Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011dda....42.0606s&link_type=abstract
American Astronomical Society, DDA meeting #42, #6.06; Bulletin of the American Astronomical Society, Vol. 43, 2011
Astronomy and Astrophysics
Astronomy
Scientific paper
Closed celestial mechanics systems have two fundamental conservation principles that enable their deeper analysis: conservation of momentum and conservation of (mechanical) energy. Of the two, conservation of momentum provides the strongest constraints as these quantities are always conserved independent of the internal interactions of the system. Conservation of energy instead involves assumptions on the nature of internal interactions within the system and is not conserved for ``real'' systems that involve tidal deformations or impacts. Thus mechanical energy generally decays through dissipation until the system has found a local or global minimum energy configuration that corresponds to its constant level of angular momentum. This observation motivates a fundamental question for celestial mechanics: What is the minimum energy configuration of a N-body system with a fixed level of angular momentum?
For a system of point masses this question cannot be fully answered as for N >= 3 we find degenerate minimum energy configurations for any fixed angular momentum. However, introduction of bodies with a finite density allows this question to be asked and studied. We call such a physically corrected system the ``Full N-Body Problem,'' as inclusion of finite density also necessitates the modeling of the rotational motion of the components and their potential contact, which is not needed for consideration of point masses. With this correction the minimum energy configurations for an N-body system can be explicitly defined and computed for a given level of angular momentum.
This talk will introduce these concepts and discuss minimum energy configurations of N-body systems, for small values of N, as a function of total angular momentum. These considerations provide strong constraints and results that more general numerical integration routines must respect. They also provide insight into how rubble pile asteroids, or any self-gravitating granular material, may evolve over time.
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