Related papers: Gravimetry, Relativity, and the Global Navigation …
We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence…
We present here a relativistic theory of gravity in which the spacetime metric is derived from a single scalar field $\Phi$. The field equation, derived from a simple variational principle, is a non-linear flat-space four-dimensional wave…
Maxwellian approximations to linear general relativity are revisited in light of relatively recent results on the degrees of freedom in the linear gravitational field. The well-known Maxwellian formalism obtained in harmonic coordinates is…
The discovery of the accelerating expansion of the Universe, thought to be driven by a mysterious form of `dark energy' constituting most of the Universe, has further revived the interest in testing Einstein's theory of General Relativity.…
Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, special relativity uses the assumption about the Euclidean structures of gravity-free…
To evaluate a potential usually one analyzes trajectories of test particles. For the Galactic Center case astronomers use bright stars or photons, so there are two basic observational techniques to investigate a gravitational potential,…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
How does one measure the gravitational field? We give explicit answers to this fundamental question and show how all components of the curvature tensor, which represents the gravitational field in Einstein's theory of General Relativity,…
We present a consistent relativistic formulation of Mach principle within a geometric theory of gravitation. In this approach, neither inertia nor free fall is assumed a priori. Instead, the motion of any local system arises from its…
In recent years, it has been rather fashionable to talk about geometric trinity of gravity. The main idea is that one can formally present the gravity equations in different terms, those of either torsion or nonmetricity instead of…
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can…
Post-relativistic gravity is a hidden variable theory for general relativity. It introduces the pre-relativistic notions absolute space, absolute time, and ether as hidden variables into general relativity. Evolution is defined by the…
In this lecture I address the issue of possible large distance modification of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions…
Symmetries and transformations are explored in the framework of entropic quantum dynamics. Two conditions arise that are required for any transformation to qualify as a symmetry. The heart of this work lies in the application of these…
We examine two far-reaching and somewhat heretic consequences of General Relativity. (i) It requires a cosmology which includes a preferred rest frame, absolute space and time. (ii) A rotating universe and time travel are strict solutions…
Teleparallel gravity, a gauge theory for the translation group, turns up as fully equivalent to Einstein's general relativity. In spite of this equivalence, it provides a whole new insight into gravitation. It breaks several paradigms…
Within the theory of General Relativity, we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. In the Schwarzschild spacetime, the solution is used to model satellite…
Analytical treatment of time transfer problem for Earth-Satellite system is presented. The development was made in a complete relativistic framework. In accordance with modern clock precision and for low altitude orbits, we neglect the…
Space-time symmetries are a crucial ingredient of any theoretical model in physics. Unlike internal symmetries, which may or may not be gauged and/or spontaneously broken, space-time symmetries do not admit any ambiguity: they are gauged by…
Orbit determination of spacecraft in orbit has been mostly dependent on either GNSS satellite signals or ground station telemetry. Both methods present their limitations, however: GNSS signals can only be used effectively in earth orbit,…