Related papers: Numerical behavior of the Keplerian Integral metho…
Ab initio calculations face the challenge of describing a complex multiscale quantum many-body system. The nuclear wave function has both strong short-range correlations and long-range contributions. Natural orbitals provide a means of…
This paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. Three approaches are examined: residual assessment, the method of modified equations, and…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
The numerical modeling of binary neutron star mergers has become a subject of much interest in recent years. While a full and accurate model of this phenomenon would require the evolution of the equations of relativistic hydrodynamics along…
In a purely Keplerian picture, the anomalistic, draconitic and sidereal orbital periods of a test particle orbiting a massive body coincide with each other. Such a degeneracy is removed when a post-Keplerian perturbing acceleration enters…
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
The validity of Kepler Laws for the {\it spherical Kepler problem} -- namely, the problem of the motion of a particle on the unit sphere {in $\mathbb R^3$} undergoing an attraction by another particle in the sphere, tangent to the geodesic…
A method for determining the orbital parameters of interacting pairs of galaxies is presented and evaluated using artificial data. The method consists of a genetic algorithm which can search efficiently through the very large space of…
Eclipsing binaries are vital for directly determining stellar parameters without reliance on models or scaling relations. Spectroscopically derived parameters of detached and semi-detached binaries allow us to determine component masses…
The computation of the Minimum Orbital Intersection Distance (MOID) is an old, but increasingly relevant problem. Fast and precise methods for MOID computation are needed to select potentially hazardous asteroids from a large catalogue. The…
Orbital parameters of planets are fitted directly to an appropriate set of observations. It is shown how to use the rigorous Deming method combined with a numerical integration of gravitation equations. In all, 65 parameters of the nine…
The eccentricity of a planet's orbit and the inclination of its orbital plane encode important information about its formation and history. However, exoplanets detected via direct-imaging are often only observed over a very small fraction…
Knowing the conserved quantities that a galaxy's stellar orbits conform to is important in helping us understand the stellar distribution and structures within the galaxy. Isolating integrals of motion and resonances are particularly…
The possibility of measuring the post-Newtonian gravitoelectric correction to the orbital period of a test particle freely orbiting a spherically symmetric mass in the Solar System is analyzed. It should be possible, in principle, to detect…
In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or…
With the discovery of now more than 500 exoplanets, we present a statistical analysis of the planetary orbital periods and their relationship to the rotation periods of their parent stars. We test whether the structure of planetary orbits,…
Studies of high-multiplicity, tightly-packed planetary systems suggest that dynamical instabilities are common and affect both the orbits and planet structures, where the compact orbits and typically low densities make physical collisions…
Planets and satellites orbiting a binary system exist in the solar system and extrasolar planetary systems. Their orbits can be significantly different from Keplerian orbits, if they are close to the binary and the secondary-to-primary mass…
Modelling the formation of super-km-sized planetesimals by gravitational collapse of regions overdense in small particles requires numerical algorithms capable of handling simultaneously hydrodynamics, particle dynamics and particle…
To date, 17 circumbinary planets have been discovered. In this paper, we focus our attention on the stability of the Kepler circumbinary planetary systems with only one planet, i.e. Kepler-16, Kepler-34, Kepler-35, Kepler-38, Kepler-64 and…