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

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

Jun 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999a%26a...346..652c&link_type=abstract

Astronomy and Astrophysics, v.346, p.652-662 (1999)

Astronomy and Astrophysics

Astrophysics

Celestial Mechanics, Stellar Dynamics, Stars: Binaries: Close

Scientific paper

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 displaystyle I_m >= ({(C(2)/(2) | E_t |)})(2,) (b) a_infty (3 v_∞(2) - 4 E_t) = 2, (c) displaystyle v_infty = [{(2)/(3) \{{2 E_t + (a_infty )({-) 1}}\}}](1/2) , where I_m is the minimum moment of inertia of the system, C is the angular momentum, E_t the total energy, a_infty the semimajor axis of the binary formed and v_infty 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.

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