Heavenly Mathematics traces the rich history of spherical trigonometry, revealing how the cultures of classical Greece, medieval Islam, and the modern West used this forgotten art to chart the heavens and the Earth. Once at the heart of astronomy and ocean-going navigation for two millennia, the discipline was also a mainstay of mathematics education for centuries and taught widely until the 1950s. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation of its elegant proofs and often surprising conclusions. Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams. This unique compendium also features easy-to-use appendixes as well as exercises that originally appeared in textbooks from the eighteenth to the early twentieth centuries.

Supernovae are among the most energetic phenomena in the Universe and - lated to almost all aspects of modern astrophysics including starburst gal- ies, cosmic ray acceleration, neutron star and black hole formation, nuc- osynthesis and ISM chemical enrichment, energy input to the ISM, cosmic distance scale determination, dark energy related cosmological acceleration, gamma-ray bursts, extra-solar system neutrino burst detection, gravity wave generation, and many more. Additionally, the past 15 years have been p- ticularly productive with many new results and new understanding due in particular to the closest SN in 400 years in SN 1987A in the Large M- ellanic Cloud, and the unusually bright and close SN 1993J and SN 1994I in the nearby galaxies M81 and M51, respectively. In addition, the disc- ery of the ?-ray burst GRB 980425 and its related supernova SN 1998bw, and the con?rmation of GRB 030329/SN 2003dh, tied the study of SNe and GRBs inextricably together. With the many developments since the last - jor supernova meeting in La Serena, Chile in 1997, we felt that it was an appropriate time to bring together experts and students interested in the subject for a meeting where SN and GRB properties and interrelationships could be discussed. The tenth anniversary of SN 1993J provided such an - portunity and, appropriately, the meeting was held in Spain where SN 1993J was discovered on the early morning of 28 March 1993 by a Spanish amateur astronomer, Francisco Garc ?a.

Astronomy and Astrophysics Abstracts aims to present a comprehensive documen tation of the literature concerning all aspects of astronomy, astrophysics, and their border fields. It is devoted to the recording, summarizing, and indexing of the relevant publications throughout the world. Astronomy and Astrophysics Abstracts is prepared by a special department of the Astronomisches Rechen-Institut under the auspices of the International Astronomical Union. Volume 39 records literature published in 1985 and received before August 15, 1985. Some older documents which we received late and which are not surveyed in earlier volumes are included too. We acknowledge with thanks contributions of our colleagues all over the world. We also express our gratitude to all organiza tions, observatories, and publishers which provide us with complimentary copies of their publications. On account of the introduction of an object index the scope of index information will be considerably enlarged beginning with this volume. In connection with the subject index an additional source to satisfy the needs of retrieval is opened up. Starting with Volume 33, all the recording, correction, and data processing work was done by means of computers. The recording was done by our technical staff members Ms. Helga Ballmann, Ms. Mona El-Choura, Ms. Monika Kohl, Ms. Sylvia Matyssek. Ms. Karin Burkhardt, Ms. Susanne Schlotelburg, and Mr. Stefan Wagner supported our task by careful proofreading. It is a pleasure to thank them all for their encouragement. Heidelberg, September 1985 The Editors Contents Introduction . . . . . . . . . . . .

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. The first volume gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. The reader will appreciate the well-written chapters on numerical solution techniques for ordinary differential equations, as well as that on orbit determination. In the second volume applications to the rotation of earth and moon, to artificial earth satellites and to the planetary system are presented. The author addresses all aspects that are of importance in high-tech applications, such as the detailed gravitational fields of all planets and the earth, the oblateness of the earth, the radiation pressure and the atmospheric drag. The concluding part of this monumental treatise explains and details state-of-the-art professional and thoroughly-tested software for celestial mechanics.

Astronomy and Astrophysics Abstracts, which has appeared in semi-annual volumes since 1969, is devoted to the recording, summarizing and indexing of astronomical publications throughout the world. It is prepared under the auspices of the International Astronomical Union (according to a resolution adopted at the 14th General Assembly in 1970). Astronomy and Astrophysics Abstracts aims to present a comprehensive documenta tion of literature in all fields of astronomy and astrophysics. Every effort will be made to ensure that the average time interval between the date of receipt of the original literature and publication of the abstracts will not exceed eight months. This time interval is near to that achieved by monthly abstracting journals, compared to which our system of accumu lating abstracts for about six months offers the advantage of greater convenience for the user. Volume 32 contains literature published in 1982 and received before February 11, 1983; some older literature which was received late and which is not recorded in earlier volumes is also included. We acknowledge with thanks contributions to this volume by Dr. J. Bou~a, Prague, who surveyed journals and publications in Czech and supplied us with abstracts in English.

