Perturbations of planetary orbit parameters due to decreasing in stellar mass and the expansion of the universe from a classical approach

Abstract

In this analysis we found the disturbances caused by the decrease in stellar mass and the expansion of the universe, to three fundamental parameters that represented the stability of a planetary orbit: the period, the semi-major axis and the eccentricity. First, by assuming much greater the mass of the star than the planetary, the star-planet interaction is reduced to a single-body problem with origin of reference system lying in the greater mass; and, through the mathematical formalism of the central forces, the variations of the three orbital parameters to be considered were obtained. As a result, the variations corresponding to the period and semi-major axis have been characterized in their mathematical structure by the terms that describe each phenomenon; namely, ξ ∼ 2.16 × 10−21 for the case of Sun, and ̈α/α ∼ 3 × 10−36 concerning the decrease in stellar mass and the expansion of the universe, respectively. In the case of eccentricity, it is shown that this parameter is an invariant quantity under the disturbances produced by these two cosmological phenomena.