Astrometry encompasses all that is necessary to provide the positions and motions of celestial bodies. This includes observational techniques, instrumentation, processing and analysis of observational data, reference systems and frames, and the resulting astronomical phenomena. Astrometry is fundamental to all other fields of astronomy, from the pointing of telescopes, to navigation and guidance systems, to distance and motion determinations for astrophysics. In the last few decades, new observational techniques have enabled improvements in accuracy by orders of magnitude. Starting from basic principles, this book provides the fundamentals for this new astrometry at milli- and micro-arcsecond accuracies. Topics include: basics of general relativity; co-ordinate systems; vectors, tensors, quaternions, and observational uncertainties; determination and use of the celestial and terrestrial reference systems and frames; applications of new observational techniques; present and future star catalogues and double star astrometry. This comprehensive reference will be invaluable for graduate students and research astronomers.

Astrometry encompasses all that is necessary to provide the positions and motions of celestial bodies. This includes observational techniques, instrumentation, processing and analysis of observational data, reference systems and frames, and the resulting astronomical phenomena. Astrometry is fundamental to all other fields of astronomy, from the pointing of telescopes, to navigation and guidance systems, to distance and motion determinations for astrophysics. In the last few decades, new observational techniques have enabled improvements in accuracy by orders of magnitude. Starting from basic principles, this book provides the fundamentals for this new astrometry at milli- and micro-arcsecond accuracies. Topics include: basics of general relativity; co-ordinate systems; vectors, tensors, quaternions, and observational uncertainties; determination and use of the celestial and terrestrial reference systems and frames; applications of new observational techniques; present and future star catalogues and double star astrometry. This comprehensive reference will be invaluable for graduate students and research astronomers.

On the occasion ofthe second edition ofthe book, it appeared necessary to up­ date information that was already seven years old. Astrometry has recorded tremendous advances during these last years, so that, in addition to cor­ recting identified errors and misprints, there are many major modifications. Among the events that forced me to modify significantly the contents of the book, the most important are the release of the Hipparcos and Tycho cata­ logues, the introduction of CCD astrometry, the decision of the International Astronomical Union to adopt a new celestial reference frame, the dramatic improvement of accurate time and frequency standards, the decision taken by space agencies to prepare several new space astrometry satellites and the development of optical interferometry. The description and the consequences of these events have been included in this edition. One of them is that a mi­ crosecond of arc or microarcsecond (uas) has become a widely used unit. On the contrary, the result was also that the importance of some in­ struments such as astrolabes or transit circles has decreased. However, I left but because their description unchanged, not only for their historical interest, newer techniques often use similar data reduction methods so that one can refer to them. Conversely, some methods or instruments have evolved and new information is included. Finally, many new references were added to the original list.

On the occasion ofthe second edition ofthe book, it appeared necessary to up­ date information that was already seven years old. Astrometry has recorded tremendous advances during these last years, so that, in addition to cor­ recting identified errors and misprints, there are many major modifications. Among the events that forced me to modify significantly the contents of the book, the most important are the release of the Hipparcos and Tycho cata­ logues, the introduction of CCD astrometry, the decision of the International Astronomical Union to adopt a new celestial reference frame, the dramatic improvement of accurate time and frequency standards, the decision taken by space agencies to prepare several new space astrometry satellites and the development of optical interferometry. The description and the consequences of these events have been included in this edition. One of them is that a mi­ crosecond of arc or microarcsecond (uas) has become a widely used unit. On the contrary, the result was also that the importance of some in­ struments such as astrolabes or transit circles has decreased. However, I left but because their description unchanged, not only for their historical interest, newer techniques often use similar data reduction methods so that one can refer to them. Conversely, some methods or instruments have evolved and new information is included. Finally, many new references were added to the original list.

Astrometry is the domain of astronomy devoted to the determination of po­ sitions and their time-variations, and by extension, the apparent dimensions and shapes of celestial bodies. Although several books describe the theoretical foundations of positional astronomy, they touch only slightly on the descrip­ tion of instruments and the procedures for obtaining actual geometrical or kinematic quantities, which are among the basic observational data in the study of the Universe and of its components. The goal of the present book is, in contrast, to provide an up-to-date description of astrometric techniques, particularly the most recent and powerful ones, whether the instruments are on the ground or in space. Until the end of the 19th century, before the development of physical as­ tronomy, all astronomical observations were directed towards obtaining posi­ tions of celestial bodies. Since then astrophysics has become the most impor­ tant domain of astronomy. With the extension of observations to almost all wavelengths from radio waves to gamma rays, with the use of very sensitive new receivers and the development of fast computers, remarkable progress has been made in the description and the understanding of the Universe.

