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Title: From geodesics of the multipole solutions to the perturbed Kepler problem

Abstract

A static and axisymmetric solution of the Einstein vacuum equations with a finite number of relativistic multipole moments (RMM) is written in multipole symmetry adapted (MSA) coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics, we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM of the source starting from the monopole (Schwarzschild correction). In particular, the perihelion precession of the orbit is calculated in terms of the quadrupole and 2{sup 4}-pole moments. Since the MSA coordinates generalize the Schwarzschild coordinates, the result obtained allows measurement of the relevance of the quadrupole moment in the first order correction to the perihelion frequency-shift.

Authors:
 [1];  [1]
  1. Departamento de Matematica Aplicada, Universidad de Salamanca, Salamanca (Spain)
Publication Date:
OSTI Identifier:
21509919
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 82; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.82.104001; (c) 2010 American Institute of Physics; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; AXIAL SYMMETRY; CORRECTIONS; EINSTEIN FIELD EQUATIONS; GEODESICS; MONOPOLES; ORBITS; PRECESSION; QUADRUPOLE MOMENTS; RELATIVISTIC RANGE; SCHWARZSCHILD METRIC; CALCULATION METHODS; ENERGY RANGE; EQUATIONS; FIELD EQUATIONS; METRICS; SYMMETRY

Citation Formats

Hernandez-Pastora, J L, Instituto Universitario de Fisica Fundamental y Matematicas, Universidad de Salamanca, Salamanca, and Ospino, J. From geodesics of the multipole solutions to the perturbed Kepler problem. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.82.104001.
Hernandez-Pastora, J L, Instituto Universitario de Fisica Fundamental y Matematicas, Universidad de Salamanca, Salamanca, & Ospino, J. From geodesics of the multipole solutions to the perturbed Kepler problem. United States. https://doi.org/10.1103/PHYSREVD.82.104001
Hernandez-Pastora, J L, Instituto Universitario de Fisica Fundamental y Matematicas, Universidad de Salamanca, Salamanca, and Ospino, J. 2010. "From geodesics of the multipole solutions to the perturbed Kepler problem". United States. https://doi.org/10.1103/PHYSREVD.82.104001.
@article{osti_21509919,
title = {From geodesics of the multipole solutions to the perturbed Kepler problem},
author = {Hernandez-Pastora, J L and Instituto Universitario de Fisica Fundamental y Matematicas, Universidad de Salamanca, Salamanca and Ospino, J},
abstractNote = {A static and axisymmetric solution of the Einstein vacuum equations with a finite number of relativistic multipole moments (RMM) is written in multipole symmetry adapted (MSA) coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics, we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM of the source starting from the monopole (Schwarzschild correction). In particular, the perihelion precession of the orbit is calculated in terms of the quadrupole and 2{sup 4}-pole moments. Since the MSA coordinates generalize the Schwarzschild coordinates, the result obtained allows measurement of the relevance of the quadrupole moment in the first order correction to the perihelion frequency-shift.},
doi = {10.1103/PHYSREVD.82.104001},
url = {https://www.osti.gov/biblio/21509919}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 10,
volume = 82,
place = {United States},
year = {Mon Nov 15 00:00:00 EST 2010},
month = {Mon Nov 15 00:00:00 EST 2010}
}