相关论文: Numerical modeling of a Global Navigation Satellit…

This article develops a protocol to synchronize clocks on board a network of satellites equipped with quantum resources. We show that, in such a constellation, satellites reinforce each other's sync capabilities, forming a common clock that…

As is well-known, the Schwarzschild metric cannot be derived based on pre-general-relativistic physics alone, which means using only special relativity, the Einstein equivalence principle and the Newtonian limit. The standard way to derive…

The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic…

We develop a method to enable collaborative modelling of gravitational lenses and lens candidates, that could be used by non-professional lens enthusiasts. It uses an existing free-form modelling program (glass), but enables the input to…

We present a method to integrate the equations of motion that govern bound, accelerated orbits in Schwarzschild spacetime. At each instant the true worldline is assumed to lie tangent to a reference geodesic, called an osculating orbit,…

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…

General Relativity (GR) is shown to be a complete theory with respect to the isochrony of the pendulum. This guarantees that time can be measured with a mechanical clock within the theory itself as a matter of principle. The proper and…

An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the…

General relativistic Gauss equations for osculating elements for bound orbits under the influence of a perturbing force in an underlying Schwarzschild space-time have been derived in terms of Weierstrass elliptic functions. Thereby, the…

Global navigation satellite systems (GNSSs) are essential in providing localization and navigation services to most of the world due to their superior coverage. However, due to high pathloss and inevitable atmospheric effect, the…

With the rapid expansion of low Earth orbit (LEO) constellations, thousands of satellites are now in operation, many equipped with onboard GNSS receivers capable of continuous orbit determination and time synchronization. This development…

Robust aiding of inertial navigation systems in GNSS-denied environments is critical for the removal of accumulated navigation error caused by the drift and bias inherent in inertial sensors. One way to perform such an aiding uses matching…

The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…

We suggest that a satellite with a stable atomic clock on board be sent through the Earth-Sun gravitational saddle point to experimentally determine whether Nature prefers static solutions of the field equations of General Relativity, such…

Time delays are a key observable in strong gravitational lensing systems. Their theoretical expression is usually written as a sum of a geometrical delay and a Shapiro delay, with cosmology entering through angular diameter distances and a…

This work is a purely syntactic geometric exploration of some few elements, which are our axioms, that in last instance it is the set of differential equations whose solutions give the geodesic lines of the Schwarzschild spacetime. We…

A generalized Newtonian potential is derived from the geodesic motion of test particles in Schwarzschild spacetime. This potential reproduces several relativistic features with higher accuracy than commonly used pseudo-Newtonian approaches.…

The case of asymptotic Minkowskian space-times is considered. A special class of asymptotic rectilinear coordinates at the spatial infinity, related to a specific system of free falling observers, is chosen. This choice is applied in…

We prove the nonlinear stability of the Schwarzschild spacetime under axially symmetric polarized perturbations, i.e. solutions of the Einstein vacuum equations for asymptotically flat $1+3$ dimensional Lorentzian metrics which admit a…

In this paper, the generalized regression neural network is used to predict the GNSS position time series. Using the IGS 24-hour final solution data for Bad Hamburg permanent GNSS station in Germany, it is shown that the larger the training…