This textbook provides details of the derivation of Lagrange's planetary equations and of the closely related Gauss's variational equations, thereby covering a sorely needed topic in existing literature. Analytical solutions can help verify the results of numerical work, giving one confidence that his or her analysis is correct. The authors-all experienced experts in astrodynamics and space missions-take on the massive derivation problem step by step in order to help readers identify and understand possible analytical solutions in their own endeavors. The stages are elementary yet rigorous; suggested student research project topics are provided. After deriving the variational equations, the authors apply them to many interesting problems, including the Earth-Moon system, the effect of an oblate planet, the perturbation of Mercury's orbit due to General Relativity, and the perturbation due to atmospheric drag. Along the way, they introduce several useful techniques such as averaging, Poincare's method of small parameters, and variation of parameters. In the end, this textbook will help students, practicing engineers, and professionals across the fields of astrodynamics, astronomy, dynamics, physics, planetary science, spacecraft missions, and others. "An extensive, detailed, yet still easy-to-follow presentation of the field of orbital perturbations." - Prof. Hanspeter Schaub, Smead Aerospace Engineering Sciences Department, University of Colorado, Boulder "This book, based on decades of teaching experience, is an invaluable resource for aerospace engineering students and practitioners alike who need an in-depth understanding of the equations they use." - Dr. Jean Albert Kechichian, The Aerospace Corporation, Retired "Today we look at perturbations through the lens of the modern computer. But knowing the why and the how is equally important. In this well organized and thorough compendium of equations and derivations, the authors bring some of the relevant gems from the past back into the contemporary literature." - Dr. David A Vallado, Senior Research Astrodynamicist, COMSPOC "The book presentation is with the thoroughness that one always sees with these authors. Their theoretical development is followed with a set of Earth orbiting and Solar System examples demonstrating the application of Lagrange's planetary equations for systems with both conservative and nonconservative forces, some of which are not seen in orbital mechanics books." - Prof. Kyle T. Alfriend, University Distinguished Professor, Texas A&M University

Observational and Theoretical Issues of Interacting Binaries was the topic of the 22nd Advanced Course of the Swiss Society for Astrophysics and Astronomy. It was the first time that binary systems were the center of attention of our course. The established concept and organisation of the Advanced Course has been retained: three scientists, all acknowledged experts in their respective fields, were each invited to give nine one-hour lectures within the period of a week. The Advanced Course took place from April 6 to 11, 1992, at Les Diablerets, a charming resort in the Swiss alps. The high level of the lectures, the international background of the 65 participants, including many young students, and the beauty of the surroundings all contributed to the success of the course. The lecture notes of this course, the 22nd in our series, are also the third to be published by Springer-Verlag. Well over half of all stars seem to exist in binary systems. The study of binary evolution is therefore essential for our understanding of stellar evolution in general. The evolution of interacting binaries contains in itself many of the problems met in other fields of modern astrophysics. This is very apparent in these lecture notes.

Dynamic compression is an experimental technique with interdisciplinary uses, ranging from enabling the creation of ultracondensed matter under previously impossible conditions to understanding the likely cause of unusual planetary magnetic fields. Readers can now gain an intuitive understanding of dynamic compression; clear and authoritative chapters examine its history and experimental method, as well as key topics including dynamic compression of liquid hydrogen, rare gas fluids and shock-induced opacity. Through an up-to-date history of dynamic compression research, Nellis also clearly shows how dynamic compression addresses and will continue to address major unanswered questions across the scientific disciplines. The past and future role of dynamic compression in studying and making materials at extreme conditions of pressure, density and temperature is made clear, and the means of doing so are explained in practical language perfectly suited for researchers and graduate students alike.

You have just discovered the literary masterpiece that answers your questions about God, life in the inhabited universe, the history and future of this world, and the life of Jesus. The Urantia Book harmonizes history, science, and religion into a philosophy of living that brings new meaning and hope into your life. If you are searching for answers, read The Urantia Book! The world needs new spiritual truth that provides modern men and women with an intellectual pathway into a personal relationship with God. Building on the world's religious heritage, The Urantia Book describes an endless destiny for humankind, teaching that living faith is the key to personal spiritual progress and eternal survival. These teachings provide new truths powerful enough to uplift and advance human thinking and believing for the next 1000 years. A third of The Urantia Book is the inspiring story of Jesus' entire life and a revelation of his original teachings. This panoramic narrative includes his birth, childhood, teenage years, adult travels and adventures, public ministry, crucifixion, and 19 resurrection appearances. This inspiring story recasts Jesus from the leading figure of Christianity into the guide for seekers of all faiths and all walks of life.

This book provides a first-hand account of modern cosmology, written by three celebrated astronomers renowned for their excellence in both research and teaching. The central theme of the book, the deep Universe, is approached in three truly complementary ways: as a coherent and smooth theory embracing the evolution of the Universe from its original radiations emerging from the hot Big Bang to the present structures of matter; as a meandering, rough road paved by our observations of stars, galaxies, and clusters; and in terms of how these approaches have been gradually developed and intertwined in the historical process that led to the modern science of cosmology.

