Astronomy and Astrophysics – Astronomy
Scientific paper
Feb 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003astl...29..126o&link_type=abstract
Astronomy Letters, vol. 29, p. 126-132 (2003)
Astronomy and Astrophysics
Astronomy
1
Scientific paper
We investigate the neighborhood of the periodic eight-like orbit found by Moore (1993) and Chenciner and Montgomery (2000). One-, two-, and three-dimensional scans in body coordinates, velocities, and masses were constructed. We found the regions of initial conditions in which the maximum mutual separation did not exceed 5 distance units during 2000 time units (about 300 periods of the initial solution). Larger deviations from the periodic solution lead to distant body ejections and escapes. The identified regions of finite motions are complex in structure. In some sections, these are simple-connected manifolds, while in other sections, stability zones alternate with escape zones. We estimated the fractal dimensions of the stability regions in three-dimensional scans: it typically ranges from 2 to 3. In some cases, we found transitions between motions along the figure of eight in its neighborhood and motions in the vicinity of a periodic Broucke orbit in the isosceles three-body problem.
Chernin Arthur D.
Orlov Valeri
Rubinov A. V.
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