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Actafutura Fax: +31 71 565 8018 Acta Futura Issue 7 Relativistic Positioning Systems and their Scientific Applications Guest Editors: Andreja Gomboc, Martin Horvat and Uroš Kostić Advanced Concepts Team http://www.esa.int/act Publication: Acta Futura, Issue 7 (2013) Editor-in-chief: Duncan James Barker Associate editors: Dario Izzo Jose M. Llorens Montolio Pacôme Delva Francesco Biscani Camilla Pandolfi Guido de Croon Luís F. Simões Daniel Hennes Published and distributed by: Advanced Concepts Team ESTEC, PPC-PF 2201 AZ, Noordwijk e Netherlands www.esa.int/gsp/ACT/publications/ActaFutura Fax: +31 71 565 8018 Cover image by S. Carloni & A. Gomboc from http://rgnss.fmf.uni-lj.si/workshop. ISSN: 2309-1940 D.O.I.:10.2420/ACT-BOK-AF Copyright ©2013- ESA Advanced Concepts Team Typeset with X TE EX Workshop on Relativistic Positioning Systems and their Scientific Applications 19-21 September 2012 Brdo near Kranj, Slovenia Organised by the Faculty of Mathematics and Physics, University of Ljubljana (UL), ESA (Advanced Concepts Team) and Centre of Excellence SPACE-SI. Organising Committee: Andreja Gomboc (UL, CE SPACE-SI) Martin Horvat (UL) Uroš Kostić (UL) Scientific Committee: Bertram Arbesser-Rastburg (ESA) Sante Carloni (ESA) Pacôme Delva (SYRTE, UPMC, Paris Obs.) Clovis Jacinto de Matos (ESA) Rune Floberghagen (ESA) Uroš Kostić (UL) Leopold Summerer (ESA) Contents Foreword 9 Autonomous Spacecraft Navigation With Pulsars 11 W. Becker, M. G. Bernhardt, and A. Jessner Restricted Post-Newtonian two-body problem with spin and its applications 29 F. Biscani, and S. Carloni Relativistic positioning systems: perspectives and prospects 35 B. Coll From emission to inertial coordinates: observational rule and inertial splitting 49 B. Coll, J. J. Ferrando, and J. A. Morales-Lladosa e concept of Autonomous Basis of Coordinates 57 A. Čadež Atomic clocks: new prospects in metrology and geodesy 67 P. Delva, and J. Lodewyck Relativistic Positioning Systems and Gravitational Perturbations 79 A. Gomboc, U. Kostić, M. Horvat, S. Carloni, and P. Delva Preliminary study for the measurement of the Lense-irring effect with the Galileo satellites 87 B. Moreno Monge, R. Koenig, and G. Michalak GPS observables in general relativity 97 C. Rovelli Relativistic Positioning Systems: Numerical Simulations 103 D. Sáez, and N. Puchades Relativistic space-time positioning: principles and strategies 111 A.Tartaglia 7 8 Foreword the last decade we have seen an enormous growth in satellite navigation systems and the utilization thereof. GPS and GLONASS are widely used for a wide range of I applications and new systems like Galileo and Beidou are being set up to widen the possibilities. All these systems have in common, that they are based on Newtonian physics. Relativistic effects (sometimes called ”Newtonian defects”) are treated as deviations that need to be corrected for. In parallel, in the last decade, a number of physicists have worked on theoretical concepts of relativistic positioning and relativistic reference frames. In a unique collaboration between the ESA Advanced Concepts Team and the Faculty of Mathematics and Physics of the University of Ljubljana with the support of the Slovenian Centre of Excellence for Space Sciences and Technologies this workshop was organised in the picturesque environment of Brdo, Slovenia. e main objectives was to bring physicists and engineers together to discuss the latest theoretical and experimental findings as well as potential implementations. e programme was set up with a view to maximising the interaction between the par- ticipants by allowing sufficient time for discussion after every presentation and at the end of every session. Five well recognized specialists were invited to give plenary lectures on key concepts and the evolution of understanding since Karl Schwarzschild and Hermann Minkowski. e workshop was also addressing potential applications from fundamental physics to rel- ativistic autonomous navigation as well as enabling technologies such as optical clocks and inter-satellite links. In the concluding discussion there was strong agreement that the workshop has achieved its objectives and that further similar events should be organised in the future. Bertram Arbesser-Rastburg (Scientific Organizing Comittee) 9 Global Navigational Satellite Systems rely on global reference frames which are fixed to the Earth via ground stations so their precision and stability in time are C limited by our knowledge of the Earth’s dynamics (e.g. plate tectonic motions, tidal effects on the Earth’s crust and variations of the Earth’s rotation rate). ese limitations could be avoided by giving to a constellation of satellites the possibility of constituting by itself a primary and autonomous positioning system, without any a priori realization of a terrestrial reference frame. Such a system leads to numerous advantages, e.g. it is a primary reference frame which is not tied to the Earth, the relativistic effects are already included in the definition of the positioning system, so there is no need to synchronize the