Estabilidad del sistema solar a partir de una perturbación en su contenido energético

Abstract

In this work we found the perturbations caused by the expansion of the universe and the decrease of the solar mass, to the stability of the solar system when it was represented in the invariance of four orbital properties: the period, the semimajor axis, the eccentricity and the precession of the orbit. In the first place, the solar system assumed as a problem of two bodies interacting, was solved by means of the mathematical formalism of the central forces and the mechanics of Hamilton-Jacobi; and by means of a perturbation in the hamitonian function referred to the center of masses, the affectations characterized in their mathematical structure were found by the terms that describe each phenomenon. Finally, these perturbations were compared by means of a quantitative analysis of the mathematical expression that represented them, and the physical meaning that emerged from the results. As a consequence, only in the case of the semimajor axis, the decrease in the solar mass achieved a ``significant'' change for planets in which the product between its period and the initial semimajor axis is comparable in orders of magnitude to the term related with de decrease of the solar mass. For all other events, the changes made by the phenomena to the orbital factors were so insignificantly small, that the solar system could be considered governed by two bodies as a stable system.