On the occasion ofthe second edition ofthe book, it appeared necessary to up­ date information that was already seven years old. Astrometry has recorded tremendous advances during these last years, so that, in addition to cor­ recting identified errors and misprints, there are many major modifications. Among the events that forced me to modify significantly the contents of the book, the most important are the release of the Hipparcos and Tycho cata­ logues, the introduction of CCD astrometry, the decision of the International Astronomical Union to adopt a new celestial reference frame, the dramatic improvement of accurate time and frequency standards, the decision taken by space agencies to prepare several new space astrometry satellites and the development of optical interferometry. The description and the consequences of these events have been included in this edition. One of them is that a mi­ crosecond of arc or microarcsecond (uas) has become a widely used unit. On the contrary, the result was also that the importance of some in­ struments such as astrolabes or transit circles has decreased. However, I left but because their description unchanged, not only for their historical interest, newer techniques often use similar data reduction methods so that one can refer to them. Conversely, some methods or instruments have evolved and new information is included. Finally, many new references were added to the original list.

The driving idea, in organizing this Symposium on "Relativity in Celestial Mechanics . and Astrometry" was that, in recent years, the ac­ curacy of several Astrometric techniques has so much increased that re­ lativistic effects are no more marginally mentioned in academic presen­ tations but have become an intrinsic part of the interpretation of all the positional data. Techniques such as V. L. B. I. , space probes, lunar lasers, etc . . . have greatly contributed to reduce the accuracy level to an angular equivalent of a few milliarc-seconds. HIPPARCOS will extend this trend to stellar astrometry and new proposals aim at gaining ano­ ther one or two orders of magnitude in observing precision. In paral­ lel, great progress has also been made in the theories of motion of ce­ lestial bodies and more rigourous treatments within the frame of general relativity become necessary. The definition of reference frames and of various coordinate times become also a major problem in the intercompa­ rison of observations produced by different methods. This Symposium gave to people using relativistic corrections in reducing their measurements or in constructing various theories of mo­ tion a chance to exchange their experience in the field and to confront it with theoreticians in general relativity. The Symposium was approved by the IAU in 1983 and it was organi­ zed by the Institute of Theoretical Astronomy of the USSR Academy of Sciences on May 28-31, 1985.

This book on reference systems is the first comprehensive review of the problem of celestial and terrestrial reference systems and frames. Over 20 years, the importance of this problem emerged slowly as the accuracy of new observational techniques improved. The topic has already been approached in several symposia such as Stresa (1967), Morioka (1971), Perth (1973), Columbus (1975, 1978 and 1985), Kiev (1977) and San Fernando (1978). Two IAU colloquia held in Turin (1974) and in Warsaw (1980) were exclusively devoted to discuss reference systems. During this time, the problem of terrestrial and celestial reference systems has been discussed also in many astronomical and geodetic symposia, but always among other topics. Thus, a review devoted solely to the definition and practical realization of such systems was needed. It is hoped that this book, containing modern comprehensive reviews of important facets of this problem will contribute not only to a better and wider understanding of the mathematics and the physics that are behind the concepts and the realizations, but also to future development in a field that can only expand with the rapidly increasing accuracy of geodetic and astronomical observations. We are pleased to thank all the authors of the book who have enthusiastically agreed to contribute to the book in their field of competence and have gracefully accepted guidance from the editors in the definition of the subject and of the interfaces with other chapters. We thank Prof. Y.

