Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005an....326..356s&link_type=abstract
Astronomische Nachrichten, Vol.326, Issue 5, p.356-361
Astronomy and Astrophysics
Astronomy
1
Celestial Mechanics, Stellar Dynamics, Methods: Analytical
Scientific paper
We generalize the well-known Hill's circular restricted three-body problem by assuming that the primary generates a Schwarzschild-type field of the form U=A/r+B/r3. The term in B influences the particle, but not the far secondary. Many concrete astronomical situations can be modelled via this problem. For the two-body problem primary-particle, a homoclinic orbit is proved to exist for a continuous range of parameters (the constants of energy and angular momentum, and the field parameter B>0). Within the restricted three-body system, we prove that, under sufficiently small perturbations from the secondary, the homoclinic orbit persists, but its stable and unstable manifolds intersect transversely. Using a result of symbolic dynamics, this means the existence of a Smale horseshoe, hence chaotic behaviour. Moreover, we find that Hill's generalized problem (in our sense) is nonintegrable.
Cucu-Dumitrescu Cătălin
Ghenescu M.
Mioc Vasile
Selaru Dan
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