Related papers: High Order Relativistic Corrections To Keplerian M…
In this talk relativistic corrections due to Geroch-Hansen multipoles for perihelion precession and node line precession of orbits in a stationary axially symmetric vacuum spacetime endowed with a plane of symmetry will be shown. Patterns…
A novel approximation method in studying the perihelion precession and planetary orbits in general relativity is to use geodesic deviation equations of first and high-orders, proposed by Kerner et.al. Using higher-order geodesic deviation…
A static and axisymmetric solution of the Einstein vacuum equations with a finite number of Relativistic Multipole Moments (RMM) is written in MSA coordinates up to certain order of approximation, and the structure of its metric components…
The problem of a test body in the Schwarzschild geometry is investigated in a Keplerian limit. Beginning with the Schwarzschild metric, a solution to the limited case of approximately elliptical (Keplerian) motion is derived in terms of…
An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for…
Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a General Relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this…
We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a linear system, which after…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
We propose a new approach in studying the planetary orbits and the perihelion precession in General Relativity by means of the Homotopy Perturbation Method (HPM).For this purpose, we give a brief review of the nonlinear geodesic equations…
In this comment we explain the discrepancies mentioned by the authors between their results and ours about the influence of the gravitational quadrupole moment in the perturbative calculation of corrections to the precession of the…
We investigate the influence of the quadrupole moment of a rotating source on the motion of a test particle in the strong field regime. For this purpose the Hartle-Thorne metric, that is an approximate solution of vacuum Einstein field…
We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity. In particular, we focus on perturbations in the form of power laws and calculate…
In order to shed some light in the meaning of the relativistic multipolar expansions we consider different static solutions of the axially symmetric vacuum Einstein equations that in the non relativistic limit have same Newtonian moments.…
The multipole moments of stationary axially symmetric vacuum or electrovacuum spacetimes can be expressed in terms of the power series expansion coefficients of the Ernst potential on the axis. In this paper we present a simpler, more…
A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters…
For stationary axially symmetric spacetimes we find a simple expression for the Lense-Thirring precession in terms of the Ernst potential. This expression is used to compute, in the weak field approximation, the major non-spherical…
Among the known exact solutions of Einstein vacuum field equations the Manko-Novikov and the Quevedo-Mashhoon metrics might be suitable ones for the description of the exterior gravitational field of some real non-collapsed body. A new…
In this paper the multipole moments of stationary asymptotically flat spacetimes are considered. We show how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on R^2. We also give a bound on the multipole…
Einstein's perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…