From geodesics of the multipole solutions to the perturbed Kepler problem

Journal Article · Mon Nov 15 00:00:00 EST 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.104001· OSTI ID:21509919

Hernandez-Pastora, J L ^[1]; Ospino, J ^[1]

---

1. Departamento de Matematica Aplicada, Universidad de Salamanca, Salamanca (Spain)

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.

• OSTI ID: 21509919
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 10; Other Information: DOI: 10.1103/PhysRevD.82.104001; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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