The true- and eccentric-anomaly parameterizations of the perturbed Kepler motion

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The true-and eccentric-anomaly parameterizations of the Kepler motion are generalized to quasi-periodic orbits, by considering perturbations of the radial part of the kinetic energy in the form of a series of negative powers of the orbital radius. A toolbox of methods for averaging observables as functions of the energy E and angular momentum L is developed. A broad range of systems governed by the generic Brumberg force, as well as recent applications in the theory of gravitational radiation, involve integrals of these functions over a period of motion. These integrals are evaluated by using the residue theorem. In the course of this work, two important questions emerge: (1) When do the true-and eccentric-anomaly parameters exist? (2) Under what circumstances, and why, are the poles in the origin? The purpose of this paper is to find the answer to these queries.

Original languageEnglish
Pages (from-to)79-84
Number of pages6
JournalAstrophysical Journal, Supplement Series
Issue number1
Publication statusPublished - Jan 1 2000


  • Binaries: close
  • Gravitation
  • Relativity

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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