Bounds on energy and angular momentum loss in the full n-body problem

Abstract

AbstractA new bound on the amended potential in an n-body system is derived and applied to the partitioning of energy and angular momentum in a disrupting gravitational aggregate. This result provides analytic insight into how energy and angular momentum can be lost or partitioned between different collections of bodies as they escape from each other. To better understand the possible outcomes in such a situation, some specific numerical tests are also performed for systems of $$N = 3, 4, 5, 6$$ N = 3 , 4 , 5 , 6 . The results confirm that disrupting systems always lose energy, with a characteristic stochastic distribution of the lost energy. We also find that the system loses most of its angular momentum, although individual escaping components can retain significant nonzero angular momentum vectors that can be uniformly distributed in space as the number of bodies in the system increases.