Related papers: Some properties of emission coordinates
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.…
Relativistic positioning systems are interesting {\em technical objects} for applications around the Earth and in the Solar system. But above all else, they are basic {\em scientific objects} allowing developing relativity from its own…
We present a variant of a Global Navigation Satellite System called a Relativistic Positioning System (RPS), which is based on emission coordinates. We modelled the RPS dynamics in a space-time around Earth, described by a perturbed…
In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events…
Relativistic positioning systems provide tensors represented in $\{\ell\ell\ell\ell\}$-frames ($\ell$ for light) dual to systems of emission coordinates. We show that any Lorentzian metric field given in such a frame is isometrically…
We calculate the special and general relativistic effects of the Global Positioning System (GPS), especially the effects depending on the small deviation of the orbit from the circular one. This effect is well known but, to our knowledge,…
A {\em relativistic positioning system} consists in a set of four clocks broadcasting their respective proper time by means of light signals. Among them, the more important ones are the {\em auto-located positioning systems,} in which every…
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\bf 73}, 084017 (2006); {\bf 74}, 104003 (2006)], where the possibility of making relativistic…
As space becomes increasingly populated with new satellites and systems, modeling and simulating existing and future systems becomes more important. The two-line element set has been a standard format for sharing data about a satellite's…
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,…
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…
Over the last fifty years since the discovery of pulsars, our understanding of where and how pulsars emit the radiation we observe has undergone significant revision. The location and mechanisms of high-energy radiation are intimately tied…
Given the extreme accuracy reached by future global space astrometry, one needs a global relativistic modeling of observations. A relativistic definition of astrometric observables is then essential to find uniquely coordinates, parallax…
In the context of relativistic positioning, the coordinates of a given user may be calculated by using suitable information broadcast by a 4-tuple of satellites. Our 4-tuples belong to the Galileo constellation. Recently, we estimated the…
We present here a method for the relativistic positioning in spacetime based on the reception of pulses from sources of electromagnetic signals whose worldline is known. The method is based on the use of a four-dimensional grid covering the…
We explore, in the general relativistic context, the properties of the recently introduced GPS coordinates, as well as those of the associated frames and coframes. We show that they are covariant, and completely independent of any observer.…
Thirty-five years after the discovery of rotation-powered pulsars, we still do not understand the fundamentals of their pulsed emission at any wavelength. Even detailed pulse profiles cannot identify the location of the emission in a…
All four giant planets in the Solar system possess irregular satellites, characterized by large, highly eccentric and/or inclined orbits that are distinct from the nearly circular, uninclined orbits of the regular satellites. This…
The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true…
Planetary satellites are an integral part of the heirarchy of planetary systems. Here we make two predictions concerning their formation. First, primordial satellites, which have an array of distinguishing characteristics, form only around…