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In this article, theory-based analytical methodologies of astrophysics employed in the modern era are suitably operated alongside a test research-grade telescope to image and determine the orbit of a near-earth asteroid from original…
The {\it concordance} cosmological model has been successfully tested throughout the last decades. Despite its successes, the fundamental nature of dark matter and dark energy is still unknown. Modifications of the gravitational action have…
This thesis investigates compact astrophysical objects within modified theories of gravity, focusing on neutron stars and strange stars. The work studies their internal structure, equilibrium, and stability in gravitational frameworks based…
This paper presents a novel Lagrangian approach to attitude tracking for rigid spacecraft using unit quaternions, where the motion equations of a spacecraft are described by a four degrees of freedom Lagrangian dynamics subject to a…
Fast and precise propagation of satellite orbits is required for mission design, orbit determination in support of operations and payload data analysis. This demand must also comply with the different accuracy requirements set by a growing…
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 improve upon a method for optimal control of quadrupedal robots which utilizes a full-order model of the system. The original method utilizes offline nonlinear optimal control to synthesize a control scheme which…
A procedure of testing the $f(R)$-theory of gravity is discussed. The latter is an extension of the general theory of relativity (GR). In order this extended theory (in some variant) to be really confirmed as a more precise theory it must…
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends…
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…
The integrability of higher-order theories of gravity is of importance in the determining the properties of these models and so their viability as models of reality. An important tool in the establishment of integrability is the singularity…
In this thesis, we focus on higher-curvature extensions of Einstein gravity as toy models to probe universal properties of conformal field theory (CFT) using the gauge/gravity duality. In this context, we are particularly interested in…
The goal of the present paper is to develop a simplified model to describe the gravitational fields of elongated asteroids. The proposed model consists of representing an elongated asteroid using a triple-particle-linkage system distributed…
A loosely packed bed of sand sits precariously on the fence between mechanically stable and flowing states. This has especially strong implications for animals or vehicles needing to navigate sandy environments, which can sink and become…
We investigate the possibility to explain theoretically the galaxy rotation curves by a gravitational potential in total absence of dark matter. To this aim an analytic fourth-order theory of gravity, nonminimally coupled with a massive…
The traditional way of estimating the gravitational field from observed motions of test objects is based on the virial relation between their kinetic and potential energy. We find a more efficient method. It is based on the natural…
The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order curvature and torsion theories of gravity. We can define effective pressure and energy density directly connected to the curvature or to…
The Newtonian limit of the most general fourth order gravity is performed with metric approach in the Jordan frame with no gauge condition. The most general theory with fourth order differential equations is obtained by generalizing the…
Self-gravitational force calculation for infinitesimally thin disks is important for studies on the evolution of galactic and protoplanetary disks. Although high-order methods have been developed for hydrodynamic and magneto-hydrodynamic…
We develop several aspects of the theory of gaseous astrophysical discs in which the gravity of the disc makes a significant contribution to its structure and dynamics. We show how the internal gravitational potential can be expanded in…