Parameter distributions of Keplerian orbits
arXiv:1012.1526 · doi:10.1088/0004-637X/728/1/66
Abstract
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We present methods for finding the probability density functions of the true anomaly, eccentric anomaly, orbital radius, and other parameters used in describing direct planetary observations. We also demonstrate the independence of the distribution of phase angle, which is highly significant in the study of direct searches, and present examples validating the derived expressions.
15 pages, 2 figures. Accepted to ApJ
References in corpus (8)
- The Keck Planet Search: Detectability and the Minimum Mass and Orbital Period Distribution of Extrasolar Planets
- Frequency of Solar-Like Systems and of Ice and Gas Giants Beyond the Snow Line from High-Magnification Microlensing Events in 2005-2008
- Inferring the eccentricity distribution
- Photometric and Obscurational Completeness
- On the Semimajor Axis Distribution of Extrasolar Gas Giant Planets: Why Hot Jupiters Are Rare Around High-Mass Stars
- New Completeness Methods for Estimating Exoplanet Discoveries by Direct Detection
- Analyzing the designs of planet finding missions
- On the Completeness of Reflex Astrometry on Extrasolar Planets near the Sensitivity Limit