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

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