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The equations of motion of compact binary systems have been derived in the post-Newtonian (PN) approximation of general relativity. The current level of accuracy is 3.5PN order. The conservative part of the equations of motion (neglecting…
We compute the Post-Newtonian parameter (PPN),$\gamma$, for scalar-tensor gravity theory when the action functional for the scalar field is a non-standard one, namely the Dirac-Born-Infeld (DBI) type action, used in the literature for a…
High-precision astrometry on sub-micro-arcsecond level in angular resolution requires accurate determination of the trajectory of a light-signal from the celestial light source through the gravitational field of the Solar system toward the…
The general relativistic corrections in the equations of motion and associated energy of a binary system of point-like masses are derived at the third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian expansion of the…
Light does not travel in a perfectly straight line when it passes near massive objects. In this work, we calculate the gravitational deflection of light using the gauge theory of unified gravity [Rep. Prog. Phys. 88, 057802 (2025)],…
This paper discusses new fundamental physics experiment to test relativistic gravity at the accuracy better than the effects of the 2nd order in the gravitational field strength. The Laser Astrometric Test Of Relativity (LATOR) mission uses…
The Parameterised Post-Newtonian (PPN) approach is the default framework for performing precision tests of gravity in nearby astrophysical systems. In recent works we have extended this approach for cosmological applications, and in this…
The rate of gravitational-wave energy loss from inspiralling binary systems of compact objects of arbitrary mass is derived through second post-Newtonian (2PN) order $O[(Gm/rc^2)^2]$ beyond the quadrupole approximation. The result has been…
This paper discusses new Fundamental physics experiment that will test relativistic gravity at the accuracy better than the effects of the second order in the gravitational field strength, ~G^2. The Laser Astrometric Test Of Relativity…
The current standard time delay formula (CSTD) in gravitational lensing and its claimed relation to the lens equation through Fermat's principle (least time principle) have been puzzling to the author for some time. We find that the…
This paper analyses the relativistic stellar aberration requirements for the Space Interferometry Mission (SIM). We address the issue of general relativistic deflection of light by the massive self-gravitating bodies. Specifically, we…
Estimation of time delays from a noisy and gapped data is one of the simplest data analysis problems in astronomy by its formulation. But as history of real experiments show, the work with observed data sets can be quite complex and…
The Lorentz covariant theory of precise Doppler measurements (PDM) based on the retarded Li\'{e}nard-Wiechert solution of the Einstein equations is described. An exact solution of equations of light propagation in the field of arbitrary…
We investigate possible a-priori "imprinting" of general relativity itself on spaceraft-based tests of it. We deal with some performed or proposed time-delay ranging experiments in the Sun's gravitational field. The "imprint" of general…
The Einstein's weak equivalence principle (WEP) is one of the foundational assumptions of general relativity and some other gravity theories. In the theory of parametrized post-Newtonian (PPN), the difference between the PPN parameters…
The global astrometric observations of a GAIA-like satellite were modeled within the PPN formulation of Post-Newtonian gravitation. An extensive experimental campaign based on realistic end-to-end simulations was conducted to establish the…
The time delay effect for planets and spacecraft is obtained from a fully relativistic modified gravity theory including a fifth force skew symmetric field by fitting to the Pioneer 10/11 anomalous acceleration data. A possible detection of…
We devise a test of nonlinear departures from general relativity (GR) using time delays in strong gravitational lenses. We use a phenomenological model of gravitational screening as a step discontinuity in the measure of curvature per unit…
As an extension of a previous work in which perihelion advances are considered only and as an attempt to find more stringent constraints on its parameters, we investigate effects on astronomical observation and experiments conducted in the…
Compact binaries with unequal masses and whose orbits are not aligned with the observer's line of sight are excellent probes of gravitational radiation beyond the quadrupole approximation. Among the compact binaries observed so far, strong…