The present monograph as well as the next one (Dorman, M2005) is a result of more than 50 years working in cosmic ray (CR) research. After graduation in December 1950 Moscow Lomonosov State University (Nuclear and Elementary Particle Physics Division, the Team of Theoretical Physics), my supervisor Professor D. I. Blokhintsev planned for me, as a winner of a Red Diploma, to continue my education as an aspirant (a graduate student) to prepare for Ph. D. in his very secret Object in the framework of what was in those time called the Atomic Problem. To my regret the KGB withheld permission, and I, together with other Jewish students who had graduated Nuclear Divisions of Moscow and Leningrad Universities and Institutes, were faced with a real prospect of being without any work. It was our good fortune that at that time there was being brought into being the new Cosmic Ray Project (what at that time was also very secret, but not as secret as the Atomic Problem), and after some time we were directed to work on this Project. It was organized and headed by Prof. S. N. Vernov (President of All-Union Section of Cosmic Rays) and Prof. N. V. Pushkov (Director of IZMIRAN); Prof. E. L. Feinberg headed the theoretical part of the Project.

This volume is the first of its kind on focusing gamma-ray telescopes. Forty-eight refereed papers provide a comprehensive overview of the scientific potential and technical challenges of this nascent tool for nuclear astrophysics. The book features articles dealing with pivotal technologies such as grazing incident mirrors, multilayer coatings, Laue- and Fresnel-lenses - and even an optic using the curvature of space-time.

With about 200,000 entries, StarBriefs Plus represents the most comprehensive and accurately validated collection of abbreviations, acronyms, contractions and symbols within astronomy, related space sciences and other related fields. As such, this invaluable reference source (and its companion volume, StarGuides Plus) should be on the reference shelf of every library, organization or individual with any interest in these areas. Besides astronomy and associated space sciences, related fields such as aeronautics, aeronomy, astronautics, atmospheric sciences, chemistry, communications, computer sciences, data processing, education, electronics, engineering, energetics, environment, geodesy, geophysics, information handling, management, mathematics, meteorology, optics, physics, remote sensing, and so on, are also covered when justified. Terms in common use and/or of general interest have also been included where appropriate.

THE EDITORS: DAVID L. BLOCK AND KENNETH C. FREEMAN (SOC CO-CHAIRS), IVANIO PUERARI, ROBERT GROESS AND LIZ K. BLOCK 1. Harvard College Observatory, 1958 The past century has truly brought about an explosive period of growth and discovery for the physical sciences as a whole, and for astronomy in particular. Galaxy morphology has reached a renaissance . . The year: 1958. The date: October 1. The venue: Harvard College Observatory. The lecturer: Walter Baade. With amazing foresight, Baade penned these words: "Young stars, supergiants and so on, make a terrific splash - lots of light. The total mass of these can be very small compared to the total mass of the system". Dr Layzer then asked the key question: " . . . the discussion raises the point of what this classification would look like if you were to ignore completely all the Population I, and just focus attention on the Population II . . . " We stand on the shoulders of giants. The great observer E. E. Barnard, in his pioneering efforts to photograph the Milky Way, devoted the major part of his life to identifying and numbering dusty "holes" and dust lanes in our Milky Way. No one could have dreamt that the pervasiveness of these cosmic dust masks (not only in our Galaxy but also in galaxies at high redshift) is so great, that their "penetration" is truly one of the pioneering challenges from both space-borne telescopes and from the ground.

Astronomy and Astrophysics Abstracts aims to present a comprehensive documen- tation ofthe literatme concerning all aspects of astronomy, astrophysics, and their border fields. lt is devoted to the recording, summarizing, and indexing of the relevant publications throughout the world. Astronomy and Astrophysics Abstracts is prepared by a special department of the Astronomisches Rechen-Institut under the auspices of the International Astronomical Union. Volume 40 records literatme published in 1985 and received before February 15, 1986. Some older documents which we received late and which arenot surveyed in earlier volumes are included too. We acknowledge with thanks contributions of our colleagues all over the world. We also express our gratitude to all organiza- tions, observatories, and publishers which provide us with complimentary copies of their publications. Starting with Volume 33, all the recording, correction, and data processing work was dorre by means of computers. The recording was dorre by om technical staff members Ms. Helga Ballmann, Ms. Mona El-Choura (t), Ms. Monika Kohl, Ms. Sylvia Matyssek. Ms. Karirr Burkhardt, Ms. Susanne Schlotelbmg, Mr. Mar- tin Schlotelburg, and Mr. Stefan Wagner supported om task by careful proof- reading. lt is a pleasure to thank them all for their encomagement.

