Related papers: Orbit Determination with the two-body Integrals. I…
Thanks to missions like Kepler and TESS, we now have access to tens of thousands of high precision, fast cadence, and long baseline stellar photometric observations. In principle, these light curves encode a vast amount of information about…
In order to get astrometric parameters achieving the precision permitted by the the forthcoming generation of astrometri cmeasurements, it will be necessary to take into account effects that were neglected until the present time. Two…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
We deal with the presence of topological defects in models for two real scalar fields. We comment on defects hosting topological defects, and we search for explicit defect solutions using the trial orbit method. As we know, under certain…
Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…
We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around a central rotating body by the general relativistic two-body spin-spin and spin-orbit interactions. We use the weak-field…
We study the dynamics of two homogeneous rigid ellipsoids subject to their mutual gravitational influence. We assume that the spin axis of each ellipsoid coincides with its shortest physical axis and is perpendicular to the orbital plane.…
We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well separated components and…
One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our potential is the fundamental solution to the Heisenberg…
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'…
We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are…
This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…
The orbital motion of a binary system is characterized by various characteristic temporal intervals which, by definition, are different from each other: the draconitic, anomalistic and sidereal periods. They all coincide in the Keplerian…
In this paper, we consider the elliptic relative equilibria of four-body problem. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic relative equilibria of $4$-bodies splits into two independent linear…
One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns.…
Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly…
This paper presents an orbit estimation using non-simultaneous horizon detector measurements in the presence of uncertainties in the celestial body rotational velocity and its geometrical characteristics. The celestial body is modelled as a…
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…