arXiv subjects

J. -F. Pascual-Sanchez

Publications and source records attributed to J. -F. Pascual-Sanchez.

4 recordsLinked to original sources

arXiv2009

Numerical treatment of the light propagation problem in the post-Newtonian formalism

The geometry of a light wavefront, evolving from a initial flat wavefront in the 3-space associated with a post-Newtonian relativistic spacetime, is studied numerically by means of the ray tracing method. For a discretization of the bidimensional light wavefront, a surface fitting technique is used to determine the curvature of this surface. The relationship between the intrinsic curvature of the wavefront and the change of the arrival time at different points on the Earth is also numerically discussed.

gr-qc↗

arXiv2009

Numerical estimation of the curvature of a light wavefront in a weak gravitational field

The geometry of a light wavefront evolving in the 3--space associated with a post-Newtonian relativistic spacetime from a flat wavefront is studied numerically by means of the ray tracing method. For a discretization of the bidimensional wavefront the surface fitting technique is used to determine the curvature of this surface at each vertex of the mesh. The relationship between the curvature of a wavefront and the change of the arrival time at different points on the Earth is also numerically discussed.

gr-qc↗

arXiv2007

The Relativistic framework of Positioning systems

Emission relativistic coordinates are a class of spacetime coordinates defined and generated by four emitters (satellites, pulsars) broadcasting their proper time by radio signals. They are the main ingredient of the simplest conceivable relativistic positioning system. The emission coordinates are independent of any observer. Receiving directly the proper time at emission of four satellites, any user or observer can measure the values of the emission coordinates, from which he/she can obtain his trajectory and hence, in particular, his position. Moreover, if and only if the four satellites also broadcast to the users the proper times they are receiving by cross-link autonavigation from the other emitters, the positioning system is called autolocated or autonomous. In an autolocated positioning system the trajectories of the satellites of the constellation can also be known by the users and they can also obtain the metric of the spacetime (the gravitational field) on the constellation. The study of autolocated relativistic positioning systems has been initiated by Coll and coll. several years ago and it has been aimed for developing an exact fully relativistic theory of positioning systems and gravimetry, based on the framework and concepts of General Relativity. This exact relativistic framework is the alternative to considering post-newtonian relativistic corrections in a classical Newtonian framework, which is the customary approach yet now used in GPS and GLONASS.

gr-qc↗

arXiv2006

Introducing Relativity in Global Navigation Satellite Systems

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. The most important relativistic effects (to order 1/c^2) are: the Einstein gravitational blue shift effect of the satellite clock frequency (Equivalence Principle of General Relativity) and the Doppler red shift of second order, due to the motion of the satellite (Special Relativity). On the other hand, in a few years the Galileo system will be built, copying the GPS system unless an alternative project is designed. In this work, it will be also shown that the SYPOR project, using fully relativistic concepts, is an alternative to a mere copy of the GPS system. According to this project, the Galileo system would be exact and there would be no need for relativistic corrections.

gr-qc↗