This book on reference systems is the first comprehensive review of the problem of celestial and terrestrial reference systems and frames. Over 20 years, the importance of this problem emerged slowly as the accuracy of new observational techniques improved. The topic has already been approached in several symposia such as Stresa (1967), Morioka (1971), Perth (1973), Columbus (1975, 1978 and 1985), Kiev (1977) and San Fernando (1978). Two IAU colloquia held in Turin (1974) and in Warsaw (1980) were exclusively devoted to discuss reference systems. During this time, the problem of terrestrial and celestial reference systems has been discussed also in many astronomical and geodetic symposia, but always among other topics. Thus, a review devoted solely to the definition and practical realization of such systems was needed. It is hoped that this book, containing modern comprehensive reviews of important facets of this problem will contribute not only to a better and wider understanding of the mathematics and the physics that are behind the concepts and the realizations, but also to future development in a field that can only expand with the rapidly increasing accuracy of geodetic and astronomical observations. We are pleased to thank all the authors of the book who have enthusiastically agreed to contribute to the book in their field of competence and have gracefully accepted guidance from the editors in the definition of the subject and of the interfaces with other chapters. We thank Prof. Y.

decision and investigative process of the scientist, they can also wri te the paragra}ils of scientific resul ts. Once a canputer research activity progresses from intuitive guesses to a systematic study, the canputer program can free the scientist to pursue new original ideas. '!his concept is illustrated in the ptper by Hut. Sussnan says "Knowledge" is knowing what not to canpute. His main message is that we must change from trying to maximize the efficiency of the canputer to maximizing the effectiveness of the scientist. The canputer is relatively cheap, it is the trained scientist who is most valuable. In the second keynote address, R. L. Duncombe (University of Texas) described the "Early Applications of Canputer Technology to Dynamical Astronany. " His talk traced the worldwide introduction of punched card equipnent and their applications through the use of the first electronic canputers. Sussman and Duncombe, therefore, provided a forecast and review of the use of computers in dynamical astronany. This proceedings is intended to provide a consolidated general view of the ptst, present, and future of the Applications of Canputer Technology to Dynamical Astronany.Of necessity this requires that the ptpers be rela ti vely short and provide references to the more canplete discussions. Thanks to the representa tion from so many different countries the proceedings give a picture of the activities worldwide. The Scientific Organizing Comnittee included K. B. IIlatnagar, V. A. Brtmberg, G. Contopoulos, A. Depri t , J. Henrard, J. Kovalevsky, Y.

Astrometry encompasses all that is necessary to provide the positions and motions of celestial bodies. This includes observational techniques, instrumentation, processing and analysis of observational data, reference systems and frames, and the resulting astronomical phenomena. Astrometry is fundamental to all other fields of astronomy, from the pointing of telescopes, to navigation and guidance systems, to distance and motion determinations for astrophysics. In the last few decades, new observational techniques have enabled improvements in accuracy by orders of magnitude. Starting from basic principles, this book provides the fundamentals for this new astrometry at milli- and micro-arcsecond accuracies. Topics include: basics of general relativity; co-ordinate systems; vectors, tensors, quaternions, and observational uncertainties; determination and use of the celestial and terrestrial reference systems and frames; applications of new observational techniques; present and future star catalogues and double star astrometry. This comprehensive reference will be invaluable for graduate students and research astronomers.

Astrometry encompasses all that is necessary to provide the positions and motions of celestial bodies. This includes observational techniques, instrumentation, processing and analysis of observational data, reference systems and frames, and the resulting astronomical phenomena. Astrometry is fundamental to all other fields of astronomy, from the pointing of telescopes, to navigation and guidance systems, to distance and motion determinations for astrophysics. In the last few decades, new observational techniques have enabled improvements in accuracy by orders of magnitude. Starting from basic principles, this book provides the fundamentals for this new astrometry at milli- and micro-arcsecond accuracies. Topics include: basics of general relativity; co-ordinate systems; vectors, tensors, quaternions, and observational uncertainties; determination and use of the celestial and terrestrial reference systems and frames; applications of new observational techniques; present and future star catalogues and double star astrometry. This comprehensive reference will be invaluable for graduate students and research astronomers.

