An algorithm for coalescence of classical objects and formation of planetary systems

TL;DR

This paper extends the central difference algorithm to include object fusion during collisions, enabling simulation of the self-assembly and long-term stability of planetary systems.

Contribution

It introduces a novel extension of Newton's discrete dynamics algorithm to model object coalescence in astrophysical simulations.

Findings

Simulated emergence of twelve stable planetary systems.

Systems remain stable over long times despite collisions.

The extended algorithm accurately models celestial object fusion.

Abstract

Isaac Newton formulated the central difference algorithm (Eur. Phys. J. Plus (2020) 135:267) when he derived his second law. The algorithm is under various names ("Verlet, leap-frog,...") the most used algorithm in simulations of complex systems in Physics and Chemistry, and it is also applied in Astrophysics. His discrete dynamics has the same qualities as his exact analytic dynamics for contineus space and time with time reversibility, symplecticity and conservation of momentum, angular momentum and energy. Here the algorithm is extended to include the fusion of objects at collisions. The extended algorithm is used to obtain the self-assembly of celestial objects at the emergence of planetary systems. The emergence of twelve planetary systems is obtained. The systems are stable over very long times, even when two "planets" collide or if a planet is engulfed by its sun.