The system of numbering the years A.D. (Anni Domini, Years of the Lord) originated with Dionysius Exiguus. Dionysius drafted a 95-year table of dates for Easter beginning with the year 532 A.D. Why Dionysius chose the year that he did to number as '1' has been a source of controversy and speculation for almost 1500 years. According to the Gospel of Luke (3.1; 3.23), Jesus was baptized in the 15th year of the emperor Tiberius and was about 30 years old at the time. The 15th year of Tiberius was A.D. 29. If Jesus was 30 years old in A.D. 29, then he was born in the year that we call 2 B.C. Most ancient authorities dated the Nativity accordingly.
Alden Mosshammer provides the first comprehensive study of early Christian methods for calculating the date of Easter to have appeared in English in more than one hundred years. He offers an entirely new history of those methods, both Latin and Greek, from the earliest such calculations in the late second century until the emergence of the Byzantine era in the seventh century. From this history, Mosshammer draws the fresh hypothesis that Dionysius did not calculate or otherwise invent a new date for the birth of Jesus, instead adopting a date that was already well established in the Greek church. Mosshammer offers compelling new conclusions on the origins of the Christian era, drawing upon evidence found in the fragments of Julius Africanus, of Panodorus of Alexandria, and in the traditions of the Armenian church.

Bad Hofgastein who made the very successful Salzburger Abend with indi- nous music from Salzburg possible. Special thanks also to the former director of the Institute of Astronomy in Vienna, Prof. Paul Jackson for his generous private donation. We should not forget our hosts Mr. and Mrs. Winkler and their employees from the hotel who made the stay quite enjoyable. None of us will forget the very last evening, when the staff of kitchen under the le- ership of the cook himself came to offer us as farewell the famous Salzburger Nockerln, a traditional Austrian dessert. Everyone got a lot of scienti?c input during the lectures and the discussions and, to summarize, we all had a spl- did week in Salzburg in the Hotel Winkler. We all hope to come again in 2008 to discuss new results and new perspectives on a high level scienti?c standard in the Gasteinertal. Rudolf Dvorak and Sylvio Ferraz-Mello Celestial Mechanics and Dynamical Astronomy (2005) 92:1-18 (c) Springer 2005 DOI 10. 1007/s10569-005-3314-7 FROM ASTROMETRY TO CELESTIAL MECHANICS: ORBIT DETERMINATION WITH VERY SHORT ARCS (Heinrich K. Eichhorn Memorial Lecture) 1 2 ? ' ANDREA MILANI and ZORAN KNEZEVIC 1 Department of Mathematics, University of Pisa, via Buonarroti 2, 56127 Pisa, Italy, e-mail: milani@dm. unipi. it 2 Astronomical Observatory, Volgina 7, 11160 Belgrade 74, Serbia and Montenegro, e-mail: zoran@aob. bg. ac.

At this time when astronomers are being surprised by the discovery of objects which emit a fabulously large amount of energy, that is the quasi-stellar radio sources and the quasi-stellar galaxies, and when by the means of space vehicles X rays, gamma rays and cosmic rays are being observed to come from the depths of interstellar space, one may ask why write a book about stars. Stars seem to be almost incidental when one looks at the universe in terms of exceedingly great energies. Nevertheless, stars exist. They are accessible to study and they have not yet revealed all their secrets. This is enough to arouse interest and to cause one to try to find answers to the questions which arise. The early type stars are particularly interesting because they are spendthrift stars pouring out their energy at a great rate. But their brilliance is also their undoing. They must evolve rather quickly, on an astrophysical scale. Thus by studying these stars we are studying a population in change. The implications from the local and from the cosmological viewpoint are important if one wishes to understand the details of stellar evolution and of galactic structure. Perhaps one of the simplest reasons for writing a book about the early type stars is to see if some of the conundrums pre sented by the spectra of these stars can be unravelled when all the available infor mation is brought together."

This book gathers selected and expanded contributions presented at the 4th Symposium on Space Optical Instruments and Applications, which was held in Delft, the Netherlands, on October 16-18, 2017. This conference series is organized by the Sino-Holland Space Optical Instruments Laboratory, a cooperative platform between China and the Netherlands. The symposium focused on key technological problems regarding optical instruments and their applications in a space context. It covered the latest developments, experiments and results on the theory, instrumentation and applications of space optics. The book is split into five main sections: The first covers optical remote sensing system design, the second focuses on advanced optical system design, and the third addresses remote sensor calibration and measurement. Remote sensing data processing and information extraction are then presented, followed by a final section on remote sensing data applications.

