Numerical modeling of material points evolution in a system with gravity

TL;DR

This study models the gravitational evolution of material points in 3D space, analyzing velocity distributions, particle evaporation, and system stability under various initial conditions, revealing weak dependence of chaos measures on initial energy ratios.

Contribution

It provides a detailed numerical analysis of gravitational particle systems, including velocity evolution, evaporation rates, and Lyapunov exponents, under different initial distributions and energy ratios.

Findings

Evaporated particle fraction varies between 0.45 and 0.63.

Lyapunov exponent is approximately 10^-5, indicating weak chaos.

Divergence time of trajectories is about 40-50 thousand years.

Abstract

The evolution of material points interacting via gravitational force in 3D space was investigated. At initial moment points with masses of 2.48 Sun masses are randomly distributed inside a cube with an edge of 5 light-years. The modeling was conducted at different initial distributions of velocities and different ratios between potential and kinetic energy of the points. As a result of modeling the time dependence of velocity distribution function of points was obtained. Dependence of particles fraction which had evaporated from initial cluster on time for different initial conditions is obtained. In particular, it was obtained that the fraction of evaporated particles varies between 0,45 and 0,63. Mutual diffusion of two classes of particles at different initial conditions in the case when at initial moment of time both classes of particles occupy equal parts of cube was investigated. The maximum Lyapunov exponent of the system with different initial conditions was calculated. The obtained value weakly depends on the ratio between initial kinetic and potential energies and amounts approximately 10^-5. Corresponding time of the particle trajectories divergence turned out to be 40-50 thousand years.