  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.