The words of this preface were written when the book was ready to go to the press; and are limited to only a few points which are best made in this place. As is intimated by the sub-title, the whole volume was written with appli cations in mind to double-star astronomy. The latter is, however, not the only branch of our science which could benefit from its contents. The same is true of certain aspects of the dynamics of stellar systems or galaxies (the stellar popula tions of which are also characterized by the fact that the mean-free-path of their constituent stars are long in comparison with the dimensions of the respective systems); the central condensations of which are high enough to approximate the gravitational action of a "mass-point." This fact did not, to be sure, escape the attention of previous investigators (in the case of globular clusters, in particular, the Roche model was introduced in their studies under the guise of polytropic models characterized by the index n = 5); though no particular attention will be paid to these in this book. But possible applications of the Roche model are not limited to problems arising in stellar astrophysics. With Coulomb forces replacing gravitation, the equilibrium model finds a close analogy in the field of electrostatics-as was pointed out already at the beginning of this century by (then young) J. H. Jeans (cf."

This book deals with the rise of mathematics in physical sciences, beginning with Galileo and Newton and extending to the present day. The book is divided into two parts. The first part gives a brief history of how mathematics was introduced into physics-despite its "unreasonable effectiveness" as famously pointed out by a distinguished physicist-and the criticisms it received from earlier thinkers. The second part takes a more philosophical approach and is intended to shed some light on that mysterious effectiveness. For this purpose, the author reviews the debate between classical philosophers on the existence of innate ideas that allow us to understand the world and also the philosophically based arguments for and against the use of mathematics in physical sciences. In this context, Schopenhauer's conceptions of causality and matter are very pertinent, and their validity is revisited in light of modern physics. The final question addressed is whether the effectiveness of mathematics can be explained by its "existence" in an independent platonic realm, as Goedel believed. The book aims at readers interested in the history and philosophy of physics. It is accessible to those with only a very basic (not professional) knowledge of physics.

The Theory Institute in Solar-Terrestrial Physics was held at Boston College 19-26 August 1982. The program consisted of a two-week School followed by the first theory conference in the field. This book is based upon the lectures presented at the School. Several years ago there was a convergence of efforts to promote the role of theory in space plasma physics. Reports from the National Academy of Sciences and NASA advisory committees documented the disciplinary maturity of solar-terrestrial physics and recommended that theorists play a greater role in the continued development of the field. The so-called theory program in solar-terrestrial physics was established by NASA in 1979 and implemented in accordance with the guidelines set forth by a panel of scientists, primarily theorists, in the field. The same panel motivated the Boston College program. Published proceedings of the school would provide curricular materials for the training of graduate students in solar-terrestrial physics. J.M. Forbes, T.E. Holzer, A.J. Hundhausen, A.D. Richmond, and G.L. Siscoe were the principal architects of the curriculum of the School, and I am grateful for their contributions. Each also lectured at the School. The chapters in this book were prepared by the authors themselves with one exception. The chapters by Parker are edited reproductions of his lectures. Unfortunately, it is our loss that the lectures of Holzer and Hundhausen are not included in the book.

This peer-reviewed book provides detailed insights into how space and its applications are, and can be used to support the development of the full range and diversity of African societies, as encapsulated in the African Union's Agenda 2063. Following on from Part 1 and 2, which were highly acclaimed by the space community, it focuses on the role of space in supporting the UN Sustainable Development Goals in Africa, but covers an even more extensive array of relevant and timely topics addressing all facets of African development. It demonstrates that, while there have been significant achievements in recent years in terms of economic and social development, which have lifted many of Africa's people out of poverty, there is still a great deal that needs to be done to fulfill the basic needs of Africa's citizens and afford them the dignity they deserve. To this end, space is already being employed in diverse fields of human endeavor to serve Africa's goals for its future, but there is much room for further incorporation of space systems and data. Providing a comprehensive overview of the role space is playing in helping Africa achieve its developmental aspirations, the book will appeal to both students and professionals in fields such as space studies, international relations, governance, and social and rural development.

This is volume 5 of Planets, Stars and Stellar Systems, a six-volume compendium of modern astronomical research, covering subjects of key interest to the main fields of contemporary astronomy. This volume on Galactic Structure and Stellar Populations, edited by Gerard F. Gilmore, presents accessible review chapters on Stellar Populations, Chemical Abundances as Population Tracers, Metal-Poor Stars and the Chemical Enrichment of the Universe, The Stellar and Sub-Stellar Initial Mass Function of Simple and Composite Populations, The Galactic Nucleus, The Galactic Bulge, Open Clusters and Their Role in the Galaxy, Star Counts and the Nature of Galactic Thick Disk, The Infrared Galaxy, Interstellar PAHs and Dust, Galactic Neutral Hydrogen, High-Velocity Clouds, Magnetic Fields in Galaxies, Astrophysics of Galactic Charged Cosmic Rays, Gamma-Ray Emission of Supernova Remnants and the Origin of Galactic Cosmic Rays, Galactic Distance Scales, Globular Cluster Dynamical Evolution, Dynamics of Disks and Warps, Mass Distribution and Rotation Curve in the Galaxy, Dark Matter in the GalacticDwarf Spheroidal Satellites, and History of Dark Matter in Galaxies.

