Parameter distributions of Keplerian orbits

Details Parameter distributions of Keplerian orbits Parameter distributions of Keplerian orbits

2010-12-07

arxiv.org/abs/1012.1526v1

2011 ApJ 728 66

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

15 pages, 2 figures. Accepted to ApJ

Scientific paper

10.1088/0004-637X/728/1/66

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.

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