Related papers: Are long-term $N$-body simulations reliable?
Analysis of large galaxy surveys requires confidence in the robustness of numerical simulation methods. The simulations are used to construct mock galaxy catalogs to validate data analysis pipelines and identify potential systematics. We…
The SecularMultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
A symplectic integrator algorithm suitable for hierarchical triple systems is formulated and tested. The positions of the stars are followed in hierarchical Jacobi coordinates, whilst the planets are referenced purely to their primary. The…
Numerous previous studies have investigated the phenomenon wherein initially spherical N-body systems are distorted to triaxial shapes. We report on an investigation of a previously described orbital instability that should oppose…
This paper explores the stability of an Earth-like planet orbiting a solar-mass star in the presence of a stellar companion using ~ 400,000 numerical integrations. Given the chaotic nature of the systems being considered, we perform a…
We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from…
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.…
The case of the planar circular restricted three-body problem is used as a test field in order to determine the character of the orbits of a small body which moves under the gravitational influence of the two heavy primary bodies. We…
Errors in numerical simulations of gravitating systems can be magnified exponentially over short periods of time. Numerical shadowing provides a way of demonstrating that the dynamics represented by numerical simulations are representative…
Gravitational N-body simulations, that is numerical solutions of the equations of motions for N particles interacting gravitationally, are widely used tools in astrophysics, with applications from few body or solar system like systems all…
The primary objective of this paper is to present a long-term numerical energy-preserving analysis of one-stage explicit symmetric and/or symplectic extended Runge--Kutta--Nystr\"{o}m (ERKN) integrators for highly oscillatory Hamiltonian…
Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of…
We study the accumulation of errors in cosmological N-body algorithms that are caused by representing the continuous distribution of matter by massive particles, comparing the PPPM and Adaptive Multigrid codes. We use for this a new measure…
A criterion for the choice of optimal softening length $\epsilon$ and time-step $dt$ for $N$-body simulations of a collisionless stellar system is analyzed. Plummer and Hernquist spheres are used as models to follow how changes in various…
We present TES, a new n-body integration code for the accurate and rapid propagation of planetary systems in the presence of close encounters. TES builds upon the classic Encke method and integrates only the perturbations to Keplerian…
In this paper we describe a new algorithm for the long-term numerical integration of the two-body problem, in which two particles interact under a Newtonian gravitational potential. Although analytical solutions exist in the unperturbed and…
The stability of rotating isotropic spherical stellar systems is investigated by using N-body simulations. Four spherical models with realistic density profiles are studied: one of them fits the luminosity profile of globular clusters,…
We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms…
In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We carry out more than 3 10^8 numerical simulations of planets between the size of Mercury and…