interactions in Multicomponent Systems from the Symmetry of Their Cycles

Abstract

Interplanetary interactions are the largest forces in our Solar System that disturb the planets from their elliptical orbits around the Sun, yet are weak (<10−3 Solar). Currently, these perturbations are computed in pairs using Hill’s model for steady-state, central forces between one circular and one elliptical ring of mass. However, forces between rings are not central. To represent interplanetary interactions, which are transient, time-dependent, and cyclical, we build upon Newton’s model of interacting point-mass pairs, focusing on circular orbits of the eight largest bodies. To probe general and evolutionary behavior, we present analytical and numerical models of the interplanetary forces and torques generated during the planetary interaction cycles. From symmetry, over a planetary interaction cycle, radial forces dominate while tangential forces average to zero. Our calculations show that orbital perturbations require millennia to quantify, but observations are only over ~165 years. Furthermore, these observations are compromised because they are predominantly made from Earth, whose geocenter occupies a complex, non-Keplerian orbit. Eccentricity and inclination data are reliable and suggest that interplanetary interactions have drawn orbital planes together while elongating the orbits of the two smallest planets. This finding is consistent with conservation principles governing the eight planets, which formed as a system and evolve as a system.