Parameter distributions of Keplerian orbits

Dmitry Savransky, Eric Cady, N. Jeremy Kasdin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 semimajor 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.

Original languageEnglish (US)
JournalAstrophysical Journal
Issue number1
StatePublished - Feb 10 2011

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Celestial mechanics
  • Methods: analytical
  • Methods: statistical
  • Planets and satellites: detection


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