Related papers: Orbit Determination with the two-body Integrals
At the second post-Newtonian (2PN) order, the secular pericentre precession $\dot\omega^\mathrm{2PN}$ of either a full two-body system made of well detached non-rotating monopole masses of comparable size and a restricted two-body system…
In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer's frame has an important role. The equations 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…
In the past two decades, since the discovery of the figure-8 orbit by Chenciner and Montgomery, the variational method has became one of the most popular tools for constructing new solutions of the $N$-body problem and its extended…
Although not designed as an astrometric instrument, Kepler is expected to produce astrometric results of a quality appropriate to support many of the astrophysical investigations enabled by its photometric results. On the basis of data…
The Hipparcos Intermediate Astrometric Data have been used lately to estimate the inclination of the orbital plane of candidate extrasolar planets. Whereas most of these investigations derive almost face-on orbits, we show that the…
Extrasolar planetary systems commonly exhibit planets on eccentric orbits, with many systems located near or within mean-motion resonances, showcasing a wide diversity of orbital architectures. Such complex systems challenge traditional…
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is…
Most methods of orbit determination are often difficult for numerical implementations since they are developed before the computer era. The recently developed mathematical technique of semi-definite programming (SDP) has been implemented…
We present a combination of tools which allows for investigation of the coupled orbital and rotational dynamics of two rigid bodies with nearly arbitrary shape and mass distribution, under the influence of their mutual gravitational…
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…
The goal of this paper is to advance mathematical and computational methodology for orbiter-to-orbiter radio tomography of small planetary objects. In this study, an advanced full waveform forward model is coupled with a total variation…
The collective dynamics of objects moving through a viscous fluid is complex and counterintuitive. A key to understanding the role of nontrivial particle shape in this complexity is the interaction of a pair of sedimenting spheroids. We…
The Earth itself is not stationary but keeps revolving, and its motion further satisfies the law of equal area according to the heliocentric doctrine. That satisfaction can be used to construct the mathematical relationships between the…
The motion of two planets around a Sun-like star under the combined effects of mutual interaction and tidal dissipation is investigated. The secular behaviour of the system is analyzed using two different approaches. First, we solve the…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
Various astrophysical processes are known, where the fly-by of a massive object affects matter initially supported against gravity by rotation. Examples are perturbations of galaxies, protoplanetary discs or planetary systems. We…
Astronomical polarimetry is a powerful technique that can provide physical information sometimes difficult or impossible to obtain by any other type of observation. Almost every class of binary star can benefit from polarimetric…
Independently developed orbit determination software is used to analyze the orbits of Pioneer 10 and 11 using Doppler data. The analysis takes into account the gravitational fields of the Sun and planets using the latest JPL ephemerides,…
In this paper we dynamically determine the mass of the Kuiper Belt Objects by exploiting the latest observational determinations of the orbital motions of the inner planets of the Solar System. Our result, in units of terrestrial masses, is…