Creating deterministic collisions between two orbiting bodies

TL;DR

This paper presents a mathematical framework for inducing deterministic collisions between orbiting bodies using a time-dependent external force, applicable to atomic and planetary systems.

Contribution

It introduces a novel method to cause guaranteed collisions by solving coupled nonlinear differential equations with a tailored force function.

Findings

Framework successfully predicts force functions for collisions

Applicable to atomic and planetary systems

Potential for controlled collision experiments

Abstract

We aim to create deterministic collisions between orbiting bodies by applying a time-dependent external force to one or both bodies, whether the bodies are mutually repulsive, as in the two- or multi-electron atomic case or mutually attractive, as in the planetary-orbit case. Specifically, we have devised a mathematical framework for causing deterministic collisions by launching an inner orbiting body to a higher energy such that this inner body is guaranteed to collide with the outer body. Our method first expresses the problem mathematically as coupled nonlinear differential equations with a time-dependent driving force and solves to find a feasible solution for the force function. Although our calculation is based strictly on classical physics, our approach is suitable for the case of helium with two highly excited electrons and is also valid for creating collisions in the gravitational case such as for our solar system.