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We make a comparison between results from numerically generated, quasi-equilibrium configurations of compact binary systems of black holes in close orbits, and results from the post-Newtonian approximation. The post-Newtonian results are…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Thierry Mora , Clifford M. Will

The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact…

Mathematical Physics · Physics 2012-06-13 Anton O. Belyakov

A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and…

Optimization and Control · Mathematics 2007-05-23 Taeyoung Lee , Melvin Leok , N. Harris McClamroch

The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of the two other bodies, the primaries, which evolve in Keplerian ellipses. A trajectory is called oscillatory if…

Dynamical Systems · Mathematics 2016-08-08 Marcel Guardia , Pau Martín , Lara Sabbagh , Tere M. Seara

We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…

Earth and Planetary Astrophysics · Physics 2019-05-07 Ioannis Gkolias , Christos Efthymiopoulos , Alessandra Celletti , Giuseppe Pucacco

The 2:1 mean motion resonance orbit was integrated at the restricted planar 3-body problem in absolute frame. Orbit of Jupiter was assumed circular. Initial Jupiter longitude was assumed zero. The Runge-Kutta method was used. The start of…

Astrophysics · Physics 2007-05-23 A. E. Rosaev

The quantitative characterization of amplitudes and periods of perturbations in orbital elements can help to our understanding the minor bodies dynamics, especially in case motion in vicinity of resonances. The main goal of this study is to…

Earth and Planetary Astrophysics · Physics 2023-01-19 Alexey Rosaev

The capture of compact bodies by black holes in galactic nuclei is an important prospective source for low frequency gravitational wave detectors, such as the planned Laser Interferometer Space Antenna. This paper calculates, using a…

General Relativity and Quantum Cosmology · Physics 2014-11-17 Jonathan R Gair , Daniel J Kennefick , Shane L Larson

In this paper we show two examples of numerical orbital integrations (Planar Circular Restricted Three Body Problem) in which even though the conservation of Jacobi's constant is near to 1 part in 10e8, the integration proves to be wrong.…

Astrophysics · Physics 2007-05-23 J. Espresate , G. Castro

The goal of this paper is to obtain an approximate solution of the restricted three-body problem in the case of small perturbations in the vicinity of, but not in exact resonance. In this paper, we study the restricted threebody problem…

Earth and Planetary Astrophysics · Physics 2025-11-11 Alexey Rosaev , Eva Plavalova , Pavel Nesterov

This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic…

General Relativity and Quantum Cosmology · Physics 2017-09-06 Mariafelicia De Laurentis

Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…

Earth and Planetary Astrophysics · Physics 2026-01-27 Felipe Arenas-Uribe

Examining the spin-orbit coupling effects for highly elliptical orbits is relevant to the mission design and operation of cislunar space assets, such as the Lunar Gateway. In high-eccentricity orbits, the gravity-gradient moment is here…

Earth and Planetary Astrophysics · Physics 2025-05-07 Erica Scantamburlo , Davide Guzzetti , Marcello Romano

In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…

General Physics · Physics 2021-04-19 Sergey Ershkov , Alla Rachinskaya

This paper studies composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. Going beyond the rotating wave approximation, it is…

Mathematical Physics · Physics 2015-05-18 Andreas Kurcz , Antonio Capolupo , Almut Beige , Emilio Del Giudice , Giuseppe Vitiello

This paper presents elements about the radial orbit instability, which occurs in spherical self-gravitating systems with a strong anisotropy in the radial velocity direction. It contains an overview on the history of radial orbit…

Astrophysics of Galaxies · Physics 2016-08-03 Lionel Maréchal , Jérôme Perez

We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a linear system, which after…

General Relativity and Quantum Cosmology · Physics 2009-11-07 R. Kerner , J. W. van Holten , R. Colistete

We derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian approximation in harmonic coordinates, with test-body equations of motion for the…

General Relativity and Quantum Cosmology · Physics 2017-03-08 Clifford M. Will , Matthew Maitra

We consider the Earth-Moon planar circular restricted three body problem and present a proof of the existence orbits, which approach arbitrarily close to one of the primary masses, and at the same time after each approach they move away…

Dynamical Systems · Mathematics 2024-01-24 Maciej J. Capiński , Aleksander Pasiut

The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…

Earth and Planetary Astrophysics · Physics 2015-06-11 Dimitri Veras , N. Wyn Evans