Related papers: Simplified solution to determination of a binary o…
Most binaries are undetected. Astrometric reductions of a system using the assumption that the object moves like a single point mass can be biased by unresolved binary stars. The discrepancy between the centre of mass of the system (which…
This paper is devoted to exploring how we can discover and study nearby (< 1-2 kpc) planetary and binary systems by observing their action as gravitational lenses. Lensing can extend the realm of nearby binaries and planets that can be…
We give another definition of orbital free entropy introduced by Hiai, Miyamoto and us, which does not need the hyperfiniteness assumption for each given random multi-variable. The present definition is somehow related to one of its several…
The optimal instant of observation of astrophysical phenomena for objects that vary on human time-sales is an important problem, as it bears on the cost-effective use of usually scarce observational facilities. In this paper we address this…
This work is based on the letter Phys. Lett. B, 865, 139484 (2025), where we developed the analytical expression of the coordinate time in terms of the eccentric anomaly at the second post-Newtonian order in General Relativity for a compact…
Orbit determination of spacecraft in orbit has been mostly dependent on either GNSS satellite signals or ground station telemetry. Both methods present their limitations, however: GNSS signals can only be used effectively in earth orbit,…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a…
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…
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions, we use basic tools of ordinary differential equations to…
We present a review of the problem of asteroid shape and spin reconstruction from generalised projections; i.e., from lightcurves, disk-resolved images, occultation silhouettes, radar range-Doppler data, and interferometry. The aim of this…
We present methodology and mission results from orbit determination of Planet Labs nanosatellites and differential-drag control of their relative motion. Orbit determination (OD) is required on Planet Labs satellites to accurately predict…
We present the notion of orbit decidability into a more general framework, exploring interesting generalizations and variations of this algorithmic problem. A recent theorem by Bogopolski-Martino-Ventura gave a renovated protagonism to this…
We briefly survey global bifurcation techniques, and illustrate their use by finding multiple positive periodic solutions to a class of second order quasilinear ODEs related to the Yamabe problem. As an application, we give a…
We propose a methodology to study the bifurcation sequences of frozen orbits when the 2nd-order fundamental model of the satellite problem is augmented with the contribution of octupolar terms and relativistic corrections. The method is…
An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture…
Mass ratios of widely separated, long-period, resolved binary stars can be directly estimated from the available data in major space astrometry catalogs, such as the ESA's Hipparcos and Gaia mission results. The method is based on the…
Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of…
I present a brief summary of three different types of binary star - astrometric, spectroscopic and eclipsing - and tabulate the properties of these systems that can be determined directly from observations. Eclipsing binary stars are the…
We prove the existence of periodic orbits of the two fixed centers problem bifurcating from the Kepler problem. We provide the analytical expressions of these periodic orbits when the mass parameter of the system is sufficiently small.