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This chapter concerns the long-term dynamical evolution of planetary systems from both theoretical and observational perspectives. We begin by discussing the planet-planet interactions that take place within our own Solar System. We then…

Earth and Planetary Astrophysics · Physics 2015-06-18 Melvyn B. Davies , Fred C. Adams , Philip Armitage , John Chambers , Eric Ford , Alessandro Morbidelli , Sean N. Raymond , Dimitri Veras

We study the orbital evolution of a three planet system with masses in the super-Earth regime resulting from the action of tides on the planets induced by the central star which cause orbital circularization. We consider systems either in…

Earth and Planetary Astrophysics · Physics 2015-06-19 John C. B. Papaloizou

(abbreviated) We use a semi-numerical approach to study the secular behavior of a system composed of a central star and two massive planets in eccentric co-planar orbits. We show that the secular dynamics of this system can be described…

Astrophysics · Physics 2009-11-10 T. A. Michtchenko , R. Malhotra

The planetary obliquity plays a significant role in determining physical properties of planetary surfaces and climate. As direct detection is constrained due to the present observation accuracy, kinetic theories are helpful to predict the…

Earth and Planetary Astrophysics · Physics 2024-06-04 Xiumin Huang , Jianghui Ji , Shangfei Liu , Ruobing Dong , Su Wang

We study orbital inclination changes associated with the precession of a disc-planet system that occurs through gravitational interaction with a binary companion on an inclined orbit. We investigate whether this scenario can account for…

Earth and Planetary Astrophysics · Physics 2014-02-14 M. Xiang-Gruess , J. C. B. Papaloizou

The orbital eccentricity of a single planet around a component of a stellar binary system with a sufficiently large mutual inclination angle is known to oscillate on a secular timescale through the Kozai mechanism. We have investigated the…

Astrophysics · Physics 2007-11-08 Genya Takeda , Ryosuke Kita , Frederic A. Rasio , Samuel M. Rubinstein

In recent years, the long-term effects of non-linear perturbations were found to be important for the evolution of the hierarchical triple system, which, for the central third body of a larger mass, can significantly suppress the…

General Relativity and Quantum Cosmology · Physics 2025-08-06 Li Hu , Rong-Gen Cai , Shao-Jiang Wang

In this letter we consider the evolution of a planetary system around a star inside a wide binary. We simulate numerically the evolution of the planetary orbits for both co-planar and highly-inclined systems. We find that the Kozai…

Astrophysics · Physics 2008-11-26 Daniel Malmberg , Melvyn B. Davies , John E. Chambers

Observations of hierarchical triple star systems show that misalignments are common both between the angular momentum vector of the inner binary and the outer companion orbit, and between the outer binary orbit and a circumtriple gas disk.…

Earth and Planetary Astrophysics · Physics 2025-03-11 Stephen Lepp , Rebecca G. Martin , Stephen H. Lubow

We study the orbital evolution of hierarchical quadruple systems composed of two binaries on a long mutual orbit, where each binary acts as a Kozai-Lidov (KL) perturber on the other. We find that the coupling between the two binaries…

Solar and Stellar Astrophysics · Physics 2014-05-28 Ondrej Pejcha , Joe M. Antognini , Benjamin J. Shappee , Todd A. Thompson

Planets have been observed in tight binary systems with separations less than 20 AU. A likely formation scenario for such systems involves a dynamical capture, after which high relative inclinations are likely and may lead to Kozai…

Earth and Planetary Astrophysics · Physics 2011-02-11 Lamya Saleh , Frederic Rasio

The Lidov-Kozai (LK) mechanism plays an important role in the secular evolution of many hierarchical triple systems. The standard LK mechanism consists of large-amplitude oscillations in eccentricity and inclination of a binary subject to…

Earth and Planetary Astrophysics · Physics 2015-06-23 Bin Liu , Diego J. Muñoz , Dong Lai

Accordling to the theory of Kozai resonance, the initial mutual inclination between a small body and a massive planet in an outer circular orbit is as high as $\sim39.2^{\circ}$ for pumping the eccentricity of the inner small body. Here we…

Earth and Planetary Astrophysics · Physics 2015-06-15 Yuan-Yuan Chen , Hui-Gen Liu , Gang Zhao , Ji-Lin Zhou

In hierarchical triple systems, the inner binary is perturbed by a distant companion. For large mutual inclinations, the Lidov-Kozai mechanism secularly excites large eccentricity and inclination oscillations of the inner binary. The…

Earth and Planetary Astrophysics · Physics 2018-09-11 Evgeni Grishin , Hagai B. Perets , Giacomo Fragione

Many triple-star systems have an inner pair with an orbital period of a few days only. A common mechanism to explain the short-period pile-up present in the observations is the migration through Lidov-Kozai cycles combined with tidal…

Earth and Planetary Astrophysics · Physics 2018-08-01 Manon Bataille , Anne-Sophie Libert , Alexandre C. M. Correia

Field stars are frequently formed in pairs, and many of these binaries are part of triples or even higher-order systems. Even though, the principles of single stellar evolution and binary evolution, have been accepted for a long time, the…

Solar and Stellar Astrophysics · Physics 2016-12-20 S. Toonen , A. Hamers , S. Portegies Zwart

The behavior of an interior test particle in the secular 3-body problem has been studied extensively. A well-known feature is the Lidov-Kozai resonance in which the test particle's argument of periapse librates about $\pm 90^\circ$ and…

Earth and Planetary Astrophysics · Physics 2018-01-10 Benjamin R. Vinson , Eugene Chiang

We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a…

Solar and Stellar Astrophysics · Physics 2015-05-30 Samuel Doolin , Katherine M. Blundell

Recent studies have shown that secular evolution of triple systems can play a major role in the evolution and interaction of their inner binaries. Very few studies explored the stellar evolution of triple systems, and in particular the mass…

Solar and Stellar Astrophysics · Physics 2015-06-19 Erez Michaely , Hagai B. Perets

Triple stars and compact objects are ubiquitously observed in nature. Their long-term evolution is complex; in particular, the von-Zeipel-Lidov-Kozai (ZLK) mechanism can potentially lead to highly eccentric encounters of the inner binary.…

Earth and Planetary Astrophysics · Physics 2022-08-03 Abhi Mangipudi , Evgeni Grishin , Alessandro A. Trani , Ilya Mandel