English
Related papers

Related papers: Empirical Stability Boundary for Hierarchical Trip…

200 papers

The orbital solutions of published multi-planet systems are not necessarily dynamically stable on timescales comparable to the lifetime of the system as a whole. For this reason, dynamical tests of the architectures of proposed exoplanetary…

Earth and Planetary Astrophysics · Physics 2020-11-30 J. P. Marshall , J. Horner , R. A. Wittenmyer , J. T. Clark , M. W. Mengel

We investigate the orbital stability of a tilted circumbinary planetary system with three giant planets. The planets are spaced by a constant number ($\Delta$) of mutual Hill radii in the range $\Delta=3.4-12.0$ such that the period ratio…

Earth and Planetary Astrophysics · Physics 2023-08-22 Cheng Chen , Rebecca G. Martin , C. J. Nixon

The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion…

Astrophysics · Physics 2008-11-26 Nader Haghighipour , Jocelyn Couetdic , Ferenc Varadi , William B. Moore

The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is…

Dynamical Systems · Mathematics 2021-09-29 M. Radwan , Nihad S. Abdel-Motelp

We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the…

Dynamical Systems · Mathematics 2017-06-01 Renato C. Calleja , Eusebius J. Doedel , Antony R. Humphries , Alexandra Lemus , Bart E. Oldeman

In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic…

Astrophysics · Physics 2015-06-24 George Voyatzis , Thomas Kotoulas

A hierarchical three-body model can be widely applied to diverse astrophysical settings, from satellite-planet-star systems to binaries around supermassive black holes. The octupole-order perturbation on the inner binary from the tertiary…

Earth and Planetary Astrophysics · Physics 2025-11-07 Xiumin Huang , Dong Lai , Bin Liu

We study the rhomboidal symmetric-mass 4-body problem in both a two-degree-of-freedom and a four-degree-of-freedom setting. Under suitable changes of variables in both settings, isolated binary collisions at the origin are regularizable.…

Dynamical Systems · Mathematics 2013-05-01 Lennard Bakker , Skyler Simmons

We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We…

Astrophysics · Physics 2009-10-22 D. Lai , F. A. Rasio , S. L. Shapiro

In hierarchical triple systems, the inner binary is slowly perturbed by a distant companion, giving rise to large-scale oscillations in eccentricity and inclination, known as von-Zeipel-Lidov-Kozai (ZLK) oscillations. Stable systems with a…

Earth and Planetary Astrophysics · Physics 2024-12-19 Evgeni Grishin

The multi-dissipative photogravitational triaxial elliptic restricted three body problem is treated. The perturbed locations of triangular points are computed. The stability of the triangular points under changing one or more perturbing…

Earth and Planetary Astrophysics · Physics 2015-06-10 F. A. Abd El-Salam

The planetary restricted three-body problem (RTBP) is considered. The primary mass M is much more than another masses mj, i=1..N, which revolve around M. The massless probe particle m moves on elliptic orbit, is perturbed by mj. It is well…

Dynamical Systems · Mathematics 2007-05-23 A. E. Rosaev

We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic existence of a symmetric periodic simultaneous binary…

Dynamical Systems · Mathematics 2015-05-18 Lennard F. Bakker , Tiancheng Ouyang , Duokui Yan , Skyler Simmons

We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first order mean motion resonance overlap (Wisdom, 1980). We show that this criterion fits the stability regions in real exoplanet…

Earth and Planetary Astrophysics · Physics 2015-06-17 C. A. Giuppone , M. H. M. Morais , A. C. M. Correia

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

Dynamical Systems · Mathematics 2020-12-29 Mark A. Pinsky

In previous papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. We considered systems with well separated components and different initial…

Earth and Planetary Astrophysics · Physics 2014-08-28 Nikolaos Georgakarakos

Binary-star exoplanetary systems are now known to be common, for both wide and close binaries. However, their orbital evolution is generally unsolvable. Special cases of the N-body problem which are in fact completely solvable include…

Earth and Planetary Astrophysics · Physics 2016-09-07 Dimitri Veras

We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20 degrees). Using the…

Earth and Planetary Astrophysics · Physics 2011-07-06 Alexandre C. M. Correia , Jacques Laskar , François Farago , Gwenaël Boué

We present a stability analysis of a large set of simulated planetary systems of three or more planets based on architectures of multiplanet systems discovered by \textit{Kepler} and \textit{K2}. We propagated 21,400 simulated planetary…

Earth and Planetary Astrophysics · Physics 2024-04-11 Kathryn Volk , Renu Malhotra

Hundreds of giant planets have been discovered so far and the quest of exo-Earths in giant planet systems has become intriguing. In this work, we aim to address the question of the possible long-term coexistence of a terrestrial companion…

Earth and Planetary Astrophysics · Physics 2018-07-18 Kyriaki I. Antoniadou , Anne-Sophie Libert