Related papers: Simple precession calculation for Mercury: a linea…
At the second post-Newtonian (2PN) order, the secular pericentre precession $\dot\omega^\mathrm{2PN}$ of either a full two-body system made of well detached non-rotating monopole masses of comparable size and a restricted two-body system…
An exact expression for the rate of dragging of inertial frames (Lense-Thirring (LT) precession) in a general stationary spacetime, is derived without invoking the weak field approximation. This expression, when used for the Kerr metric,…
Using the standard formalism of Lorentz transformation of the special theory of relativity, we derive the exact expression of the Thomas precession rate for an electron in a classical circular orbit around the nucleus of a hydrogen-like…
Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post--Newtonian physics. As a result, the differential equations of motion in Newtonian physics are replaced by functional differential equations,…
Corrections to the relativistic orbits are studied considering higher order approximations induced by gravitomagnetic effects. We discuss in details how such corrections come out taking into account magnetic components in the weak field…
Newton's Theorem of Revolving Orbits derives the force that is necessary to explain a particular precession that leaves the shape of an orbit unchanged. Newton showed that for an orbiting body that is already subject to any central force,…
Cosmology relies on a coarse-grained description of the universe, assumed to be valid on large length scales. However, the nonlinearity of general relativity makes coarse-graining extremely difficult. We here address this problem by…
Within the framework of modified Newtonian gravity it is shown that the corrected Newtonian scheme can't explain both Mercury's perihelion advance and the bending of light at the same time.
It is attempted to obtain the masses of the celestial bodies, the initial conditions of their motion, and the constant of gravitation, by a global parameter optimization. First, a numerical solution of the N-bodies problem for mass points…
Unparticle exchange gives rise to long range forces which deviate from the inverse square law due to non-canonical dimension of unparticles. It is well known that a potential of the form $r^{-n}$ where $n$ is not equal to one gives rise to…
We compare Mercury's precession test in standard General Relativity (GR), Brans-Dicke theories (BD), and Palatini f(R)-theories. We avoid post Newtonian (PN) approximation and compute exact precession in these theories. We show that the…
We develop a direct geometric method to determine the orbital parameters and mass of a planet, and we then apply the method to Neptune using high-precision data for the other planets in the solar system. The method is direct in the sense…
A modification to the vis-viva equation that accounts for general relativistic effects is introduced to enhance the accuracy of predictions of orbital motion and precession. The updated equation reduces to the traditional vis-viva equation…
This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic…
The relativistic precession model (RPM) can be used to obtain a precise measurement of the mass and spin of a black hole when the appropriate set of quasi periodic oscillations is detected in the power-density spectrum of an accreting black…
A simple general relativity theory for objects moving in gravitational fields is developed based on studying the behavior of an atom in a gravitational field. The theory is applied to calculate the satellite time dilation, light deflection…
In this paper, we investigate the anomalous planets precession in the nearly-newtonian gravitational regime. This limit is obtained from the application of the slow motion condition to the geodesic equations without altering the geodesic…
A simple and clear method is proposed to calculate the averaged motion of the apsis line in the Moon orbit. The obtained result is $3^{\circ}1'12''$ for the starry period of the Moon revolution around the Earth or $40^{\circ}22'48''$ per…
The general relativistic Lense-Thirring precessions of the perihelia of the inner planets of the Solar System are about 10^-3 arcseconds per century. Recent improvements in planetary orbit determination may yield the first observational…
An analysis based on the direct torque equations including tidal dissipation and a viscous core-mantle coupling is used to determine the damping time scales of O(10^5) years for free precession of the spin about the Cassini state and free…