Related papers: Long-term planetary integration with individual ti…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
Apart from being chaotic, the inner planets in the Solar System constitute an open system, as they are forced by the regular long-term motion of the outer ones. No integrals of motion can bound a priori the stochastic wanderings in their…
We investigate the collective behaviour of particle orbits in the vicinity of magnetic reconnection in Earth's magneto-tail. Various regions of different kinds of orbital stability of particle motions are found. We locate regimes of…
The period of a Morse oscillator and mathematical pendulum system are obtained, accurate to 100 significant digits, by forward period analysis (FPA). From these results, the long-term [0, 10^60] (time unit) solutions, which overlap from the…
Closely-packed multi-planet systems are known to experience dynamical instability if the spacings between the planets are too small. Such instability can be tempered by the frictional forces acting on the planets from gaseous discs. A…
Time-symmetric integration schemes share with symplectic schemes the property that their energy errors show a much better behavior than is the case for generic integration schemes. Allowing adaptive time steps typically leads to a loss of…
We computed Lyapunov times ($T_L$) for a sample of trans-Neptunian objects (TNOs) and outer main-belt asteroids (MBAs) using three numerical approaches: the variational method and two implementations of the renormalization technique. For…
We propose that the presence of additional planets in extrasolar planetary systems can be detected by long-term transit timing studies. If a transiting planet is on an eccentric orbit then the presence of another planet causes a secular…
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
We implement an efficient method to quantify time-dependent orbital complexity in gravitational $N$-body simulations. The technique, which we name DWaTIM, is based on a discrete wavelet transform of velocity orbital time series. The wavelet…
The late stages of terrestrial planet formation are dominated by giant impacts that collectively influence the growth, composition and habitability of any planets that form. Hitherto, numerical models designed to explore these late stage…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
Numerical N-body simulations are commonly used to explore stability regions around exoplanets, offering insights into the possible existence of satellites and ring systems. This study aims to utilize Machine Learning (ML) techniques to…
Symplectic integrators are the preferred method of solving conservative $N$-body problems in cosmological, stellar cluster, and planetary system simulations because of their superior error properties and ability to compute orbital…
Terrestrial planet formation theory is at a bottleneck, with the growing realization that pairwise collisions are treated far too simply. Here, and in our companion paper (Cambioni et al. 2019) that introduces the training methodology, we…
In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones.…
The aim of this paper is to compare different sources of stochasticity in the solar system. More precisely we study the importance of the long term influence of asteroids on the chaotic dynamics of the solar system. We show that the effects…
Over the course of the recent decades, $N$-body simulations have become a standard tool for quantifying the gravitational perturbations that ensue in planet-forming disks. Within the context of such simulations, massive non-central bodies…
The transits of a planet on a Keplerian orbit occur at time intervals exactly equal to the period of the orbit. If a second planet is introduced the orbit is not Keplerian and the transits are no longer exactly periodic. We compute the…
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…