Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003arep...47..963o&link_type=abstract
Astronomy Reports, vol. 47, Issue 11, p.963-973
Astronomy and Astrophysics
Astronomy
Scientific paper
We analyze the general 2D isosceles three-body problem for various ratios ɛ of the mass of the central body to the mass of each of the other two bodies. We set the initial conditions using two parameters: the virial coefficient k and the parameter , where is the relative velocity of the two outer bodies and is the velocity of the central body relative to the center of mass of the outer bodies. We compare statistical dependences between evolutionary parameters of triple systems with various values of ɛ, and analyze the k and μ dependences of the number of crossings of the center of mass of the triple system by the central body and the lifetime of the system. We construct the functions R max(r max), where r max and R max are the maximum achievable distances between the outer bodies, and between the central body and the center of mass of the outer bodies in the triple system. The parameter ɛ proves to be the most important parameter of the problem, and determines the relationship between the measures of the regular and stochastic trajectories. However, there exist “seeds” of stochasticity, even at small ɛ˜10-2. The measure of the stochastic orbits increases with ɛ; when ɛ≥10, virtually the entire region of the initial conditions corresponds to stochastic trajectories.
Martynova Alija I.
Orlov Valeri
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