On the occasion ofthe second edition ofthe book, it appeared necessary to up­ date information that was already seven years old. Astrometry has recorded tremendous advances during these last years, so that, in addition to cor­ recting identified errors and misprints, there are many major modifications. Among the events that forced me to modify significantly the contents of the book, the most important are the release of the Hipparcos and Tycho cata­ logues, the introduction of CCD astrometry, the decision of the International Astronomical Union to adopt a new celestial reference frame, the dramatic improvement of accurate time and frequency standards, the decision taken by space agencies to prepare several new space astrometry satellites and the development of optical interferometry. The description and the consequences of these events have been included in this edition. One of them is that a mi­ crosecond of arc or microarcsecond (uas) has become a widely used unit. On the contrary, the result was also that the importance of some in­ struments such as astrolabes or transit circles has decreased. However, I left but because their description unchanged, not only for their historical interest, newer techniques often use similar data reduction methods so that one can refer to them. Conversely, some methods or instruments have evolved and new information is included. Finally, many new references were added to the original list.

On the occasion ofthe second edition ofthe book, it appeared necessary to up­ date information that was already seven years old. Astrometry has recorded tremendous advances during these last years, so that, in addition to cor­ recting identified errors and misprints, there are many major modifications. Among the events that forced me to modify significantly the contents of the book, the most important are the release of the Hipparcos and Tycho cata­ logues, the introduction of CCD astrometry, the decision of the International Astronomical Union to adopt a new celestial reference frame, the dramatic improvement of accurate time and frequency standards, the decision taken by space agencies to prepare several new space astrometry satellites and the development of optical interferometry. The description and the consequences of these events have been included in this edition. One of them is that a mi­ crosecond of arc or microarcsecond (uas) has become a widely used unit. On the contrary, the result was also that the importance of some in­ struments such as astrolabes or transit circles has decreased. However, I left but because their description unchanged, not only for their historical interest, newer techniques often use similar data reduction methods so that one can refer to them. Conversely, some methods or instruments have evolved and new information is included. Finally, many new references were added to the original list.

Astrometry is the domain of astronomy devoted to the determination of po­ sitions and their time-variations, and by extension, the apparent dimensions and shapes of celestial bodies. Although several books describe the theoretical foundations of positional astronomy, they touch only slightly on the descrip­ tion of instruments and the procedures for obtaining actual geometrical or kinematic quantities, which are among the basic observational data in the study of the Universe and of its components. The goal of the present book is, in contrast, to provide an up-to-date description of astrometric techniques, particularly the most recent and powerful ones, whether the instruments are on the ground or in space. Until the end of the 19th century, before the development of physical as­ tronomy, all astronomical observations were directed towards obtaining posi­ tions of celestial bodies. Since then astrophysics has become the most impor­ tant domain of astronomy. With the extension of observations to almost all wavelengths from radio waves to gamma rays, with the use of very sensitive new receivers and the development of fast computers, remarkable progress has been made in the description and the understanding of the Universe.

On the occasion ofthe second edition ofthe book, it appeared necessary to up­ date information that was already seven years old. Astrometry has recorded tremendous advances during these last years, so that, in addition to cor­ recting identified errors and misprints, there are many major modifications. Among the events that forced me to modify significantly the contents of the book, the most important are the release of the Hipparcos and Tycho cata­ logues, the introduction of CCD astrometry, the decision of the International Astronomical Union to adopt a new celestial reference frame, the dramatic improvement of accurate time and frequency standards, the decision taken by space agencies to prepare several new space astrometry satellites and the development of optical interferometry. The description and the consequences of these events have been included in this edition. One of them is that a mi­ crosecond of arc or microarcsecond (uas) has become a widely used unit. On the contrary, the result was also that the importance of some in­ struments such as astrolabes or transit circles has decreased. However, I left but because their description unchanged, not only for their historical interest, newer techniques often use similar data reduction methods so that one can refer to them. Conversely, some methods or instruments have evolved and new information is included. Finally, many new references were added to the original list.

The driving idea, in organizing this Symposium on "Relativity in Celestial Mechanics . and Astrometry" was that, in recent years, the ac­ curacy of several Astrometric techniques has so much increased that re­ lativistic effects are no more marginally mentioned in academic presen­ tations but have become an intrinsic part of the interpretation of all the positional data. Techniques such as V. L. B. I. , space probes, lunar lasers, etc . . . have greatly contributed to reduce the accuracy level to an angular equivalent of a few milliarc-seconds. HIPPARCOS will extend this trend to stellar astrometry and new proposals aim at gaining ano­ ther one or two orders of magnitude in observing precision. In paral­ lel, great progress has also been made in the theories of motion of ce­ lestial bodies and more rigourous treatments within the frame of general relativity become necessary. The definition of reference frames and of various coordinate times become also a major problem in the intercompa­ rison of observations produced by different methods. This Symposium gave to people using relativistic corrections in reducing their measurements or in constructing various theories of mo­ tion a chance to exchange their experience in the field and to confront it with theoreticians in general relativity. The Symposium was approved by the IAU in 1983 and it was organi­ zed by the Institute of Theoretical Astronomy of the USSR Academy of Sciences on May 28-31, 1985.

