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We show that a recently proposed numerical technique for the calculation of unstable periodic orbits in chaotic attractors is capable of finding the least unstable periodic orbits of any given order. This is achieved by introducing a…

chao-dyn · Physics 2009-10-31 Fotis K. Diakonos , Peter Schmelcher , O. Biham

Gravitational waves from binary black hole mergers have allowed us to directly observe stellar-mass black hole binaries for the first time, and therefore explore their formation channels. One of the ways to infer how a binary system is…

General Relativity and Quantum Cosmology · Physics 2022-10-26 Teagan A. Clarke , Isobel M. Romero-Shaw , Paul D. Lasky , Eric Thrane

Gaia parallax measurements for stars with poor astrometric fits -- as evidenced by high renormalized unit weight error (RUWE) -- are often assumed to be unreliable, but the extent and nature of their biases remain poorly quantified. High…

Solar and Stellar Astrophysics · Physics 2025-05-23 Kareem El-Badry

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…

Space Physics · Physics 2018-10-24 Helene Ma , Giovanni F. Gronchi , Davide Bracali Cioci

By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…

Dynamical Systems · Mathematics 2011-02-10 Bhooshan Rajpathak , Harish K. Pillai , Santanu Bandopadhyay

We employ differential astrometric methods to establish a small field reference frame stable at the micro-arcsecond ($\mu$as) level on short timescales using high-cadence simulated observations taken by Gaia in February 2017 of a bright…

Instrumentation and Methods for Astrophysics · Physics 2019-02-20 Ummi Abbas , Beatrice Bucciarelli , Mario G. Lattanzi

When an asteroid has a few observations over a short time span the information contained in the observational arc could be so little that a full orbit determination may be not possible. One of the methods developed in recent years to…

Optimization and Control · Mathematics 2020-11-11 A. Del Vigna

We introduce a new method to perform preliminary orbit determination for space debris on low Earth orbits (LEO). This method works with tracks of radar observations: each track is composed by $n\ge 4$ topocentric position vectors per pass…

Mathematical Physics · Physics 2015-01-30 Giovanni F. Gronchi , Linda Dimare , Davide Bracali Cioci , Helene Ma

The recent Gaia Data Release 3 has unveiled a catalog of over eight hundred thousand binary systems, providing orbital solutions for half of them. Since most of them are unresolved astrometric binaries, several astrophysical parameters that…

Solar and Stellar Astrophysics · Physics 2023-07-10 Xabier Pérez-Couto , Jose Á. Docobo , Pedro P. Campo

Several celestial bodies in co-orbital configurations exist in the solar system. However, co-orbital exoplanets have not yet been discovered. This lack may result from a degeneracy between the signal induced by co-orbital planets and other…

Earth and Planetary Astrophysics · Physics 2016-03-28 Adrien Leleu , Philippe Robutel , Alexandre C. M. Correia

The Hipparcos catalog and its Double and Multiple System Annex (DMSA) lists 4099 components with individual proper motions and coordinates on the epoch 1991.25. Many of these long-period binary stars are also present in the Gaia Data…

Solar and Stellar Astrophysics · Physics 2020-12-02 Valeri V. Makarov

Asteroids with companions constitute an excellent sample for studying the collisional and dynamical evolution of minor planets. The currently known binary population were discovered by different complementary techniques that produce, for…

Binary asteroids probe thermal-radiation effects on the main-belt asteroids' evolution. We discuss the possibility of detecting binary minor planet systems by the astrometric wobble of the center-of-light around the center-of-mass. This…

Earth and Planetary Astrophysics · Physics 2023-01-11 Noam Segev , Eran O. Ofek , David Polishook

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…

Astrophysics · Physics 2015-06-24 Hideki Asada , Toshio Akasaka , Masumi Kasai

We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Matthews spectrum for eccentric orbits. This demonstrates that the location of the peak…

General Relativity and Quantum Cosmology · Physics 2011-05-18 Christopher P. L. Berry , Jonathan R. Gair

This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…

Earth and Planetary Astrophysics · Physics 2022-02-02 Ethan Burnett , Hanspeter Schaub

Gravitational waves (GWs) cause the apparent position of distant stars to oscillate with a characteristic pattern on the sky. Astrometric measurements (e.g. those made by Gaia) therefore provide a new way to search for GWs. The main…

Instrumentation and Methods for Astrophysics · Physics 2019-07-08 Christopher J. Moore , Deyan P. Mihaylov , Anthony Lasenby , Gerard Gilmore

A considerable number of astrometric binaries whose positions on the sky do not obey the standard model of mean position, parallax and linear proper motion, were observed by the Hipparcos satellite. Some of them remain non-discovered, and…

Astrophysics · Physics 2009-11-11 Alexey Goldin , Valeri Makarov

A global network of laser interferometric gravitational wave detectors is projected to be in operation by around the turn of the century. Here, the noisy output of a single instrument is examined. A gravitational wave is assumed to have…

General Relativity and Quantum Cosmology · Physics 2009-10-30 David Nicholson , Alberto Vecchio

Given their extremely large distances and small apparent sizes, quasars are generally considered as objects with near-zero parallax and proper motion. However, some special quasars may have abnormal astrometric characteristics, such as…

Astrophysics of Galaxies · Physics 2022-03-09 Qi-Qi Wu , Shi-Long Liao , Xiang Ji , Zhao-Xiang Qi , Zhen-Ya Zheng Ru-Qiu Lin , Ying-Kang Zhang , Tao An