Precession of Pericenter: A More Accurate Approach

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 exact expressions without resorting to a-priori simplifying assumptions on the orbital geometry of the test particle. Our formulas allow us to put constraints on the parameters of the DM distributions considered in several local astronomical an...

From Mercury's perihelion precession (open question from 1845 to 1915) to Gravity Probe-B satellite (first proposal in 1959, launch in 2004), General Relativity had to deal with precession phenomena. Perihelion advancement precession (Einstein), geodetic (de Sitter), gravitomagnetic (Lense-Thirring) and spin-spin (Pugh-Schiff) precession are compared with all Newtonian terms in cases of weak and strong gravitational fields. Qualitative models and order of magnitude estimates ...

Relativistic Newtonian Dynamics, the simple model used previously for predicting accurately the anomalous precession of Mercury, is now applied to predict the periastron advance of a binary. The classical treatment of a binary as a two-body problem is modified to account for the influence of the gravitational potential on spacetime. Without curving spacetime, the model predicts the identical equation for the relativistic periastron advance as the post-Newtonian approximation ...

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 approach, we generalize the calculation of orbital precession and the elliptical trajectory of neutral test particles to Kerr$-$Newman space-times. One of the advantage of this method is that, for small eccentricities, one obtains trajectori...

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 under Newtonian conditions and is a more accurate tool for astrodynamics than the traditional equation. Preliminary simulation results demonstrate the application potential of the modified vis-viva equation for more complex n-body systems. ...

The advance of perihelion for geodesic motion on the galactic plane of some exact general relativistic disc solutions is calculated. Approximate analytical and numerical results are presented for the static Chazy-Curzon and the Schwarzschild discs in Weyl coordinates, the Schwarzschid disc in isotropic coordinantes and the stationary Kerr disc in the Weyl-Lewis-Papapetrou metrics. It is found that for these disc models the advance of perihelion may be an increasing or decreas...

Higher order corrections are obtained for the perihelion precession in binary systems like OJ287, Sagittarius A*-S2 and H1821+643 using both the Schwarzschild metric and the Kerr metric to take into account the spin effect. The corrections are performed considering the third root of the motion equation and developing the expansion in terms of $\epsilon \equiv r_s/\left(a(1-e^2)\right)$ and $\epsilon^{*} \equiv \left(1- \frac{2 \alpha E'}{cJ}\right) \epsilon $.The results are ...

We find a new solution to calculate the relativistic orbital periastron advance of a test-body subject to a post-Newtonian (PN) central force field, for relativistic models and theories beyond Einstein. This analitycal formula has general validity that includes all the PN contributions to the dynamics and is useful for high-precision gravitational tests. The solution is directly applicable to corrective potentials of various forms, without the need for numerical integration. ...

The region around the center of our Galaxy is very dense of stars. The kinematics of inner moving stars in the Galaxy (the so called S-stars) has been deeply studied by different research groups leading to the conclusion of the existence of a very compact object (Sgr A$^*$, likely a supermassive black hole) responsible for their high speed. Here we start from the observational evidence of orbital apsidal line precession for the S2 (also called S0-2) star to investigate on a t...

We present the first analytical computation of the (conservative) gravitational self-force correction to the periastron advance around a spinning black hole. Our result is accurate to the second order in the rotational parameter and through the 9.5 post-Newtonian level. It has been obtained as the circular limit of the correction to the gyroscope precession invariant along slightly eccentric equatorial orbits in the Kerr spacetime. The latter result is also new and we anticip...