clocks, the reference frame is very precise and stable, a better understanding of the principles of positioning systems, the new coordinates defined are measurable directly and as such open new possibilities in experimental physics and astronomy, the system can be used for extra- terrestrial navigation with the use of pulsars as clocks, etc. e workshop ”Relativistic Positioning Systems and their Scientific Applications” was co- organised by the University of Ljubljana, the Center of Excellence SPACE-SI and the Eu- ropean Space Agency (ESA). It was held at Brdo, Slovenia from September 19th to 21st, 2012. It aimed at bringing together people working on different aspects of relativistic po- sitioning systems, and giving them the possibility to interact with each other and exchange ideas and knowledge in a direct way. During the three days of the workshop, we had the op- portunity to hear the contributions covering most of the above topics. In these proceedings we try to encompass all the concepts which were presented and discussed on this occasion. e positive responses of the participants show that the area of Relativistic Positioning Sys- tem research is certainly interesting and lively one, and we hope that it will continue to attract interest and people to work in further development of Relativistic Positioning Sys- tems. Andreja Gomboc, Martin Horvat and Uroš Kostić (Guest Editors) 10 Acta Futura 7 (2013) 11-28 Acta DOI: 10.2420/AF07.2013.11 Futura Autonomous Spacecraft Navigation With Pulsars W B,* Max-Planck-Institut für extraterrestrische Physik, Gießenbachstraße, 85748 Garching, Germany Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany M G. B, Max-Planck-Institut für extraterrestrische Physik, Gießenbachstraße, 85748 Garching, Germany A J Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany Abstract. An external reference system suitable tained by tracking stations on Earth, and optical data for deep space navigation can be defined by fast from an on-board camera during encounters with solar spinning and strongly magnetized neutron stars, system bodies. Radio measurements taken by ground called pulsars. eir beamed periodic signals have stations provide very accurate information on the dis- timing stabilities comparable to atomic clocks and tance and the radial velocity of the spacecraft with typi- provide characteristic temporal signatures that can cal random errors of about 1 m and 0.1 mm/s, respec- be used as natural navigation beacons, quite sim- tively [43]. e components of position and velocity ilar to the use of GPS satellites for navigation on Earth. By comparing pulse arrival times measured perpendicular to the Earth-spacecraft line, however, are on-board a spacecraft with predicted pulse arrivals subject to much larger errors due to the limited angular at a reference location, the spacecraft position can resolution of the radio antennas. Interferometric meth- be determined autonomously and with high accu- ods can improve the angular resolution to about 25 nrad, racy everywhere in the solar system and beyond. corresponding to an uncertainty in the spacecraft posi- e unique properties of pulsars make clear already tion of about 4 km per astronomical unit (AU) of dis- today that such a navigation system will have its tance between Earth and spacecraft [37]. With increas- application in future astronautics. In this paper we ing distance from Earth, the position error increases as describe the basic principle of spacecraft navigation well, e.g., reaching a level of uncertainty of the order using pulsars and report on the current develop- of ±200 km at the orbit of Pluto and ±500 km at the ment status of this novel technology. distance of Voyager 1. Nevertheless, this technique has been used successfully to send space probes to all planets 1 Introduction in the solar system and to study asteroids and comets at close range. However, it might be necessary for future Today, the standard method of navigation for interplan- missions to overcome the disadvantages of this method, etary spacecraft is a combined use of radio data, ob- namely the dependency on ground-based control and maintenance, the increasing position and velocity un- *Corresponding author. E-mail: [email protected] 11 Acta Futura 7 (2013) / 11-28 W. Becker et al. certainty with increasing distance from Earth as well as A possible improvement in precision by a factor of 10 the large propagation delay and weakening of the signals was estimated if better (high-gain) radio antennas were at large distances. It is therefore desirable to automate available for the observations. the procedures of orbit determination and orbit control in order to support autonomous space missions. Possible implementations of autonomous navigation systems were already discussed in the early days of space Chester & Butman [22] adopted this idea and pro- flight [4]. In principle, the orbit of a spacecraft can posed to use X-ray pulsars, of which about one dozen be determined by measuring angles between solar sys- were known at the time, instead of radio pulsars.
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