The Sitnikov problem - A Complete Picture of Phase Space

Details The Sitnikov problem - A Complete Picture of Phase Space The Sitnikov problem - A Complete Picture of Phase Space

May 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007padeu..19..129d&link_type=abstract

Publications of the Astronomy Department of the Eötvös University (PADEU), 2007, ISBN 963 463 557, Vol. 19. Edited by B. Érdi a

Astronomy and Astrophysics

Astronomy

1

Scientific paper

We discuss the results of an extensive numerical study of the Sitnikov Problem, where two equally massive primaries have Keplerian orbits while a third body moves perpendicular to their plane of motion through their common barycenter. The possible motions are discussed in the surfaces of section with respect to the eccentricity e of the primaries and the initial distance of the third mass. Besides the shrinking of the main land with increasing e of the primaries we can observe the dominance of the 2:1 periodic orbit, which disappears (reappears) via pitchfork bifurcation (inverse pitchfork bifurcation). On one hand the presence of sticky regions close to stable islands and sticky fingers far into the chaotic sea is very well visible in the respective plots. On the other hand 'escape channels' showing orbits with very small escape times are also present for any value of the eccentricity.

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