Related papers: Empirical Stability Boundary for Hierarchical Trip…
A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical…
We examine the stability of hierarchical triple systems using direct $N$-body simulations without adopting a secular perturbation approximation. We estimate their disruption timescales in addition to the mere stable/unstable criterion, with…
In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We carry out more than 3 10^8 numerical simulations of planets between the size of Mercury and…
Context: Numerous theoretical studies of the stellar dynamics of triple systems have been carried out, but fewer purely empirical studies that have addressed planetary orbits within these systems. Most of these empirical studies have been…
The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…
Hierarchical triple systems play a crucial role in various astrophysical contexts, and therefore the understanding of their stability is important. Traditional empirical stability criteria rely on a threshold value of $Q$, the ratio between…
In this paper we study numerically the effect of the initial mutual orbital inclination on the stability of hierarchical triple systems with initially circular orbits. Our aim is to investigate the possibility that the stability boundary…
We explore the stability of gravitational triple systems comprising a central massive body and a tight binary of less massive pairs. In the present paper, we focus on improving the Hill-type stability criterion for the binary in those…
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical…
Nowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem…
Understanding the long-term evolution of hierarchical triple systems is challenging due to its inherent chaotic nature, and it requires computationally expensive simulations. Here we propose a convolutional neural network model to predict…
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…
We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill…
A symplectic integrator algorithm suitable for hierarchical triple systems is formulated and tested. The positions of the stars are followed in hierarchical Jacobi coordinates, whilst the planets are referenced purely to their primary. The…
This paper investigates the secular motion of a massless asteroid within the framework of the double-averaged elliptic restricted three-body problem. By employing Poincar\'e variables, we analyze the stability properties of asteroid orbits…
The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly…
We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…
In previous hydrodynamical simulations, we found a mechanism for nearly circular binary stars, like Kepler-413, to trap two planets in a stable 1:1 resonance. Therefore, the stability of coorbital configurations becomes a relevant question…
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…