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Loss of Energy and Angular Momentum in Disrupting N-body Systems

Presentation #106.03 in the session “Impacts, Collisions, and Disruptions”.

Published onJun 01, 2021

Loss of Energy and Angular Momentum in Disrupting N-body Systems

This work studies how the initial energy and angular momentum of an N-body system is lost as the system naturally disrupts due to multi-body dynamical interactions. The systems studied are close to initially symmetric N-body configurations, which under the influence of gravitational attraction between the bodies generally end up as ejected singles or pairs of bodies. These types of self-disrupting systems are of particular interest in their applications to problems in the field of astromechanics, such as in rubble-pile asteroid formation. The specific question of interest is the amount of angular momentum and energy that is lost from an original distribution of bodies due to gravitational ejection.The initial conditions were chosen to be symmetric N-gon central configurations with random perturbations applied to the position of one of the bodies. These systems were then propagated in time using the nondimensional Jacobi formulation of the N-body problem until either a maximum duration of time was reached or all but two bodies had been ejected. At the final state, orbital parameters of the ejected bodies were calculated and how the energy and angular momentum were partitioned between the ejected masses and the remaining masses was determined. By repeating this process for a number of random perturbations, general results were identified by analyzing the aggregate statistics of these simulations. This study specifically considered systems consisting of between 3 and 6 bodies with equal masses, with ejections of pairs of bodies being considered for systems where N > 3. Two sets of simulations for N=3 have already been completed with 1000 simulation runs per set. The third body was ejected in just under 97.5% of these simulations, 2.2% of these simulations reached the maximum propagation time, and just under 0.4% produced an error, likely due to close approaches. In 79.5% of all simulations a departure was detected in the first 5% of the maximum propagation time. Of the simulations where a departure was detected, the percentage of the total angular momentum taken by the ejected body appeared to follow a normal distribution with a mean of 88.7% and a standard deviation of 5.3%. Also of note, in 1.7% of these runs, the angular momentum taken by the ejected body was larger in magnitude than the initial total angular momentum vector, meaning that the remaining binary was forced to rotate in the opposite direction. The percentage of the total energy taken by the ejected body followed a different pattern than the angular momentum. As the percentage of energy taken by the ejected body increased, the number of simulations that produced this result decreased dramatically. One third of these simulations resulted in the ejected body taking less than 4.23% of the initial energy, one third resulted in the ejected body taking between 4.23% and 11.5%, and the final third resulted in the ejected body taking between 11.5% and 53.54%. Additional data is being generated for 4 and 5 body systems, with the goal of performing preliminary analysis on 6 and 7 body systems.