Abstract
We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m 1 = m 2 = 0.5) rotating in the x, y plane and vary the mass of the third particle, 0 m 3 < 10-3, placed initially on the z-axis. We begin by finding for the restricted problem (with m 3 = 0) an apparently infinite sequence of stability intervals on the z-axis, whose width grows and tends to a fixed non-zero value, as we move away from z = 0. We then estimate the extent of "islands" of bounded motion in x, y, z space about these intervals and show that it also increases as |z| grows. Turning to the so-called extended Sitnikov problem, where the third particle moves only along the z-axis, we find that, as m 3 increases, the domain of allowed motion grows significantly and chaotic regions in phase space appear through a series of saddle-node bifurcations. Finally, we concentrate on the general 3-body problem and demonstrate that, for very small masses, m 3 ≈ 10 -6, the "islands" of bounded motion about the z-axis stability intervals are larger than the ones for m 3 = 0. Furthermore, as m 3 increases, it is the regions of bounded motion closest to z = 0 that disappear first, while the ones further away "disperse" at larger m 3 values, thus providing further evidence of an increasing stability of the motion away from the plane of the two primaries, as observed in the m 3 = 0 case.
Original language | English |
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Pages (from-to) | 129-148 |
Number of pages | 20 |
Journal | Celestial Mechanics and Dynamical Astronomy |
Volume | 99 |
Issue number | 2 |
DOIs | |
Publication status | Published - Oct 1 2007 |
Keywords
- "Islands" of bounded motion
- Extended and general Sitnikov problem
- Restricted 3-body Sitnikov problem
- Stability intervals
ASJC Scopus subject areas
- Modelling and Simulation
- Mathematical Physics
- Astronomy and Astrophysics
- Space and Planetary Science
- Computational Mathematics
- Applied Mathematics