Related papers: Equilibria in the secular, non-coplanar two-planet…
Gravitational perturbations in multi-planet systems caused by an accompanying star are the subject of this investigation. Our dynamical model is based on the binary star HD41004 AB where a giant planet orbits HD41004 A. We modify the…
We investigate the non-resonant, 3-D (spatial) model of the hierarchical system composed of point-mass stellar (or sub-stellar) binary and a low-mass companion (a circumbinary planet or a brown dwarf). We take into account the leading…
The eccentricity evolution of multiple planet systems can provide valuable constraints on planet formation models. Unfortunately, the inevitable uncertainties in the current orbital elements can lead to significant ambiguities in the nature…
We present a semi-analytical correction to the seminal solution for the secular motion of a planet's orbit under gravitational influence of an external perturber derived by Heppenheimer (1978). A comparison between analytical predictions…
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…
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…
The secular approximation for the evolution of hierarchical triple configurations has proven to be very useful in many astrophysical contexts, from planetary to triple-star systems. In this approximation the orbits may change shape and…
The non-resonant secular dynamics of compact planetary systems are modeled by a perturbing function which is usually expanded in eccentricity and absolute inclination with respect to the invariant plane. Here, the expressions are given in a…
We investigate the secular dynamics of two-planet coplanar systems evolving under mutual gravitational interactions and dissipative forces. We consider two mechanisms responsible for the planetary migration: star-planet (or…
The secular Laplace-Lagrange orbital solution, decomposing eccentricities into a set of uniformly precessing eigenmodes is a classical result that is typically solved numerically. However, in the limit where orbits are closely spaced,…
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on…
We revisit the secular 3D planetary three-body problem aiming to provide a unified formalism for studying the structure of the phase space for progressively higher values of the mutual inclination $i_{mut}$ between the two planets' orbits.…
In this article, equilibrium points and families of periodic orbits in the vicinity of the collinear equilibrium points of a binary asteroid system are investigated with respect to the angular velocity of the secondary body, the mass ratio…
We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation…
The large increase in exoplanet discoveries in the last two decades showed a variety of systems whose stability is not clear. In this work we chose the $\upsilon$ Andromedae system as the basis of our studies in dynamical stability. This…
We consider a basic planetary system composed by a Sun like star, a Jupiter-like planet an a Neptune-like planet in a wide range of orbital configurations not limited to the hierarchical case. We present atlases of resonances showing the…
In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the…
Motivated by the practical interest in the third-body perturbation as a natural cleaning mechanism for high-altitude Earth orbits, we investigate the dynamics stemming from the secular Hamiltonian associated with the lunar perturbation,…
Binary and multiple star systems are extreme environments for the formation and long-term presence of extrasolar planets. Circumstellar planets are subject to gravitational perturbations from the distant companion star, and this interaction…
We introduce a quasi-periodic restricted Hamiltonian to describe the secular motion of a small-mass planet in a multi-planetary system. In particular, we refer to the motion of $\upsilon$-And $b$ which is the innermost planet among those…