Simple, Accurate, Approximate Orbits in the Logarithmic and a Range of Power-Law Galactic Potentials
arXiv:astro-ph/0512261 · doi:10.1086/500196
Abstract
Curves in a family derived from powers of the polar coordinate formula for ellipses are found to provide good fits to bound orbits in a range of power-law potentials. This range includes the well-known (Keplerian) and logarithmic potentials. These approximate orbits, called p-ellipses, retain some of the basic geometric properties of ellipses. They satisfy and generalize Newton's apsidal precession formula, which is one of the reasons for their surprising accuracy. Because of their simplicity the p-ellipses make very useful tools for studying trends among power-law potentials, and especially the occurence of closed orbits. The occurence of closed or nearly closed orbits in different potentials highlights the possibility of period resonances between precessing, eccentric orbits and circular orbits, or between the precession period of multi-lobed closed orbits and satellite periods. These orbits and their resonances promise to help illuminate a number of problems in galaxy and accretion disk dynamics.
arXiv comment38 pages, 8 figures, 1 table, accepted for the Astron. J
References in corpus (11)
- A Universal Density Profile from Hierarchical Clustering
- Dynamical insight into dark-matter haloes
- Galaxy Collisions
- Cores of Dark Matter Halos Correlate with Disk Scale Lengths
- A map for eccentric orbits in triaxial potentials
- 2dFGRS and SDSS Galaxy Group Density Profiles
- Approximating Stellar Orbits: Improving on Epicycle Theory
- Orbits in Extended Mass Distributions: General Results and the Spirographic Approximation
- Isolated and non-isolated dark matter halos and the NFW profile
- Simple Models for the Distribution of Dark Matter
- Global Dynamics in the Singular Logarithmic Potential
Cited by in corpus (17)
- Timelike geodesics in Naked Singularity and Black Hole Spacetimes
- Short-term dynamical evolution of grand-design spirals in barred galaxies
- Candidate Tidal Dwarf Galaxies in Arp 305: Lessons on Dwarf Detachment and Globular Cluster Formation
- The symmetries and scaling of tidal tails in galaxies
- Towards an observational test of black hole versus naked singularity at the galactic center
- Applying the Analytic Theory of Colliding Ring Galaxies
- Analytic Central Orbits and their Transformation Group
- Natural orbit approximations in single power-law potentials
- A Study of the Orbits of the Logarithmic Potential for Galaxies
- Lindblad Zones: resonant eccentric orbits to aid bar and spiral formation in galaxy discs
- Retrograde Precession of Relativistic Orbits and the Quest for Charged Black Holes
- Dark Matter Redistribution Explains Galaxy Growth and Rotation Curve Development
- Closed, spirograph-like orbits in power law central potentials
- The monotonicity of the apsidal angle in power-law potential systems
- A Warp in Progress: H I and Radio Continuum Observations of the Spiral NGC 3145
- Post-Newtonian properties of EMRI with Power Law Potential
- Orbits in elementary, power-law galaxy bars: 1. Occurence and role of single loops