All chapters of the handbook were written by practicing professionals. They include sufficient background material and references to the current literature to allow readers to learn enough about a specialty within astronomy, astrophysics and cosmology to get started on their own practical research projects. In the spirit of the series Stars and Stellar Systems published by Chicago University Press in the 1960s and 1970s, each chapter of Planets, Stars and Stellar Systems can stand on its own as a fundamental review of its respective sub-discipline, and each volume can be used as a textbook or recommended reference work for advanced undergraduate or postgraduate courses. Advanced students and professional astronomers in their roles as both lecturers and researchers will welcome Planets, Stars and Stellar Systems as a comprehensive and pedagogical reference work on astronomy, astrophysics and cosmology.

Influenced by astronomy education research, 21st Century Astronomy offers a complete pedagogical and media package that facilitates learning by doing, while the new one-column design makes the Fifth Edition the most accessible introductory text available today.

With exoplanets being discovered daily, Earth is still the only planet we know of that is home to creatures who seek a coherent explanation for the structure, origins, and fate of the universe, and of humanity s place within it. Today, science and religion are the two major cultural entities on our planet that share this goal of coherent understanding, though their interpretation of evidence differs dramatically. Many scientists look at the known universe and conclude we are here by chance. The renowned astronomer and historian of science Owen Gingerich looks at the same evidence along with the fact that the universe is comprehensible to our minds and sees it as proof for the planning and intentions of a Creator-God. He believes that the idea of a universe without God is an oxymoron, a self-contradiction. God s Planet" exposes the fallacy in thinking that science and religion can be kept apart.

Gingerich frames his argument around three questions: Was Copernicus right, in dethroning Earth from its place at the center of the universe? Was Darwin right, in placing humans securely in an evolving animal kingdom? And was Hoyle right, in identifying physical constants in nature that seem singularly tuned to allow the existence of intelligent life on planet Earth? Using these episodes from the history of science, Gingerich demonstrates that cultural attitudes, including religious or antireligious beliefs, play a significant role in what passes as scientific understanding. The more rigorous science becomes over time, the more clearly God s handiwork can be comprehended."

G. MICHAUD Dipartement de Physique Universiti de Montrial c. P. 6128, succursale A Montrial, Que. , H3C 317 Canada The aim of IAU Symposium 145 was to use the photospheric abundances of the chemical elements to give us some hint of the past evolution and of the current structure of stars. At the invitation on the Bulgarian Academy o/Sciences, it brought together one hundred and fifty one scientists from 21 countries to 71atni Pjasaci (Golden Sands), Bulgaria, for a five day meeting. The processes discussed included accretion, mass loss, mass exchange, convection, turbulence, meridional circulation, and diffusion in addition to nuclear reactions. Observationally, spectroscopy was involved. New telescopes and instruments have considerably extended the scope of spectroscopy over the last few years. Space telescopes, such as IUE, have allowed the development of far UV spectroscopy. The access to the infrared has proven critical for probing cool stars. Large ground based telescopes have allowed fainter objects to be observed especially when they are equipped with more efficient detectors such as CCDs and Reticons. The co-adding of digitalized photographic plates has extended their usefulness. It has become possible to make high resolution, high signal to noise observations of objects that could only be observed at low resolution in former days. Weak lines can now be measured with accuracy, allowing the precise determination of the abundances of elements as rare as lithium and the determination of precise limits to isotopic ratios.

Approaching the settlement of our Moon from a practical perspective, this book is well suited for space program planners. It addresses a variety of human factor topics involved in colonizing Earth's Moon, including: history, philosophy, science, engineering, agriculture, medicine, politics & policy, sociology, and anthropology. Each chapter identifies the complex, interdisciplinary issues of the human factor that arise in the early phases of settlement on the Moon. Besides practical issues, there is some emphasis placed on preserving, protecting, and experiencing the lunar environment across a broad range of occupations, from scientists to soldiers and engineers to construction workers. The book identifies utilitarian and visionary factors that shape human lives on the Moon. It offers recommendations for program planners in the government and commercial sectors and serves as a helpful resource for academic researchers. Together, the coauthors ask and attempt to answer: "How will lunar society be different?"

