Related papers: Numerical behavior of the Keplerian Integral metho…

The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…

The modern optical telescopes produce a huge number of asteroid observations, that are grouped into very short arcs (VSAs), each containing a few observations of the same object in one single night. To decide whether two VSAs, collected in…

We review two initial orbit determination methods for too short arcs (TSAs) of optical observations of a solar system body. These methods employ the conservation laws of Kepler's problem, and allow to attempt the linkage of TSAs referring…

We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…

A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…

It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…

Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…

We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm,…

We report on the orbital architectures of Kepler systems having multiple planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. (2013). These data show 899 transiting…

A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the…

We develop a numerical scheme for the Kepler problem that preserves exactly all first integrals: angular momentum, total energy, and the Laplace-Runge-Lenz vector. This property ensures that orbital trajectories retain their precise shape…

This paper reviews the standard algorithm for converting spacecraft state vectors to Keplerian orbital elements with a focus on its computer implementation. It analyzes the shortcomings of the scheme as described in the literature, and…

In this paper, a new parametrization of the relative motion between two satellites orbiting a central body is presented. The parametrization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the…

Context. To identify the real associations of small bodies, we can use synthetic sets of orbits generated by various methods. These are not perfect methods, therefore the assessment of their quality is an essential task. Aims. In this…

We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in (Gronchi et al 2015), which uses a…

In this paper we present our results of numerical integrations of orbits of fictive massless particle in vicinity of resonance. Our goal is to study the dependences of period (frequency) of resonance perturbations and the width of the…

We report on the properties of eclipsing binaries from the Kepler mission with a newly developed photometric modeling code, which uses the light curve, spectral energy distribution of each binary, and stellar evolution models to infer…

Kepler mission is a powerful tool in the study the different types of astrophysical objects or events in the distant Universe. However, the spacecraft gives also the opportunity to study Solar System objects passing in the telescope field…

The observation data for artificial celestial body 43096, which had been obtained during 2006-2012 within the framework of international project "The Scientific Network of Optical Instruments for Astrometric and Photometric Observations" -…

The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…