Journal Article

High-inclination orbits in the secular quadrupolar three-body problem

F. Farago and J. Laskar

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 401, issue 2, pages 1189-1198
Published in print January 2010 | ISSN: 0035-8711
Published online January 2010 | e-ISSN: 1365-2966 | DOI:
High-inclination orbits in the secular quadrupolar three-body problem

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The Lidov–Kozai mechanism allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner body, and later extended to the quadrupolar secular non-restricted three-body problem. In this paper, we propose a different point of view on the problem by looking first at the restricted problem where the massless particle is the outer body. In this situation, equilibria at high mutual inclination appear, which corresponds to the population of stable particles that Verrier & Evans find in stable, high-inclination circumbinary orbits around one of the components of the quadruple star HD 98800. We provide a simple analytical framework using a vectorial formalism for these situations. We also look at the evolution of these high-inclination equilibria in the non-restricted case.

Keywords: methods: analytical; methods: N-body simulations; celestial mechanics; planetary systems

Journal Article.  6842 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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