Related papers: Simplified solution to determination of a binary o…
The relationship between geometric and variational principles remains central to Nonlinear Analysis. This paper introduces the \textbf{Orbit-Summability Fixed Point Criterion}, a novel, purely dynamical condition, and establishes its…
We compute the number of orbits of pairs in a finitely generated torsion module (more generally, a module of bounded order) over a discrete valuation ring. The answer is found to be a polynomial in the cardinality of the residue field whose…
Abstract abridged. Eclipsing binary systems provide the opportunity to measure the fundamental parameters of their component stars in a stellar-model-independent way. This makes them ideal candidates for testing and calibrating theories of…
The apparent positions of planets are determined by means of the fundamental ephemerides, the precession-nutation models of the Earth, the gravitational effects and aberrations et al. Around 2000, many astrometrical conceptions, models and…
The general tensorial form of the orbit-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements with respect to…
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…
More than 340 non-eclipsing binaries of A-F stars as primaries at intermediate periods (100-1000 d) were newly found by uninterrupted photometry with ultra high-precision taken over 4 yr by Kepler space mission via the phase modulation of…
Because the distant retrograde orbits dynamics inherently depends on special functions, approximate analytical solutions in the literature are commonly constrained to providing rough approximations of the qualitative behavior. We rely on…
We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…
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.…
The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning…
Recently we derived the next-to-next-to-leading order post-Newtonian Hamiltonians at spin-orbit and spin(1)-spin(2) level for a binary system of compact objects. In this talk the derivation of them will be shortly outlined at an…
We present theoretical analysis of the astrometric searches for extrasolar planets with the Space Interferometry Mission (SIM). Particularly, we derive a model for the future measurements with SIM and discuss the problem of reliable…
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. Here we study the onset of instability for an Earth-type planet that is…
We examine characteristics of circumbinary orbits in the context of current planet formation scenarios. Analytical perturbation theory predicts the existence of nested circumbinary orbits that are generalizations of circular paths around a…
Generalized parameter estimation-based observers have proven very successful to deal with systems described in state-affine form. In this paper, we enlarge the domain of applicability of this method proposing an algebraic procedure to…
We present a planar four-body model, called the Binary Asteroid Problem, for the motion of two asteroids (having small but positive masses) moving under the gravitational attraction of each other, and under the gravitational attraction of…
After a brief introduction into the asteroseismic modelling of stars, we provide a compilation of the current seismic estimates of the core overshooting parameter and of the rotational frequency of single and binary massive stars. These…
The orbits of visual binary systems still attract many of the working groups in astronomy. These orbits are the most important and reliable source of the stellar masse. In the present paper, we are going to compute orbits and dynamical…
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…