Test of gravitomagnetism with satellites around the Earth

We focus on the possibility of measuring the gravitomagnetic effects due to the rotation of the Earth, by means of a space-based experiment that exploits satellites in geostationary orbits. Due to the rotation of the Earth, there is an asymmetry in the propagation of electromagnetic signals in opposite directions along a closed path around the Earth. We work out the delays between the two counter-propagating beams for a simple configuration, and suggest that accurate time measurements could allow, in principle, to detect the gravitomagnetic effect of the EarthComment: 6 pages, 3 figures; revised to match the version accepted for publication in EPJ

Lorentz contraction and accelerated systems

The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising when the world lines correspond to physically connected or disconnected objects. In all cases the special theory of relativity proves to be completely self-consistentComment: 7 pages, LaTeX, to be published in European Journal of Physic

Mapping Cartesian Coordinates into Emission Coordinates: some Toy Models

After briefly reviewing the relativistic approach to positioning systems based on the introduction of the emission coordinates, we show how explicit maps can be obtained between the Cartesian coordinates and the emission coordinates, for suitably chosen set of emitters, whose world-lines are supposed to be known by the users. We consider Minkowski space-time and the space-time where a small inhomogeineity is introduced (i.e. a small "gravitational" field), both in 1+1 and 1+3 dimensions.Comment: 13 pages, 7 figures, Accepted for publication in International Journal of Modern Physics

A relativistic navigation system for space

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 fourdimensional grid covering the whole spacetime and made of the null hypersurfaces representing the propagating pulses. In our first approach to the problem of positioning we consider radio-pulsars at infinity as primary sources of the required signals. The reason is that, besides being very good clocks, pulsars can be considered as being fixed stars for reasonably long times. The positioning is obtained linearizing the worldline of the observer for times of the order of a few periods of the signals. We present an exercise where the use of our method applied to the signals from four real pulsars permits the reconstruction of the motion of the Earth with respect to the fixed stars during three days. The uncertainties and the constraints of the method are discussed and the possibilities of using mov- ing artificial sources carried around by celestial bodies or spacecrafts in the Solar System is also discusse

A relativistic positioning system exploiting pulsating sources for navigation across the Solar System and beyond

We introduce an operational approach to the use of pulsating sources, located at spatial infinity, for defining a relativistic positioning and navigation system, based on the use of null four-vectors in a flatMinkowskian spacetime. We describe our approach and discuss the validity of it and of the other approximations we have considered in actual physical situations. As a prototypical case, we show how pulsars can be used to define such a positioning system: the reception of the pulses for a set of different sources whose positions in the sky and periods are assumed to be known allows the determination of the user's coordinates and spacetime trajectory, in the reference frame where the sources are at rest. In order to confirm the viability of the method, we consider an application example reconstructing the world-line of an idealized Earth in the reference frame of distant pulsars: in particular we have simulated the arrival times of the signals fromfour pulsars at the location of the Parkes radiotelescope in Australia. After pointing out the simplifications we have made, we discuss the accuracy of the method. Eventually, we suggest that the method could actually be used for navigation across the Solar System and be based on artificial sources, rather than pulsar

Pulsars as celestial beacons to detect the motion of the Earth

In order to show the principle viability of a recently proposed relativistic positioning method based on the use of pulsed signals from sources at infinity, we present an application example reconstructing the world-line of an idealized Earth in the reference frame of distant pulsars. The method considers the null four-vectors built from the period of the pulses and the direction cosines of the propagation from each source. Starting from a simplified problem (a receiver at rest) we have been able to calibrate our procedure, evidencing the influence of the uncertainty on the arrival times of the pulses as measured by the receiver, and of the numerical treatment of the data. The most relevant parameter turns out to be the accuracy of the clock used by the receiver. Actually the uncertainty used in the simulations combines both the accuracy of the clock and the fluctuations in the sources. As an evocative example the method has then been applied to the case of an ideal observer moving as a point on the surface of the Earth. The input have been the simulated arrival times of the signals from four pulsars at the location of the Parkes radiotelescope in Australia. Some substantial simplifications have been made both excluding the problems of visibility due to the actual size of the planet, and the behaviour of the sources. A rough application of the method to a three days run gives a correct result with a poor accuracy. The accuracy is then enhanced to the order of a few hundred meters if a continuous set of data is assumed. The method could actually be used for navigation across the solar system and be based on artificial sources, rather than pulsars. The viability of the method, whose additional value is in the self-sufficiency, i.e. independence from any control from other operators, has been confirmed.Comment: 11 pages, 3 eps figures; revised to match the version accepted for publication in IJMP

From Kerr to Heisenberg

In this paper we consider the space-time of a charged mass endowed with an angular momentum. The geometry is described by the exact Kerr-Newman solution of the Einstein equations. The peculiar symmetry, though exact, is usually described in terms of the gravito-magnetic field originated by the angular momentum of the source. A typical product of this geometry is represented by the generalized Sagnac effect. We write down the explicit form for the right/left asymmetry of the times of flight of two counter-rotating light beams along a circular trajectory. Letting the circle shrink to the origin the asymmetry stays finite. Furthermore it becomes independent both from the charge of the source (then its electromagnetic field) and from Newton's constant: it is then associated only to the symmetry produced by the gravitomagnetic field. When introducing, for the source, the spin of a Fermion, the lowest limit of the Heisenberg uncertainty formula for energy and time appears.Comment: 8 pages, to appear in Entrop

The Gravitomagnetic measurement of the angular momentum of celestial bodies

The asymmetry in the time delay for light rays propagating on opposite sides of a spinning body is analyzed. A frequency shift in the perceived signals is found. A practical procedure is proposed for evidencing the asymmetry, allowing for a measurement of the specific angular momentum of the rotating mass. Orders of magnitude are discussed.Comment: 4 pages, LaTeX, submitted to the Proceedings of the "X Marcel Grossmann Meeting on General Relativity" in Rio de Janeiro, Brazil, July 20-26 (2003

Gravitational Faraday Rotation in Binary Pulsar Systems

We study the gravitational Faraday rotation, on linearly polarized light rays emitted by a pulsar, orbiting another compact object. We relate the rotation angle to the orbital phase of the emitting pulsar, as well as to other parameters describing its orbit and the orientation of the angular momentum of the binary companion. We give numerical estimates of the effect for the double-pulsar system PSR J0737-3039, and we note that the expected magnitude is exceedingly small, making the effect unlikely to be observed with present technology. It is however interesting per se, since in this phenomenon, gravito-magnetism plays a leading role, unlike what happens, for instance, when studying light bending or gravitational time delay, where it appears as a correction to the gravito-electric contribution. Also, we envisage the possibility that this effect could be relevant, at least in principle, for a pulsar orbiting a non charged black-hole.Comment: 6 pages, 3 figures, minor revision; to appear in MNRA

A null frame for spacetime positioning by means of pulsating sources

We introduce an operational approach to the use of pulsating sources, located at spatial infinity, for defining a relativistic positioning and navigation system, based on the use of four-dimensional bases of null four-vectors, in flat spacetime. As a prototypical case, we show how pulsars can be used to define such a positioning system. The reception of the pulses for a set of different sources whose positions in the sky and periods are assumed to be known allows the determination of the user's coordinates and spacetime trajectory, in the reference frame where the sources are at rest. We describe our approach in flat Minkowski spacetime, and discuss the validity of this and other approximations we have considered.Comment: 19 pages, revised to match the version accepted for publication in Advances in Space Researc