The true and eccentric anomaly parametrizations of the perturbed Kepler motion

Abstract

The true and eccentric anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits, by considering perturbations of the radial part of the kinetic energy in a form of a series of negative powers of the orbital radius. A toolchest 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 and 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 does the true and eccentric anomaly parameter 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.

arXiv comment19 pages, to appear in ApJ Suppl

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• Eccentric first post-Newtonian waveforms for compact binaries in frequency domain with Hansen coefficients
• Post-Keplerian corrections to the orbital periods of a two-body system and their measurability
• Gravitational waveforms for finite mass binaries
• Gravitational waveforms from a Lense-Thirring system
• Secular momentum transport by gravitational waves from spinning compact binaries
• An Efficient Method for the Evaluation of Secular Effects in the Perturbed Keplerian Motion