Equilibria in the secular, non-coplanar two-planet problem

Cezary Migaszewski; Krzysztof Gozdziewski

doi:10.1111/j.1365-2966.2009.14552.x

Home/Archive/arXiv

arXiv · 0812.2949

Equilibria in the secular, non-coplanar two-planet problem

Cezary Migaszewski·Krzysztof Gozdziewski

View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate the secular dynamics of a planetary system composed of the parent star and two massive planets in mutually inclined orbits. The dynamics are investigated in wide ranges of semi-major axes ratios (0.1-0.667), and planetary masses ratios (0.25-2) as well as in the whole permitted ranges of the energy and total angular momentum. The secular model is constructed by semi-analytic averaging of the three-body system. We focus on equilibria of the secular Hamiltonian (periodic solutions of the full system), and we analyze their stability. We attempt to classify families of these solutions in terms of the angular momentum integral. We identified new equilibria, yet unknown in the literature. Our results are general and may be applied to a wide class of three-body systems, including configurations with a star and brown dwarfs and sub-stellar objects. We also describe some technical aspects of the semi-numerical averaging. The HD 12661 planetary system is investigated as an example configuration.

Explore related subjects

astro-ph

Keep this discovery

BibTeX RIS

Cezary Migaszewski, Krzysztof Gozdziewski. 2009-02-02. Equilibria in the secular, non-coplanar two-planet problem. https://doi.org/10.1111/j.1365-2966.2009.14552.x

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2019

Classical analysis of the rotational dynamic of spiral galaxies: Quo Vadis Dark Matter?

In this paper we study a stellar dynamic model for the stars' rotational-dynamics, with a distribution of its own mass, rotating around its center with a higher density, like spiral galaxies happen, by means of a classical calculus of the rotation velocities of a particle around its rotational axis, inside a smoothed distribution of matter. The stars are supposed to be particles and their distribution in the galaxy is modelled as a matter distribution inversely proportional to its distance from its center. Two kinds of matter distribution are supposed: one with constant density, and other with radial distribution. Two types of galaxy symmetry are also considered: spherical and oblate ellipsoidal. Using only classical mechanics arguments it is shown that the calculated velocity distribution inside the galaxy is similar to that obtained from astronomical observations, without the necessity of suppose the existence of dark matter or other phenomena.

astro-ph↗

arXiv2019

AIRES: A system for air shower simulations

The AIRES (AIR-shower Extended Simulations) system is a set of programs and subroutines to realistically simulate particle showers produced after the incidence of high energy cosmic rays on the Earth's atmosphere, and to manage all the related output data. The current version includes a series of improvements with respect to previous releases that are explained in detail in this manual and/or the web site aires.fisica.unlp.edu.ar from where the software can be downloaded. Among such improvements, it is worth mentioning: (i) High energy hadronic collisions can be simulated usign the the well-known hadronic models EPOS, QGSJET, or SIBYLL, all of them in their LHC-tuned versions. (ii) Detailed simulation of unstable hadron decays. (iii) The inclusion of a series of pre-compiled, ready to use, external special particle modules, that are characteristic of AIRES since its early versions. Such modules allow, for example, to easily simulate multi-primary particle showers. (iv) An exhaustive revision of the atmospheric profile models, including annual average profiles for geographcal locations corresponding to currently in operation ultra-high energu shower observatories; and also the capability of accepting user-defined custom atmospheric profiles.

astro-ph↗

arXiv2019

A new paradigm for the universe

This book provides a completely new approach to understanding the universe. The main idea is that the principal objects in the universe form a spectrum unified by the presence of a massive or hypermassive black hole. These objects are variously called quasars, active galaxies and spiral galaxies. The key to understanding their dynamics is angular momentum and the key tool, and main innovative idea of this work, is a proper formulation of "Mach's principle" using Sciama's ideas. In essence, what is provided here is a totally new paradigm for the universe. In this paradigm, there is no big bang, and the universe is many orders of magnitude older than current estimates for its age. Indeed there is no natural limit for its age.

astro-ph↗