NUMERICAL CALCULATION OF THE PLEIADES PROBLEM IN CAS MAXIMA ENVIRONMENT

Abstract

Model problems of celestial mechanics are described by means of differential equations or their systems. It is well known that the many-body problem is intractable in an analytical form, so numerical methods must be used to simulate the motion of stars or their clusters. For gravitationally bound objects, problems arise that are difficult to model even with a computer, since the model under consideration is often rigid, i.e., there is a significant dependence of the solution evolution on the initial conditions. This paper proposes a scheme for solving the seven-body problem of the Pleiades star cluster. The calculations are carried out in the open system of computer algebra Maxima, which provides all the necessary tools for both direct calculations and visualization of the results. The method of solving the Runge-Kutta-Felberg differential equations of the 5th order is used, and graphs of stellar trajectories and the dependence of their apparent coordinates on the celestial sphere on time are plotted.