"Key processes in Solar-Terrestrial Physics" deals with a nice selection of key phenomena concerning Solar-Terrestrial relations. During the week of October 4-9, 2009, about 160 participants from 19 countries met at the Itamambuca resort area of Ubatuba, Sao Paulo, Brazil to discuss the influence of solar variability on geophysical and heliospheric phenomena at a conference organized by the International Living With a Star (ILWS) Program of NASA and by the National Institute of Space Research (INPE) of Brazil. Five of the invited review talks of this Conference are being published in this special issue, plus one (on magnetospheric reconnection) especially invited to cover a missing important subject within the Solar-Terrestrial physics domain. Previously published in Space Science Reviews journal, Vol. 158/1, 2011.

When I wasa child, growing up in South America,I often went camping in the wild and hence had direct access to the wondrous Southern sky; the Southern Cross was all mine at the time. Little did I know then that the study of the sky would take such a huge importance in my life, and that in the end astronomy and astrophysics would in many ways become my country and my religion. I have lived in several di?erent countries, and when asked my nationality, I am always very tempted to reply: astronomer. I started as a theorist, and my only dream in my youth was to spend nights thinking and calculating, with paper and pencil, and to have the impression by dawn that I had understood something new. So at the time astronomy was seen or dreamt by me as a solitary endeavour, with periodic encounters with my wise adviser and professors; it is this model that I adopted when doing my PhD work. My generation has lived through many revolutions of all kinds. Those in astronomy, I believe, remain particularly remarkable, and I am a true product of them. Now, I elect to live and work in large organizations, and to share my endeavours with many people. And I relish the series of Andr e Heck on Organizations and Strategies in Astronomy, which help us recover our memories, reconstitute our own story, and read with glee about our neighbouring or far-away colleagues.

Knowledge about the outer heliosphere and the interstellar medium, which were long treated as two separate fields, has improved dramatically over the past 25 years as a consequence of recent developments: The discovery of interstellar pickup ions and neutral helium inside the heliosphere, the determination of the interstellar hydrogen distribution in the heliosphere obtained using backscattered solar Lyman-alpha radiation, the prediction and subsequent detection of the hydrogen wall just outside of the heliopause, the development of detailed global models for the interaction of solar wind plasma with the interstellar medium, and most recently, direct in-situ plasma and field measurements inside of the heliosheath. At the same time, our understanding of the nearby galactic environment, including the composition and dynamics of the warm gas clouds and hot gas in the local bubble, has benefited greatly from absorption-line spectroscopy using nearby stars as background sources and dynamic modeling. The present volume provides a synopsis of these developments organised into seven sections: Dominant physical processes in the termination shock and heliosheath, three-dimensional shape and structure of the dynamic heliosphere, relation of the plasmas and dust inside and outside of the heliosphere, origin and properties of the very local interstellar medium, energy and pressure equilibria in the local bubble, physical processes in the multiphase interstellar medium inside of the local bubble, and the roles that magnetic fields play in the outer heliosphere and the local bubble. The last theme is probably the most basic of all as magnetic fields play important roles in most of the phenomena discussed here. The volume concludes with four papers providing the "big picture" by looking at the time evolution of both the heliosphere and the local bubble, looking beyond the local bubble, and finally addressing the challenges in modeling the interface between the two media.

The reviews presented in this volume cover a huge range of cluster of galaxies topics. Readers will find the book essential reading on subjects such as the physics of the ICM gas, the internal cluster dynamics, and the detection of clusters using different observational techniques. The expert chapter authors also cover the huge advances being made in analytical or numerical modeling of clusters, weak and strong lensing effects, and the large scale structure as traced by clusters.

This book presents studies of complexity in the context of nonequilibrium phenomena using theory, modeling, simulations, and experiments, both in the laboratory and in nature.

Emission lines provide a powerful tool to study the physical properties and chemical compositions of astrophysical objects in the Universe, from the first stars to objects in our galaxy. The analysis of emission lines allows us to estimate the star formation rate and initial mass function of ionizing stellar populations, and the properties of active galactic nuclei. This book presents lectures from the eighteenth Winter School of the Canary Islands Astrophysics Institute (IAC), devoted to emission lines and the astrophysical objects that produce them. Written by prestigious researchers and experienced observers, it covers the formation of emission lines and the different sources that produce them. It shows how emission lines in different wavelengths, from ultraviolet to near infrared, can provide essential information on understanding the formation and evolution of astrophysical objects. It also includes practical tutorials for data reduction, making this a valuable reference for researchers and graduate students.

