Related papers: Modeling approaches for precise relativistic orbit…
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 reexamine non-Einsteinian effects observable in the orbital motion of low-orbit artificial Earth satellites. The motivations for doing so are twofold: (i) recent theoretical studies suggest that the correct theory of gravity might…
We derive exact expressions for the relativistic redshift between an Earth-bound observer, that is meant to model a standard clock on the Earth's surface, and various (geodesic) observers in the Schwarzschild spacetime. We assume that the…
We numerically investigate the impact of GTR on the orbital part of the satellite-to-satellite range \rho and range-rate \dot\rho of the twin GRACE A/B spacecrafts through their dynamical equations of motion integrated in an Earth-centered…
We study gravitational lensing by compact objects in gravity theories that can be written in a Post-Post-Newtonian (PPN) framework: i.e., the metric is static and spherically symmetric, and can be written as a Taylor series in m/r, where m…
The Schr\"odinger-Newton model describes self-gravitating quantum particles, and it is often cited to explain the gravitational collapse of the wave function and the localization of macroscopic objects. However, this model is completely…
With continuous advances in technologies related to deep space ranging and satellite gravity gradiometry, corrections from general relativity to the dynamics of relative orbital motions will certainly become important. In this work, we…
We develop a "hybrid approximative scheme" in the framework of the post-Newtonian approximation for computing general-relativistic polytropic models simulating neutron stars in critical rigid rotation. We treat the differential equations…
The problem of a compact binary system whose components move on circular orbits is addressed using two different approximation techniques in general relativity. The post-Newtonian (PN) approximation involves an expansion in powers of…
The advance of the pericenter of the orbit of a test body around a massive body in general relativity can be calculated in a number of ways. In one method, one studies the geodesic equation in the exact Schwarzschild geometry and finds the…
Testing the effects predicted by the General Theory of Relativity, in its linearized weak field and slow motion approximation, in the Solar System is difficult because they are very small. Among them the post-Newtonian gravitomagnetic…
We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a linear system, which after…
We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe…
Obtaining accurate estimates of satellite drag coefficients in low Earth orbit is a crucial component in positioning and collision avoidance. Simulators can produce accurate estimates, but their computational expense is much too large for…
We consider the gravity assist maneuver, that is, a correction of spacecraft motion at its passing near a planet, as a tool for evaluating the Eddington post-Newtonian parameters $\beta$ and $\gamma$, characterizing vacuum spherically…
Recently, Ciufolini et al. reported on a test of the general relativistic gravitomagnetic Lense-Thirring effect by analyzing about 3.5 years of laser ranging data to the LAGEOS, LAGEOS II, LARES geodetic satellites orbiting the Earth. By…
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.…
With rapid development of techniques for astronomical observations, the precision of measurements has been significantly increasing. Theories of astronomical relativistic reference systems, which are the foundation for processing and…
The GRACE mission has been providing valuable new information on time variations in the Earth's gravity field since 2002. In addition, the GRACE Follow-On mission is scheduled to be flown soon after the end of life of the GRACE mission in…
Today, the Global Navigation Satellite Systems, used as global positioning systems, are the GPS and the GLONASS. They are based on a Newtonian model and hence they are only operative when several relativistic effects are taken into account.…