Astronomy, especially naked-eye astronomy, is a wonderful way for children and young people to engage with the world and universe around them. Many children quickly become fascinated with stars, planets and comets, learning skills that also help them develop generally. This book is a perfect introduction to astronomy for any child, whether or not they have a telescope. It explains the visible constellations and then explores the sun, moon, planets, comets and meteorites. Colour illustrations and diagrams at every stage help children relate what they are reading to what they can see in the sky. Suitable for budding astronomers in both the northern and southern hemispheres, and in polar, temperate or tropical latitudes (i.e., everywhere), this is an ideal introduction the wonders of stargazing.

Hidden from human view, accessible only to sensitive receivers attached to huge radio telescopes, giant versions of backyard satellite dishes, the invisible universe beyond our senses continues to fascinate and intrigue our imaginations. We cannot really comprehend what it means to say that a galaxy is exploding, yet that is the nature of some of the distant radio sources in the furthest reaches of space. Closer to home, in the Milky Way galaxy, radio astronomers listen patiently to the ticking of pulsars that tell of star death and states of matter of awesome densities. And between the stars, radio emission from a host of over 120 complex molecules radiate outward to reveal a tale about chemical processes that produce the very stuff of life. And all of this happens out there in the universe hidden from our eyes, even when aided by the Hubble Space Telescope. This is the story of radio astronomy, of how radio waves are generated by stars, supernova, quasars, colliding galaxies, and by the very beginnings of the universe itself. with those huge dishes in the New Mexico desert, in a remote valley in Puerto Rico, in the green Pocahontas Valley in West Virginia, as well as dozens of other remote sites around the world. With each of these observatories, the scientists collect and analyze their data, listening to the radio signals from space, in order to learn what is out there, and perhaps even if someone else may be listening as well.

The first biography of a pioneering scientist who made significant contributions to our understanding of dark matter and championed the advancement of women in science. One of the great lingering mysteries of the universe is dark matter. Scientists are not sure what it is, but most believe it's out there, and in abundance. The astronomer who finally convinced many of them was Vera Rubin. When Rubin died in 2016, she was regarded as one of the most influential astronomers of her era. Her research on the rotation of spiral galaxies was groundbreaking, and her observations contributed significantly to the confirmation of dark matter, a most notable achievement. In Vera Rubin: A Life, prolific science writers Jacqueline Mitton and Simon Mitton provide a detailed, accessible overview of Rubin's work, showing how she leveraged immense curiosity, profound intelligence, and novel technologies to help transform our understanding of the cosmos. But Rubin's impact was not limited to her contributions to scientific knowledge. She also helped to transform scientific practice by promoting the careers of women researchers. Not content to be an inspiration, Rubin was a mentor and a champion. She advocated for hiring women faculty, inviting women speakers to major conferences, and honoring women with awards that were historically the exclusive province of men. Rubin's papers and correspondence yield vivid insights into her life and work, as she faced down gender discrimination and met the demands of family and research throughout a long and influential career. Deftly written, with both scientific experts and general readers in mind, Vera Rubin is a portrait of a woman with insatiable curiosity about the universe who never stopped asking questions and encouraging other women to do the same.

Has anyone ever seen with their own eyes that the Earth goes around the sun? Even to this day, no one has. However, 500 and even 2000 years ago, some astronomers managed to point out that this is the case. At that time, people's range of activities was strictly confined, the technology and tools used were extremely primitive, and many of the mathematical methods used today had not been developed. How did those astronomers make and verify this discovery? This book explains this exciting demonstration process. It enables anyone with a basic junior-high-school knowledge of geometry and a certain degree of spatial imagination to understand this and other interesting discoveries in the solar system. By demonstrating this interesting process, the book not only satisfies readers' curiosity using the simplest mathematics, but also inspires them to explore the new and unknown world.

The symposium Star Clusters in the Era of Large Surveys was held in Lisbon on Sep 9-10 during the JENAM 2010. It served as a platform for discussing what and how recent, on-going and planned large-area ground-based and space-based surveys can contribute to producing a major leap in this research field, which has a strong European history.

Scientific topics addressed included: cluster searches, clustered vs. isolated star formation, large-scale star formation, enrichment of the field population, structure, populations and evolution of the Milky Way, cluster dynamics (internal and within the Milky Way), variability of stars in clusters (from time-resolved surveys), analysis techniques for large samples and archiving.

This proceedings book provides a snapshot of the ongoing discussion on the role of large surveys in star cluster research, and serves as a reference volume for the state-of-the art in the field.

