Vertical-Critical Periodic Orbits in the General Three-Body Problem

Details Vertical-Critical Periodic Orbits in the General Three-Body Problem Vertical-Critical Periodic Orbits in the General Three-Body Problem

Sep 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997ap%26ss.253...73p&link_type=abstract

Astrophysics and Space Science, Volume 253, Issue 1, pp.73-85

Astronomy and Astrophysics

Astrophysics

1

Scientific paper

We present special generating plane orbits, the vertical-critical orbits, of the coplanar general three-body problem. These are determined numerically for various values of m3, for the entire range of the mass ratio of the two primaries. The vertical-critical orbits are necessary in order to specify the vertically stable segments of the families of plane periodic orbits, and they are also the starting points of the families of the simplest possible three-dimensional periodic orbits, namely the simple and double periodic. The initial conditions of the vertical-critical periodic orbits of the basic families l, m, i, h, b and c and their stability parameters are determined.

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