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We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an astronomical N-body system. To do this, we generalize…
We develop a fully gauge invariant analysis of gravitational wave polarizations in metric f(R) gravity with a particular focus on the modified Starobinsky model, whose constant curvature solution provides a natural deSitter background for…
I propose an alternative $f(R)$ theory of gravity constructed by applying the function $f$ directly to the Ricci tensor instead of the Ricci scalar. The main goal of this study is to derive the resulting modified Einstein equations for the…
We present a comprehensive theoretical framework for gravitational wave (GW) propagation and their \textbf{nonlinear backreaction} in $f(R, G)$ modified gravity. By developing a scalar-tensor formulation with two auxiliary fields, we…
In this paper, we use the metric coefficients and the equation of motion in the 2nd post-Newtonian approximation in scalar-tensor theory including intermediate range gravity to derive the deflection of light and compare it with previous…
The high accuracy now reached in the VLBI Earth Orientation Parameters (EOP) determination requires looking further at the various geophysical contributions to variations in EOP. The determination of the Earth gravity field from space…
Stationary Random Functions have been successfully applied in geostatistical applications for decades. In some instances, the assumption of a homogeneous spatial dependence structure across the entire domain of interest is unrealistic. A…
Conventional Feedback-Linearization-based controller, applied to the tilt-rotor (eight inputs), results in the extensive changes in the tilting angles, which are not expected in practice. To solve this problem, we introduce the novel…
Rigid motion computation or estimation is a cornerstone in numerous fields. Attitude computation can be achieved by integrating the angular velocity measured by gyroscopes, the accuracy of which is crucially important for the dead-reckoning…
In the past, the gravitational acceleration on the surface of the Earth, $g$, has been measured in many ways. Various methods include the use of a pendulum as well as models involving the use of a mass on a spring. We have designed a new…
In this work we investigate whether a certain phenomenological extension to the general relativity (GR), in the form of a gravitational phase transition (GPT) in the Universe, can reduce the external $Planck$ tensions with the local Hubble…
We present a new gravitational lens modelling technique designed to model high-resolution interferometric observations with large numbers of visibilities without the need to pre-average the data in time or frequency. We demonstrate the…
The precisions of existing gravitational calibrators for gravitational wave observatories are limited by their dependence on the relative position between the calibrators and the observatory's test masses. Here we present a novel geometry…
In this contribution we present two new proposals for measuring the general relativistic gravitomagnetic component of the gravitational field of the Earth. One proposal consists of the measurement of the difference of the rates of the…
In order to make a pinpoint landing on the Moon, the spacecraft's navigation system must be accurate. To achieve the desired accuracy, navigational drift caused by the inertial sensors must be corrected. One way to correct this drift is to…
We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test…
Estimating the 6-degrees-of-freedom (6DoF) pose of a spacecraft from a single image is critical for autonomous operations like in-orbit servicing and space debris removal. Existing state-of-the-art methods often rely on iterative…
Gravity theory is the basis of modern cosmological models. Thirring-Feynman's tensor field approach to gravitation is an alternative to General Relativity (GR). Though Field Gravity (FG) approach is still developing subject, it opens new…
We propose a novel positional encoding for learning graph on Transformer architecture. Existing approaches either linearize a graph to encode absolute position in the sequence of nodes, or encode relative position with another node using…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…