Related papers: Significant improvement in planetary system simula…
Although the discovery of the chaotic motion of the inner planets in the solar system dates back to more than thirty years ago, the secular chaos of their orbits still dares more analytical analyses. Apart from the high-dimensional…
A minimal requirement for simulating multi-scale systems is to reproduce the statistical behavior of the slow variables. In particular, a good numerical method should accurately aproximate the probability density function of the…
Central stars of extra-solar planetary systems are metal-rich. Planet accretion or initial surmetallicity can explain this observationnal fact. These scenarios can be tested with asteroseismology. We calibrate two stellar models, one with…
In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones.…
Symplectic integration of autonomous Hamiltonian systems is a well-known field of study in geometric numerical integration, but for non-autonomous systems the situation is less clear, since symplectic structure requires an even number of…
The dynamics of small bodies perturbed by an eccentric planet was done mostly under the assumption of well separated orbits using analytical approximations appropriate for the hierarchical case. In this work we study the dynamics of small…
The existence of explicit symplectic integrators for general nonseparable Hamiltonian systems is an open and important problem in both numerical analysis and computing in science and engineering, as explicit integrators are usually more…
Due to the chaotic nature of the Solar System, the question of its dynamic long-term stability can only be answered in a statistical sense, e.g. based on numerical ensemble integrations of nearby orbits. Destabilization, including…
Recently a new class of numerical integration methods -- ``mixed variable symplectic integrators'' -- has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of…
An efficient Bayesian technique for estimation problems in fundamental stellar astronomy is tested on simulated data for a binary observed both astrometrically and spectroscopically. Posterior distributions are computed for the components'…
Correct distributions of extrasolar systems for their orbital parameters (semi-major axes, period, eccentricity) and physical characteristics (mass, spectral type of parent star) are received. Orbital resonances in extrasolar systems are…
The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g. the three-body problem). The main…
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends…
In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper we identify the causes for this lack of performance, and find that they fall…
This paper explores the stability of an Earth-like planet orbiting a solar-mass star in the presence of a stellar companion using ~ 400,000 numerical integrations. Given the chaotic nature of the systems being considered, we perform a…
We describe an algorithm for long-term planetary orbit integrations, including the dominant post-Newtonian effects, that employs individual timesteps for each planet. The algorithm is symplectic and exhibits short-term errors that are…
The unparalleled photometric data obtained by NASA's Kepler Space Telescope has led to improved understanding of red-giant stars and binary stars. We discuss the characterization of known eccentric system, containing a solar-like…
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
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…