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arXiv · 1904.03896

On the classification of orbits in the three-dimensional Copenhagen problem with oblate primaries

Euaggelos E. Zotos·Jan Nagler
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Abstract

The character of motion for the three-dimensional circular restricted three-body problem with oblate primaries is investigated. The orbits of the test particle are classified into four types: non-escaping regular orbits around the primaries, trapped chaotic (or sticky) orbits, escaping orbits that pass over the Lagrange saddle points $L_2$ and $L_3$, and orbits that lead the test particle to collide with one of the primary bodies. We numerically explore the motion of the test particle by presenting color-coded diagrams, where the initial conditions are mapped to the orbit type and studied as a function of the total orbital energy, the initial value of the $z$-coordinate and the oblateness coefficient. The fraction of the collision orbits, measured on the color-coded diagrams, show an algebraic dependence on the oblateness coefficient, which can be derived by simple semi-theoretical arguments.

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Euaggelos E. Zotos, Jan Nagler. 2019-04-08. On the classification of orbits in the three-dimensional Copenhagen problem with oblate primaries. https://doi.org/10.1016/j.ijnonlinmec.2018.10.009

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