Classification of orbits in the plane isosceles three-body problem

Details Classification of orbits in the plane isosceles three-body problem Classification of orbits in the plane isosceles three-body problem

Jul 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002mnras.333..495o&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 333, Issue 3, pp. 495-500.

Astronomy and Astrophysics

Astronomy

5

Gravitation, Stellar Dynamics, Celestial Mechanics, Gravitation, Stellar Dynamics, Celestial Mechanics

Scientific paper

The general plane isosceles three-body problem is considered for different ratios of the central body mass to the masses of other bodies. The central body goes through the middle of the segment connecting the other bodies along the perpendicular to this segment. The initial conditions are chosen by two parameters: the virial ratio k and the parameter \mu =r\cdot /\sqrt{r\cdot 2+R\cdot 2}, where rdot is the relative velocity of the `outer' bodies, and Rdot is the velocity of the `central' body with respect to the mass centre of the `outer' bodies. The equations of motion are numerically integrated until one of three times: the time of escape of the central body, its time of ejection with R>100d, or 1000τ (here d is the mean size, and τ is the mean crossing time of the triple system). The regions corresponding to escapes of the central body after different numbers of triple approaches are found at the plane of parameters k∈(0,1) and μ∈(-1,1). The regions of stable motions are revealed. The zones of regular and stochastic orbits are outlined. The fraction of stochastic trajectories increases with the central mass. The fraction of stable orbits is highest for equal masses of the bodies.

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