M. M. Shapiro and J. P. Wefel AN OVERVIEW OF COSMIC RAY RESEARCH: COMPOSITION, ACCELERATION AND PROPAGATION J. P. Wefel PROPAGATION AND TRANSFOR'1ATIONS OF cosme RAYS: 41 FROM SOURCES TO EARTH R. Silberberg, C. H. Tsao, J. R. Letaw and M. M. Shapiro 71 ULTRA HEAVY NUCLEI IN THE COSMIC RADIATION W. R. Binns GALACTIC COSMIC RAY HYDROGEN AND HELIUM 91 J. J. Beatty COSMIC RAYS OF THE HIGHEST ENERGIES 97 J. Szabelski STARS AND COSMIC RAYS 105 I. COOL STARS T. Montmerle STARS AND COSMIC RAYS 131 II. HOT STARS T. Montmerle ON THE POSSIBLE CONTRIBUTION OF WC STARS TO ISOTOPIC 153 ANOMALIES IN COSMIC RAYS AND METEORITES J. B. Blake and D. S. P. Dearborn GAMMA-RAY VIEWS ON THE GALACTIC COSMIC-RAY DISTRIBUTION 163 H. Bloemen VlIl RADIO ASTRONOMY AND COSMIC RAYS 175 K. W. Weiler PARTICLE ACCELERATION IN GALACTIC SUPERNOVA REMNANTS 205 D. A. Green PULSARS AS COSMIC RAY PARTICLE ACCELERATORS -- NEW RESULTS 215 ON THE DYNAMICS OF PROTONS IN VACUUM FIELDS K. o. Thie1heim CONDITIONS FOR ACCELERATION OF SUPER-HIGH ENERGY COSMIC RAYS 227 IN ACTIVE GALACTIC NUCLEI W. H. Sorrell COSMIC RAYS AND A STABLE HYDROSTATIC EQUILIBRIUM OF THE GALAXY 235 H. B10emen VRE AND URE GAMMA P Y OBSERVATIONS BY GROUND BASED 241 DETECTORS W. Stamm 15 HADRON AND MUON COMPONENTS IN PHOTON SHOWERS AT 10 eV 255 Ch. P. Vankov and J. N. Stamenov MONOPOLES, MUONS, NEUTRINOS AND CYGNUS X-3 261 M. L. Cherry, S. Corbato, D. Kieda, K. Lande, and C. K.

Introduction. Phase Transitions in the Early Universe and Defect Formation; T.W.B. Kibble. The Topological Classification of Defects; M. Kleman. Introduction to Growth Kinetics Problems; G.F. Mazenko. Dynamics of Cosmological Phase Transitions: What Can We Learn from Condensed Matter Physics? N. Goldenfeld. Topological Defects and Phase Ordering Dynamics; A.J. Bray. The Production of Strings and Monopoles at Phase Transitions; R.J Rivers, T.S. Evans. Geometry of Defect Scattering; N.S. Manton. Theory of Fluctuating Nonholonomic Fields and Applications: Statistical Mechanics of Vortices and Defects and New Physical Laws in Spaces with Curvature and Torsion; H. Kleinert. String Network Evolution; E.P.S. Shellard. Global Field Dynamics and Cosmological Structure Formation; R. Durrer. Electroweak Baryogenesis; N.G. Turok. Dynamics of Cosmic Strings and Other Brane Models; B. Carter. Cosmological Experiments in Superfluids and Superconductors; W. Zurek. Cosmological Experiments in Liquid 4He-Problems and Prospects; P.C. Hendry et al. Index.

This book presents carefully edited and peer-reviewed papers from the 2nd International Workshop on Occultations for Probing Atmosphere and Climate (OPAC-2), held in Graz, Austria. It starts with a general introductory paper and proceeds to address the full range from methodology in general via specific occultation methods (GNSS-LEO, LEO-LEO, stellar and solar) to the use of occultation data, with focus on atmospheric physics, meteorology and climate.

This thesis represents a breakthrough in our understanding of the noise processes in Microwave Kinetic Inductance Detectors (MKIDs). While the detection of ultraviolet to near-infrared light is useful for a variety of applications from dark matter searches to biological imaging and astronomy, the performance of these detectors often limits the achievable science. The author's work explains the limits on spectral resolution broadening, and uses this knowledge to more than double the world record spectral resolution for an MKID suitable for optical and near-IR astrophysics, with emphasis on developing detectors for exoplanet detection. The techniques developed have implication for phonon control in many different devices, particularly in limiting cosmic ray-induced decoherence in superconducting qubits. In addition, this thesis is highly accessible, with a thorough, pedagogical approach that will benefit generations of students in this area.