This book on reference systems is the first comprehensive review of the problem of celestial and terrestrial reference systems and frames. Over 20 years, the importance of this problem emerged slowly as the accuracy of new observational techniques improved. The topic has already been approached in several symposia such as Stresa (1967), Morioka (1971), Perth (1973), Columbus (1975, 1978 and 1985), Kiev (1977) and San Fernando (1978). Two IAU colloquia held in Turin (1974) and in Warsaw (1980) were exclusively devoted to discuss reference systems. During this time, the problem of terrestrial and celestial reference systems has been discussed also in many astronomical and geodetic symposia, but always among other topics. Thus, a review devoted solely to the definition and practical realization of such systems was needed. It is hoped that this book, containing modern comprehensive reviews of important facets of this problem will contribute not only to a better and wider understanding of the mathematics and the physics that are behind the concepts and the realizations, but also to future development in a field that can only expand with the rapidly increasing accuracy of geodetic and astronomical observations. We are pleased to thank all the authors of the book who have enthusiastically agreed to contribute to the book in their field of competence and have gracefully accepted guidance from the editors in the definition of the subject and of the interfaces with other chapters. We thank Prof. Y.

This book on reference systems is the first comprehensive review of the problem of celestial and terrestrial reference systems and frames. Over 20 years, the importance of this problem emerged slowly as the accuracy of new observational techniques improved. The topic has already been approached in several symposia such as Stresa (1967), Morioka (1971), Perth (1973), Columbus (1975, 1978 and 1985), Kiev (1977) and San Fernando (1978). Two IAU colloquia held in Turin (1974) and in Warsaw (1980) were exclusively devoted to discuss reference systems. During this time, the problem of terrestrial and celestial reference systems has been discussed also in many astronomical and geodetic symposia, but always among other topics. Thus, a review devoted solely to the definition and practical realization of such systems was needed. It is hoped that this book, containing modern comprehensive reviews of important facets of this problem will contribute not only to a better and wider understanding of the mathematics and the physics that are behind the concepts and the realizations, but also to future development in a field that can only expand with the rapidly increasing accuracy of geodetic and astronomical observations. We are pleased to thank all the authors of the book who have enthusiastically agreed to contribute to the book in their field of competence and have gracefully accepted guidance from the editors in the definition of the subject and of the interfaces with other chapters. We thank Prof. Y.

decision and investigative process of the scientist, they can also wri te the paragra}ils of scientific resul ts. Once a canputer research activity progresses from intuitive guesses to a systematic study, the canputer program can free the scientist to pursue new original ideas. '!his concept is illustrated in the ptper by Hut. Sussnan says "Knowledge" is knowing what not to canpute. His main message is that we must change from trying to maximize the efficiency of the canputer to maximizing the effectiveness of the scientist. The canputer is relatively cheap, it is the trained scientist who is most valuable. In the second keynote address, R. L. Duncombe (University of Texas) described the "Early Applications of Canputer Technology to Dynamical Astronany. " His talk traced the worldwide introduction of punched card equipnent and their applications through the use of the first electronic canputers. Sussman and Duncombe, therefore, provided a forecast and review of the use of computers in dynamical astronany. This proceedings is intended to provide a consolidated general view of the ptst, present, and future of the Applications of Canputer Technology to Dynamical Astronany.Of necessity this requires that the ptpers be rela ti vely short and provide references to the more canplete discussions. Thanks to the representa tion from so many different countries the proceedings give a picture of the activities worldwide. The Scientific Organizing Comnittee included K. B. IIlatnagar, V. A. Brtmberg, G. Contopoulos, A. Depri t , J. Henrard, J. Kovalevsky, Y.