The relativistic factor in the orbital dynamics of point masses

Benitez, Federico; Gallardo, Tabaré

doi:10.1007/s10569-008-9146-5

Cited by 24 publications

(25 citation statements)

References 45 publications

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“…As mentioned in Refs. [1][2][3][4], the influence exerted by general relativity upon the dynamics of the bodies in our Solar System should not be neglected. In particular, Wanex [2] demonstrated that the difference between the final positions of Newtonian and relativistic trajectories in the restricted three-body problem made of a space probe, the Earth, and the Moon becomes considerably larger for bounded chaotic orbits than for bounded regular orbits.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the post-Newtonian circular restricted three-body problem with compact objects

Huang

2014

Phys. Rev. D

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By applying scaling transformations to distance and time, we obtain the first post-Newtonian equations of motion for a relativistic circular restricted three-body problem, where the Newtonian terms do not depend on the separation of a parent binary, though the post-Newtonian terms do. The postNewtonian contributions consist of the relativistic effects from the circular orbital frequencies between the primaries and those from the primaries to a third body. When the former post-Newtonian contribution and the nonrelativistic terms are considered, the post-Newtonian dynamics are qualitatively different from the Newtonian dynamics if the separation between the two primaries is insufficiently large. When the latter post-Newtonian contribution is also included, some orbits become unstable. By scanning the dependence of the dynamics on the separation with fast Lyapunov indicators, the separation is classified into three domains for dynamically unstable, bounded chaotic, and bounded regular dynamics.

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Section: Introductionmentioning

confidence: 99%

Dynamics of the post-Newtonian circular restricted three-body problem with compact objects

Huang

2014

Phys. Rev. D

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“…Galactic star clusters with massive central black holes [1,2], triple systems with a relativistic compact inner binary [3,4,5,6,7,8], binary black hole coalescence in the presence of a third body [9,10,11], and even the stability of the solar system [12] have been studied using combinations of N-body techniques and relativistic dynamics.…”

Section: Introductionmentioning

confidence: 99%

Post-Newtonian effects in N -body dynamics: conserved quantities in hierarchical triple systems

Will¹

2014

Class. Quantum Grav.

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Abstract. Conventional approaches to incorporating general relativistic effects into the dynamics of N -body systems containing central black holes, or of hierarchical triple systems with a relativistic inner binary, may not be adequate when the goal is to study the evolution of the system over a timescale related to relativistic secular effects, such as the precession of the pericenter. For such problems, it may necessary to include postNewtonian "cross terms" in the equations of motion in order to capture relativistic effects consistently over the long timescales. Cross terms are post-Newtonian (PN) terms that explicitly couple the two-body relativistic perturbations with the Newtonian perturbations due to other bodies in the system. In this paper, we show that the total energy and the normal component of total angular momentum of a hierarchical triple system is manifestly conserved to Newtonian order over the relativistic pericenter precession timescale of the inner binary if and only if PN cross-term effects in the equations of motion are taken carefully into account.

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“…Naoz et al (2013) provide the full Hamiltonian for a triple system (see also Schäfer 1987). The equations of motion are given by Newhall et al (1983) and Benitez & Gallardo (2008). These accelerations and Hamiltonian are implemented in gr full.…”

Section: Appendix A: Operator Theorymentioning

confidence: 99%

REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations

Tamayo

Rein

Shi

et al. 2019

Monthly Notices of the Royal Astronomical Society

181

129

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Symplectic methods, in particular the Wisdom-Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophysically important effects are dissipative. The consequences of incorporating such forces into otherwise symplectic schemes is not always clear. We show that moving to a general framework of non-commutative operators (dissipative or not) clarifies many of these questions, and that several important properties of symplectic schemes carry over to the general case. In particular, we show that explicit splitting schemes generically exploit symmetries in the applied external forces which often strongly suppress integration errors. Furthermore, we demonstrate that so-called 'symplectic correctors' (which reduce energy errors by orders of magnitude at fixed computational cost) apply equally well to weakly dissipative systems and can thus be more generally thought of as 'weak splitting correctors.' Finally, we show that previously advocated approaches of incorporating additional forces into symplectic methods work well for dissipative forces, but give qualitatively wrong answers for conservative but velocity-dependent forces like post-Newtonian corrections. We release REBOUNDx, an opensource C library for incorporating additional effects into REBOUND N-body integrations, together with a convenient PYTHON wrapper. All effects are machine-independent and we provide a binary format that interfaces with the SimulationArchive class in REBOUND to enable the sharing and reproducibility of results. Users can add effects from a list of pre-implemented astrophysical forces, or contribute new ones.

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The relativistic factor in the orbital dynamics of point masses

Cited by 24 publications

References 45 publications

Dynamics of the post-Newtonian circular restricted three-body problem with compact objects

Dynamics of the post-Newtonian circular restricted three-body problem with compact objects

Post-Newtonian effects in N -body dynamics: conserved quantities in hierarchical triple systems

REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations

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