Related papers: Simple precession calculation for Mercury: a linea…
The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of $v/c$, important differences in the predicted angle of precession appear, depending on the…
We present new mathematical alternatives for explaining rotation curves of spiral galaxies in the MOND context. For given total masses, it is shown that various mathematical alternatives to MOND, while predicting flat rotation curves for…
The calculus of apsidal precession frequencies of the planets is developed by means of a perturbation thecnique. A model of concentric rings (ring model), suitable for improving calculations, is introduced. Conclusive remarks concerning a…
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
We investigate the extent to which pseudo-Newtonian gravitational potentials can reproduce classic tests of general relativity without resorting to full general relativistic formalisms. This is useful for the researchers seeking intuitive…
We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces…
We analytically calculate the secular precession of the pericenter of a test particle orbiting a central body surrounded by a continuous distribution of Dark Matter (DM) by using some commonly adopted density profiles for it. We obtain…
We report a search for new gravitational physics phenomena based on Einstein-Cartan theory of General Relativity including spacetime torsion. Starting from the parametrized torsion framework of Mao, Tegmark, Guth and Cabi, we analyze the…
It is attempted to derive the general relativistic (GR) equation of motion for planet and its solution solely by the special relativity (SR) techniques. The motion of a planet relative to the sun and that of the sun to the planet are solved…
The possibility of measuring the post-Newtonian gravitoelectric correction to the orbital period of a test particle freely orbiting a spherically symmetric mass in the Solar System is analyzed. It should be possible, in principle, to detect…
We present a detailed analysis of all possible regular precessions of a heavy asymmetric body with a fixed point not coinciding with the center of mass. The calculations are done in terms of the rotation matrix, by writing the Euler-Poisson…
The precession of Mercury's perihelion is reinspected by the principle of least action. The anomalous advancement of the apside line that is customarily accounted by the theory of general relativity, is ascribed to the gravitational effect…
Possible explanations of the recently reported anomalous increase of the eccentricity of the lunar orbit are sought in terms of classical Newtonian mechanics, general relativity, and long-range modifications of gravity.
Modified uncertainty principle and non-commutative variables may phenomenologically account for quantum gravity effects, independently of the considered theory of quantum gravity. We show that quantum fluids enable experimental analogs and…
The upcoming space missions, MESSENGER and BepiColombo with onboard instrumentation capable of measuring the rotational parameters stimulate the objective to reach an accurate theory of the rotational motion of Mercury. For obtaining the…
A significant fraction of an exoplanet transit model evaluation time is spent calculating projected distances between the planet and its host star. This is a relatively fast operation for a circular orbit, but slower for an eccentric one.…
In this paper, I re-examine the question of a possible explanation of the anomalous advance of Mercury's perihelion by the existence of the hypothetical planet Vulcan proposed by Le Verrier, whose orbit would be located inside the orbit of…
We present calculations of gyroscope precession in spacetimes described by Levi-Civita and Lewis metrics, under different circumstances. By doing so we are able to establish a link between the parameters of the metrics and observable…
We present a novel solution of the Mercury perihelion advance shift in the new gravity model. It is found that the non-relativistic reduction of the Dirac equation with the gravitational potential produces the new gravitational potential of…
We used recently produced Solar System ephemerides, which incorporate two years of ranging observations to the MESSENGER spacecraft, to extract the secular orbital elements for Mercury and associated uncertainties. As Mercury is in a stable…