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The dynamical history of a planetary system is recorded in the present day architecture of its constituent planets' sizes, orbital periods, and eccentricities. Studying the relationships between these quantities for large populations…

Earth and Planetary Astrophysics · Physics 2026-03-26 Gregory J. Gilbert , Erik A. Petigura , Paige M. Entrican

We study the gravitational dynamics of quasi-hierarchical triple systems, where the outer orbital period is significantly longer than the inner one, but the outer orbit is extremely eccentric, rendering the time at pericentre comparable to…

High Energy Astrophysical Phenomena · Physics 2026-03-10 Yonadav Barry Ginat , Jakob Stegmann , Johan Samsing

Multiple systems play an important role in the evolution of star clusters. First we discuss several formation mechanisms which depend on the presence of binaries, either primordial or of dynamical origin. Hierarchical configurations are…

Astrophysics · Physics 2007-05-23 Sverre J. Aarseth , Rosemary A. Mardling

The three-body problem has been studied for more than three centuries [1,2], and has received much attention in recent years [3-5]. It shows complex dynamical phenomena due to the mutual gravitational interaction of the three bodies. Triple…

Chaotic Dynamics · Physics 2021-01-05 Xiaoming Li , Xiaochen Li , Shijun Liao

We use numerical $N$-body experiments to explore the statistics of multiple systems formed in small-$N$ subclusters, i.e. the distributions of orbital semi-major axis, $a$, orbital eccentricity, $e$, mass ratio, $q$, mutual orbital…

Astrophysics of Galaxies · Physics 2025-07-28 Hannah Ambrose , Anthony Whitworth

Hierarchical quadruple systems arise naturally in stellar binaries and triples that harbour planets. Examples are hot Jupiters (HJs) in stellar triple systems, and planetary companions to HJs in stellar binaries. The secular dynamical…

Earth and Planetary Astrophysics · Physics 2017-06-19 Adrian S. Hamers , Dong Lai

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 warm Jupiters (WJs) have substantial eccentricities, which are linked to their formation and migration histories. This paper explores eccentricity excitation of WJs due to planet-planet scattering, beginning with 3-4 planets in…

Earth and Planetary Astrophysics · Physics 2020-01-08 Kassandra R. Anderson , Dong Lai , Bonan Pu

In this paper, we present the analysis of the stellar system HIP 101227 to determine the actual number of components in the system, and their properties. We use dynamical modeling and complex spectrophotometric (involving atmospheric…

A sample of 278 triple systems with outer separations under 300 au and resolved inner pairs is studied, focusing on the mutual alignment between inner and outer orbits. The degree of alignment increases with (i) decreasing outer separation,…

Solar and Stellar Astrophysics · Physics 2026-01-09 Andrei Tokovinin

We study how close-in systems such as those detected by Kepler are affected by the dynamics of bodies in the outer system. We consider two scenarios: outer systems of giant planets potentially unstable to planet--planet scattering, and wide…

Earth and Planetary Astrophysics · Physics 2017-05-03 Alexander J Mustill , Melvyn B Davies , Anders Johansen

We present a detailed analysis of the orbital stability of the HD 181433 planetary system, finding it to exhibit strong dynamical instability across a wide range of orbital eccentricities, semi-major axes, and mutual inclinations. We also…

We study the orbital properties of stars in four (published) simulations of thick disks formed by: i) accretion from disrupted satellites, ii) heating of a pre-existing thin disk by a minor merger, iii) radial migration and iv) gas rich…

The known extrasolar multiple-planet systems share a surprising dynamical attribute: they cluster just beyond the Hill stability boundary. Here we show that the planet-planet scattering model, which naturally explains the observed exoplanet…

Earth and Planetary Astrophysics · Physics 2011-02-11 Sean N. Raymond , Rory Barnes , Dimitri Veras , Philip J. Armitage , Noel Gorelick , Richard Greenberg

We derive analytical expressions for the change in the orbital eccentricity of a binary following a distant encounter with a third star on a hyperbolic or parabolic orbit. To establish the accuracy of these expressions, we present detailed…

Astrophysics · Physics 2015-06-24 Douglas C. Heggie , Frederic A. Rasio

The orbital eccentricity distribution of exoplanets is shaped by a combination of dynamical processes, reflecting both formation conditions and long-term evolution. Probing the orbital dynamics of planets in the kinematic thin and thick…

To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…

Earth and Planetary Astrophysics · Physics 2024-07-31 Caleb Lammers , Sam Hadden , Norman Murray

A widely explored pathway for hot Jupiter (HJ) formation is high-eccentricity migration driven by von Zeipel-Lidov-Kozai cycles induced by an exterior companion. However, for a distant or low-mass companion, this mechanism typically demands…

Earth and Planetary Astrophysics · Physics 2025-11-17 Eritas Yang , Yubo Su

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

Recent observation of microlensing technique reveals two giant planets at 2.3 AU and 4.6 AU around the star OGLE-06-109L. The eccentricity of the outer planet (ec) is estimated to be 0.11(+0.17,-0.04), comparable to that of Saturn…

Earth and Planetary Astrophysics · Physics 2014-11-20 Su Wang , Gang Zhao , Ji-Lin Zhou