Computer Science
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008em%26p..103..105p&link_type=abstract
Earth, Moon, and Planets, Volume 103, Issue 3-4, pp. 105-118
Computer Science
Hill Problem, Oblate Secondary, Multiple-Periodic Orbits, Stability, Bifurcations, Escape And Collision Orbits
Scientific paper
We study the multiple periodic orbits of Hill’s problem with oblate secondary. In particular, the network of families of double and triple symmetric periodic orbits is determined numerically for an arbitrary value of the oblateness coefficient of the secondary. The stability of the families is computed and critical orbits are determined. Attention is paid to the critical orbits at which families of non-symmetric periodic orbits bifurcate from the families of symmetric periodic orbits. Six such bifurcations are found, one for double-periodic and five for triple-periodic orbits. Critical orbits at which families of sub-multiple symmetric periodic orbits bifurcate are also discussed. Finally, we present the full network of families of multiple periodic orbits (up to multiplicity 12) together with the parts of the space of initial conditions corresponding to escape and collision orbits, obtaining a global view of the orbital behavior of this model problem.
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