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Dynamical evolution of triple systems with big differences in the masses of bodies. A criterion for stability

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Abstract

The dynamical evolution of about 1.5 million planar hierarchical triple systems with a negative total energy and different-mass bodies is investigated by computer simulations. We considered both cases — prograde and retrograde motions of bodies. For every system, calculations were carried out either till a time when the Marchal'set al. (1984) criterion of escape of a body from a triple system was satisfied (the unstable triple systems) or during 1000 rotations of a total system (the stable triple systems). Computations were carried out on three computers-Sunstations in the Physical Research Laboratory, Ahmedabad, India during several months continuously. We changed smoothly the initial value of the coefficient of hierarchy of triples

$$q = r_{3 - 12} /r_{12} $$

Wherer 12 is a distance between close bodiesM1,M2 andr 3–12 is a distance between their center of masses and a distant bodyM3. We define critical (minimum) values of the coefficientq of hierarchy of stable triple systems with a relative accuracy δq=1%. Ratios of masses of bodies belong to the interval [0.13, 244.00].

A possibility of extention of these results for hierarchical subsystems with different multiplicities inside clusters is discussed.

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  1. Department of Aerospace Engineering, University of Texas at Austin, 78712-1085, TX, USA

    J. Anosova

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  1. J. Anosova
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Anosova, J. Dynamical evolution of triple systems with big differences in the masses of bodies. A criterion for stability. Astrophys Space Sci 238, 223–238 (1996). https://doi.org/10.1007/BF00641690

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  • DOI: https://doi.org/10.1007/BF00641690

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