Currently under construction in Northern Chile, the Atacama Large Millimeter Array (ALMA) is the most ambitious astronomy facility under construction. This book describes the enormous capabilities of ALMA, the state of the project, and most notably the scientific prospects of such a unique facility. The book includes reviews and recent results on most hot topics of modern astronomy. It looks forward to the revolutionary results that are likely to be obtained with ALMA.

Light scattering by densely packed inhomogeneous media is a particularly ch- lenging optics problem. In most cases, only approximate methods are used for the calculations. However, in the case where only a small number of macroscopic sc- tering particles are in contact (clusters or aggregates) it is possible to obtain exact results solving Maxwell's equations. Simulations are possible, however, only for a relativelysmallnumberofparticles,especiallyiftheirsizesarelargerthanthewa- length of incident light. The ?rst review chapter in PartI of this volume, prepared by Yasuhiko Okada, presents modern numerical techniques used for the simulation of optical characteristics of densely packed groups of spherical particles. In this case, Mie theory cannot provide accurate results because particles are located in the near ?eld of each other and strongly interact. As a matter of fact, Maxwell's equations must be solved not for each particle separately but for the ensemble as a whole in this case. The author describes techniques for the generation of shapes of aggregates. The orientation averaging is performed by a numerical integration with respect to Euler angles. The numerical aspects of various techniques such as the T-matrix method, discrete dipole approximation, the ?nite di?erence time domain method, e?ective medium theory, and generalized multi-particle Mie so- tion are presented. Recent advances in numerical techniques such as the grouping and adding method and also numerical orientation averaging using a Monte Carlo method are discussed in great depth.

It is the stars, The stars above us, govern our conditions. William Shakespeare, King Lear A Few Words about What, Why and How The structure of the stars in general, and the Sun in particular, has been the subject of extensivescienti?cresearchanddebateforoveracentury.Thediscoveryofquantum theoryduringthe?rsthalfofthenineteenthcenturyprovidedmuchofthetheoretical background needed to understand the making of the stars and how they live off their energysource. Progress in the theoryof stellar structurewasmade through extensive discussions and controversies between the giants of the ?elds, as well as brilliant discoveries by astronomers. In this book, we shall carefully expose the building of the theory of stellar structure and evolution, and explain how our understanding of the stars has emerged from this background of incessant debate. About hundred years were required for astrophysics to answer the crucial ques tions: What is the energy source of the stars? How are the stars made? How do they evolve and eventually die? The answers to these questions have profound im plications for astrophysics, physics, and biology, and the question of how we our selves come to be here. While we already possess many of the answers, the theory of stellar structure is far from being complete, and there are many open questions, for example, concerning the mechanisms which trigger giant supernova explosions. Many internal hydrodynamic processes remain a mystery. Yet some global pictures can indeed be outlined, and this is what we shall attempt to do here.

In their search for solutions to problems concerning the dynamics of the Earth as a self-gravitating body, the authors have applied the fundamentals found in their book "Jacobi Dynamics" (1987, Reidel). First, satellite observations have shown that the Earth does not remain in hydrostatic equilibrium, which forms the physical basis of modern geodynamics. Secondly, satellite data have established a relationship between the planet's polar moment of inertia and the potential of the Earth's outer force field, which proves the most basic point of Jacobi dynamics. This allowed the authors to revise their derivation of the classical virial theorem, introducing the concept of a volumetric force and volumetric moment, and so to obtain a generalized virial theorem in the form of Jacobi's equation. The main dynamical effects are: the kinetic energy of oscillation of the interacting particles, which explains the physical meaning and nature of gravitational forces; separation of shells of a self-gravitating body with respect to its mass density; differences in angular velocities of the shell's rotation; continuity in variance of the potential of the outer gravitational force field, together with reductions in the envelope of the interacting masses (volumetric center of gravity); the nature of Earth, Moon and satellite precession; the nature and generating mechanism of the planet's electromagnetic field; the common nature of gravitational and electromagnetic energy, and other related issues. The work is a logical continuation of the book "Jacobi Dynamics" and is intended for researchers, teachers and students engaged in theoretical and experimental research in various branches of astronomy, geophysics, planetology and cosmogony, and for students of celestial, statistical, quantum and relativistic mechanics and hydrodynamics.

