Physics
Scientific paper
Aug 1972
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972cemec...6...84s&link_type=abstract
Celestial Mechanics, Volume 6, Issue 1, pp.84-107
Physics
26
Scientific paper
This is a study of the dynamical behavior of three point masses moving under their mutual gravitational attraction in a plane. The initial positions and velocities are identical for all cases studied and only the masses of the participating bodies change in the series of numerical experiments. In this way the effect of the coupling terms in the differential equations of motion are investigated. The motion in all 125 cases begins with an interplay between the three bodies, followed by temporary ejections or by an eventual escape. The total mass of the system is kept constant while the massratios change from 1 to 5. The initial velocities being zero, the total energy is negative in all cases. Approximately 74% of the cases disintegrated (i.e. two bodies formed a binary and the third body escaped) in less than 140 time units, 47% in less than 50 time units and 10% ended in escape in less than 10 time units. Considering three stars with total mass 12M &sun;, initially placed at 3, 4 and 5 parsec distances (or three galaxies with mass 2.4×1012 M &sun;, initially placed 30, 40 and 50 kpc apart), the unit of time (approximately the crossing time) becomes 1.5×107 y (3.2×107 y). The average time of disintegration was found to be of the order of 109 y. The average semi-major axis of the binaries left behind after disintegration was 0.7 parsec and the average value of the eccentricity was 0.76. The effect of the masses on the escapes was established and it was found that the bodynot with the smallest mass escaped in 13% of the disintegrated cases. The cases which did not disintegrate in 150 time units were analyzed in detail and the time of their eventual escape was estimated. The numerical results are tabulated regarding escape time, ejection period, total energy, escape energy, terminal velocity, semi-major axis, and eccentricity. The evolution of triple systems is followed from interplays through ejections to escapes and the orbital parameters for the separation of these classes are estimated.
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