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Astron. Astrophys. 346, 652-662 (1999)

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Escape with the formation of a binary in two-dimensional three-body problem. I

Navin Chandra and K.B. Bhatnagar

Centre for Fundamental Research in Space Dynamics and Celestial Mechanics IA/47C, Ashok Vihar, New Delhi-110 052, India

Received 10 September 1998 / Accepted 25 January 1999


The escape with the formation of a binary in three-body problem is studied in a series of two papers. This paper deals with the systematic regularity of escape with the formation of a binary with low perturbing velocities for equal masses in the evolution of stellar systems in a plane. The main results are: (a) For triple close approaches [FORMULA] (b) [FORMULA] (c) [FORMULA] where [FORMULA] is the minimum moment of inertia of the system, C is the angular momentum, [FORMULA] the total energy, [FORMULA] the semimajor axis of the binary formed and [FORMULA] the escape velocity of the escaper. Our results also indicate that the conjecture of Szebehely (1977), viz. "The measure of escaping orbits is significantly higher than the measure of stable orbits" is likely to be true. Further our result regarding escape probability is in contrast to the result of Agekian's et al. (1969). The second paper deals with certain parameters of the participating bodies in 3D space.

Key words: celestial mechanics, stellar dynamics – stars: binaries: close

© European Southern Observatory (ESO) 1999

Online publication: May 21, 1999