Derivation of Evolutionary Equations in the Many-Body Problem with Isotropically Varying Masses Using Computer Algebra

Abstract

The influence of the variability of the masses of celestial bodies on the dynamic evolution of planetary systems is investigated in the case when the masses of the bodies change isotropically at different rates, and the laws of mass change are assumed to be arbitrary given functions of time. The classical problem of n + 1 bodies of variable mass when $$n$$ bodies move around a central star in quasi-elliptic nonintersecting orbits and interact according to the law of universal gravitation is used as a model of multi-planet system. Differential equations of body motion in terms of the osculating elements of aperiodic motion in quasi-conic sections are derived. An algorithm for calculating the perturbing function in the form of power series in small parameters and the derivation of differential equations determining the secular perturbations of the orbital elements are discussed. All symbolic computations are carried out using the computer algebra system Wolfram Mathematica.

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