Related papers: Analytical estimates of secular frequencies for bi…
Linear equations with periodic coefficients describe the behavior of various dynamical systems. This studying is devoted to their applications to the planetary restricted three-body problem (RTBP). Here we consider the Laplace method for…
Planets are observed to orbit the component star(s) of stellar binary systems on so-called circumprimary or circumsecondary orbits, as well as around the entire binary system on so-called circumbinary orbits. Depending on the orbital…
The secular stellar mass-loss causes an amplification of the orbital separation in fragile, common proper motion, binary systems with separations of the order of 1000 A.U. In these systems, companions evolve as two independent coeval stars…
Context: Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational…
We consider the secular dynamics of a binary and a planet in terms of non-restricted, hierarchical three-body problem, including the general relativity corrections to the Newtonian gravity. We determine regions in the parameter space where…
The calculus of apsidal precession frequencies of the planets is developed by means of a perturbation thecnique. A model of concentric rings (ring model), suitable for improving calculations, is introduced. Conclusive remarks concerning a…
More than 10% of extra-solar planets (EPs) orbit in a binary or multiple stellar system. We investigated the motion of planets revolving in binary systems in the frame of the particular case of the three body problem. We carried out an…
We examine the effect of secular perturbations by giant planets on systems of multiple, lower mass planets orbiting Sun-like stars. We simulate the effects of forcing both eccentricity and inclination, separately and together. We compare…
Binary black hole simulations with black hole excision using spectral methods require a coordinate transformation into a co-rotating coordinate system where the black holes are essentially at rest. This paper presents and discusses two…
Among the numerous discoveries resulting from the {\it Kepler} mission are a plethora of compact planetary systems that provide deep insights into planet formation theories. The architecture of such compact systems also produces unique…
We herein utilize the general three-body problem (GTBP) as a model, in order to simulate resonant systems consisting of a star and two planets, where at least one of them is highly eccentric. We study them in terms of their long-term…
Short and ultra-short planets are a peculiar type of exoplanets with periods as short as a few days or less. Although it is challenging to detect them, already several are observed with many additional candidates. If these planets have…
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.…
We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces…
The habitability of planets in binary star systems depends not only on the radiation environment created by the two stars, but also on the perturbations to planetary orbits and rotation produced by the gravitational field of the binary and…
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…
Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help…
We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well separated components and…
Spurred by the discovery of numerous exoplanets in multiple systems, binaries have become in recent years one of the main topics in planet formation research. Numerous studies have investigated to what extent the presence of a stellar…
Planets have been observed in tight binary systems with separations less than 20 AU. A likely formation scenario for such systems involves a dynamical capture, after which high relative inclinations are likely and may lead to Kozai…