Limits on Energy and Angular Momentum in the Full N-Body Problem

The range of energies and angular momentum that exist for the full N-Body problem when components are resting on each other is studied. Using a simple model of equal sized spheres, lower and upper bounds on a system’s energy are found for the collection to remain connected as a single body, up to N = 21. The lower bound is developed based on a continuum limit combined with the packing fraction of a granular media. To find the upper bound we use previous results on the existence and stability of a “straight-line” Euler resting configuration of N bodies that represents the extreme limit of a connected single body. Combined, these provide a range of energies and angular momentum values that a collection of N bodies can sustain before the system must fission into two or more components. Connections between these limits and other bounds on full N-body systems are investigated.