Astronomy and Astrophysics Abstracts aims to present a comprehensive documen- tation of the literature concerning all aspects of astronomy, astrophysies, and their border fields. It is devoted to the recording, summarizing, and indexing of the relevant publications throughout the world. Astronomy and Astrophysics Abstracts is prepared by a special department of the Astronomisches Rechen-Institut under the auspices of the International Astronomical Union. Volume 44 records literature published in 1987 and received before February 15, 1988. Some older documents which we received late and which are not surveyed in earlier volumes are inc1uded too. We acknowledge with thanks contributions of our colleagues all over the world. We also express our gratitude to all organiza- tions, observatories, and publishers which provide us with complimentary copies of their publications. Dr. Siegfried Bohme retired from his duties as co-editor of Astronomy and Astro- physics Abstracts on December 31, 1987. Since 1950 he partieipated in the biblio- graphie work of the institute. He served as a reviewer for the Astronomischer Jahresbericht and became one of the editors of Astronomy and Astrophysics Ab- stracts in 1969. After his retirement in 1975 he took care of, particularly, the Russian literature on a voluntary basis for 12 years. It is a pleasure to thank Siegfried Bohme for his valuable contributions. Starting with Volume 33, all the recording, correction, and data processing work was done by means of computers. The recording was done by our technical staff members Ms. Helga Ballmann, Ms. Christiane Jehn, Ms. Monika Kohl, Ms.

From the reviews: Astronomy and Astrophysics Abstracts has appeared in semi-annual volumes since 1969 and it has already become one of the fundamental publications in the fields of astronomy, astrophysics and neighbouring sciences. It is the most important English-language abstracting journal in the mentioned branches. ... The abstracts are classified under more than hundred subject categories, thus permitting a quick survey of the whole extended material. The AAA is a valuable and important publication for all students and scientists working in the fields of astronomy and related sciences. As such it represents a necessary ingredient of any astronomical library all over the world." Space Science Reviews #1 "Dividing the whole field plus related subjects into 108 categories, each work is numbered and most are accompanied by brief abstracts. Fairly comprehensive cross-referencing links relevant papers to more than one category, and exhaustive author and subject indices are to be found at the back, making the catalogues easy to use. The series appears to be so complete in its coverage and always less than a year out of date that I shall certainly have to make a little more space on those shelves for future volumes." The Observatory Magazine #1

Astronomy and Astrophysics Abstracts, which has appeared in semi-annual volumes since 1969, is de voted to the recording, summarizing and indexing of astronomical publications throughout the world. It is prepared under the auspices of the International Astronomical Union (according to a resolution adopted at the 14th General Assembly in 1970). Astronomy and Astrophysics Abstracts aims to present a comprehensive documentation of literature in all fields of astronomy and astrophysics. Every effort will be made to ensure that the average time interval between the date of receipt of the original literature and publication of the abstracts will not exceed eight months. This time interval is near to that achieved by monthly abstracting journals, com pared to which our system of accumulating abstracts for about six months offers the advantage of greater convenience for the user. Volume 18 contains literature published in 1976 and received before March 1, 1977; some older liter ature which was received late and which is not recorded in earlier volumes is also included.

Devised for a quantitative understanding of the physics of the universe from the solar system through the milky way to clusters of galaxies all the way to cosmology, this acclaimed text offers among the most concise and most critical ones of extant works. Special chapters are devoted to magnetic and radiation processes, disks, black-hole candidacy, bipolar flows, cosmic rays, gamma-ray bursts, image distortions, and special sources. At the same time, planet earth is viewed as the arena for life, with plants and animals having evolved to homo sapiens during cosmic time. This text is unique in covering the basic qualitative and quantitative tools, formulae as well as numbers, needed to for the precise interpretation of frontline phenomena.

Astronomy isthemostancientsciencehumanshavepracticedonEarth. Itisascienceofextremesandoflargenumbers:extremesoftime-fromthe big bang to in?nity -, of distances, of temperatures, of density and masses, ofmagnetic?eld,etc.Itisasciencewhichishighlyvisible,notonlybecause stars and planets are accessible in the sky to the multitude, but also - cause the telescopes themselves are easily distinguishable, usually on top of scenic mountains, and also because their cost usually represent a subst- tialproportionofthenation'sbudgetandofthetaxpayerscontributionsto that budget. As such, astronomy cannot pass unnoticed. It touches on the origins of matter, of the Universe where we live, on life and on our destiny. It touches on philosophy as well as on religion. Astronomy is the direct c- tactofhumankindwithitsoriginsandtheimmensityofuniversalnature.It is indeed a science of observation where experimentation is practically - possible and which is ruled by mathematics, physics, chemistry, statistical analysis and modelling, while o?ering the largest number of veri?cations of the most advanced theories of fundamental physics such as general r- st ativity and gravitation. At the beginning of the 21 century astronomy is clearly a multidisciplinary activity touching on all aspects of science. It is therefore logical that in the past and still now, astronomy has attracted the most famous scientists, be they pure observers, mathematicians, physicists, biologists, experimentalists, and even politicians.