The Precession of Test Orbits in the Circumbinary Exoplanet Systems

The new analytical R-toroid method is applied to study the apsidal and nodal precession of test orbits in the circumbinary exo-systems Kepler-16, Kepler-35, Kepler-38, Kepler-413, Kepler-453, Kepler-1661, Kepler-1647, and TOI-1338. For each system from the sample, we (1) created superposition of thr...

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Bibliographic Details
Published in:Astronomy reports 2022-11, Vol.66 (11), p.1063-1073
Main Authors: Kondratyev, B. P., Kornoukhov, V. S.
Format: Article
Language:English
Subjects:
Astronomy
Extrasolar planets
Gravitational fields
Observations and Techniques
Orbits
Perturbation
Physics
Physics and Astronomy
Precession
Research methods
Zonal harmonics
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Summary:The new analytical R-toroid method is applied to study the apsidal and nodal precession of test orbits in the circumbinary exo-systems Kepler-16, Kepler-35, Kepler-38, Kepler-413, Kepler-453, Kepler-1661, Kepler-1647, and TOI-1338. For each system from the sample, we (1) created superposition of three R‑toroids, (2) estimated angular momenta of the stellar pair and planet relative to the Laplace plane, (3) found coefficients of the second and fourth zonal harmonics, and (4) deduced and solved equations for the frequencies of both types of the precession at test orbits. In the R-toroid gravitational field, a ratio of the apsidal and nodal precession periods at the zero inclination Gaussian ring was found to equal (–2). Research methods for the circumbinary system known from the literature proved to be the subcases of the approach developed herewith; out method additionally considers the eccentricities and orbital inclinations of the bodies to the Laplace plane, as well as the gravitational perturbation from the third body (the planet).
ISSN:1063-7729
1562-6881
DOI:10.1134/S1063772922110105