Related papers: Empirical Stability Boundary for Hierarchical Trip…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
It is well established that certain detached eclipsing binary stars exhibit apsidal motions whose value is in disagreement with with calculated deviations from Keplerian motion based on tidal effects and the general theory of relativity.…
We study the dynamical stability and fates of hierarchical (in semi-major axis) two-planet systems with arbitrary eccentricities and mutual inclinations. We run a large number of long-term numerical integrations and use the Support Vector…
The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We…
Motivated by the current search for exomoons, this paper considers the stability of tidal equilibrium for hierarchical three-body systems containing a star, a planet, and a moon. In this treatment, the energy and angular momentum budgets…
The dynamical stability of tightly packed exoplanetary systems remains poorly understood. While for a two-planet system a sharp stability boundary exists, numerical simulations of three and more planet systems show that they can experience…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
We study the dynamical stability of planetary systems consisting of one hypothetical terrestrial mass planet ($1 $ or $10 \mearth$) and one massive planet ($10 \mearth - 10 \mjup$). We consider masses and orbits that cover the range of…
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…
While there have been many studies examining the stability of hierarchical triple systems, the meaning of ``stability'' is somewhat vague and has been interpreted differently in previous literatures. The present paper focuses on ``Lagrange…
This study examines the dynamics of the third body in an elliptic restricted three-body problem (ERTBP) framework, taking into account perturbations from radiation pressure, oblateness, and elongation of the primary bodies, as well as…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
Multiple analytical and empirical stability criteria have been derived in the literature for two planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well…
The rectilinear elliptic restricted Three Body Problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity $e'=1$, but the collision of the…
Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of…
With $n$-body simulations we investigate the stability of tilted circumbinary planetary systems consisting of two nonzero mass planets. The planets are initially in circular orbits that are coplanar to each other, as would be expected if…
The three-body problem is arguably the oldest open question in astrophysics, and has resisted a general analytic solution for centuries. Various implementations of perturbation theory provide solutions in portions of parameter space, but…
The secular approximation of the hierarchical three body systems has been proven to be very useful in addressing many astrophysical systems, from planets, stars to black holes. In such a system two objects are on a tight orbit, and the…
The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their…