期刊
ASTROPHYSICAL JOURNAL LETTERS
卷 785, 期 1, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/2041-8205/785/1/L3
关键词
chaos; gravitation; methods: numerical; methods: statistical; planets and satellites: dynamical evolution and stability; stars: kinematics and dynamics
资金
- Netherlands Research Council NWO [643.200.503, 639.073.803, 614.061.608]
- Netherlands Research School for Astronomy (NOVA)
The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-body interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.
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