Solving Many Point Particle Interactions Using the Kepler Route

Events in nature can be described using fields and their associated partial differential equations, or equivalently, the mechanics of interaction of point particles described by ordinary differential equations. The field approach can be looked at as the statistical average of the particle approach and in this sense is more economical for computing. The particle approach, on the other hand, is more fundamental but requires enormous computing power as the model has to follow the movements of every individual particle in the interaction. The present work aims at reducing such computing task by solving the problem of many particle interactions (under a central force environment) in an analytical form for one pair of particlesusing a Kepler type formula- giving the position of the particle as a function of time only. The resulting (analytical) formula is then used to write the result of the many-particle interaction using simple vector superposition. This approach takes less computing time and can give greater numerical stability when the distances between the particles become small and the force grows as the inverse square of the separation distance.