Orbital Dynamics of Circumbinary Planets

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Monthly Notices of the Royal Astronomical Society





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We investigate the dynamics of a non-zero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semimajor axis by means of numerical simulations. Previous studies investigated the secular dynamics mainly by approximate analytic methods. In the stationary inclination state, the planet and binary precess together with no change in relative tilt. For both prograde and retrograde planetary orbits, we explore the conditions for planetary orbital libration versus circulation and the conditions for stationary inclination. As was predicted by analytic models, for sufficiently high initial inclination, a prograde planet’s orbit librates about the stationary tilted state. For a fixed binary eccentricity, the stationary angle is a monotonically decreasing function of the ratio of the planet-to-binary angular momentum j. The larger j, the stronger the evolutionary changes in the binary eccentricity and inclination. We also calculate the critical tilt angle that separates the circulating from the librating orbits for both prograde and retrograde planet orbits. The properties of the librating orbits and stationary angles are quite different for prograde versus retrograde orbits. The results of the numerical simulations are in very good quantitative agreement with the analytic models. Our results have implications for circumbinary planet formation and evolution.


Methods: Analytical; Celestial Mechanics; Binaries: General


Astrophysics and Astronomy | Physical Sciences and Mathematics




Erratum: [Orbital Dynamics of Circumbinary Planets]

Cheng Chen, Alessia Franchini, Stephen H Lubow, Rebecca G Martin, Erratum: [Orbital dynamics of circumbinary planets], Monthly Notices of the Royal Astronomical Society, Volume 495, Issue 1, June 2020, Page 141, https://doi.org/10.1093/mnras/staa1143

Equation (3) in Chen et al. (2019) contained two errors. There was a missing term of + 90, and the vectors should be unit vectors. These typos that did not affect the results of our calculations. See full text for equation.

ϕ = tan − 1 ⁡ ( l ^ p ⋅ ( l ^ b × e ^ b ) l ^ p ⋅ e ^ b ) + 90 ∘

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