Written by a leading expert on comets, this textbook is divided into seven main elements with a view to allowing advanced students to appreciate the interconnections between the different elements. The author opens with a brief introductory segment on the motivation for studying comets and the overall scope of the book. The first chapter describes fundamental aspects most usually addressed by ground-based observation. The author then looks at the basic physical phenomena in four separate chapters addressing the nucleus, the emitted gas, the emitted dust, and the solar wind interaction. Each chapter introduces the basic physics and chemistry but then new specific measurements by Rosetta instruments at comet Churyumov-Gerasimenko are brought in. A concerted effort has been made to distinguish between established fact and conjecture. Deviations and inconsistencies are brought out and their significance explained. Links to previous observations of comets Tempel 1, Wild 2, Hartley 2, Halley and others are made. The author then closes with three smaller chapters on related objects, the loss of comets, and prospects for future exploration. This textbook includes over 275 graphics and figures - most of which are original. Thorough explanations and derivations are included throughout the chapters. The text is therefore designed to support MSc. students and new PhD students in the field wanting to gain a solid overview of the state-of-the-art.

Offers an accessible text and reference (a cosmic-ray manual) for graduate students entering the field and high-energy astrophysicists will find this an accessible cosmic-ray manual Easy to read for the general astronomer, the first part describes the standard model of cosmic rays based on our understanding of modern particle physics. Presents the acceleration scenario in some detail in supernovae explosions as well as in the passage of cosmic rays through the Galaxy. Compares experimental data in the atmosphere as well as underground are compared with theoretical models

The last decade of this century has seen a renewed interest in the dynamics and physics of the small bodies of the Solar System, Asteroids, Comets and Meteors. New observational evidences such as the discovery of the Edgeworth-Kuiper belt, refined numerical tools such as the symplectic integrators, analytical tools such as semi-numerical perturbation algorithms and in general a better understanding of the dynamics of Hamiltonian systems, all these factors have converged to make possible and worthwhile the study, over very long time spans, of these "minor" objects. Also the public, the media and even some political assell}blies have become aware that these "minor" objects of our planetary environnement could become deadly weapons. Apparently they did have a role in Earth history and a role more ominous than "predicting" defeat (or victory, why not?) to batches of credulous rulers. Remembering what may have happened to the dinosaurs but keeping all the discretion necessary to avoid creating irrational scares, it may not be unwise or irrelevant to improve our knowledge of the physics and dynamics of these objects and to study in particular their interactions with our planet.

Long-term monitoring is of fundamental significance in solving many important problems in astrophysics and, furthermore, has unequalled value in extending observational runs with small telescopes for the education of young astronomers in order to teach them how to secure high-quality observational data over many years. The Impact of Long-Term Monitoring on Variable Star Research contains reports based on the analysis of data collected in the visible, IR and radio measurement ranges, as well as the design and history of well known photometric systems. Though the reporting of novel results forms an important part of the book, there are also reports of eight discussion sessions covering more general areas, such as extinction monitoring, the problems of archival storage of astronomical data, service observation, the role played by long-term monitoring in graduate teaching and thesis supervision, the interplay between the great observational effort and theory, the contribution of LTM to new knowledge of fundamental data, and the increasing decommissioning of telescopes of modest aperture.

The observation, in 1919 by A.S. Eddington and collaborators, of the gra- tational de?ection of light by the Sun proved one of the many predictions of Einstein's Theory of General Relativity: The Sun was the ?rst example of a gravitational lens. In 1936, Albert Einstein published an article in which he suggested - ing stars as gravitational lenses. A year later, Fritz Zwicky pointed out that galaxies would act as lenses much more likely than stars, and also gave a list of possible applications, as a means to determine the dark matter content of galaxies and clusters of galaxies. It was only in 1979 that the ?rst example of an extragalactic gravitational lens was provided by the observation of the distant quasar QSO 0957+0561, by D. Walsh, R.F. Carswell, and R.J. Weymann. A few years later, the ?rst lens showing images in the form of arcs was detected. The theory, observations, and applications of gravitational lensing cons- tute one of the most rapidly growing branches of astrophysics. The gravi- tional de?ection of light generated by mass concentrations along a light path producesmagni?cation,multiplicity,anddistortionofimages,anddelaysp- ton propagation from one line of sight relative to another. The huge amount of scienti?c work produced over the last decade on gravitational lensing has clearly revealed its already substantial and wide impact, and its potential for future astrophysical applications.

Processes governing the evolution of planetesimals are critical to understanding how rocky planets are formed, how water is delivered to them, the origin of planetary atmospheres, how cores and magnetic dynamos develop, and ultimately, which planets have the potential to be habitable. Theoretical advances and new data from asteroid and meteorite observations, coupled with spacecraft missions such as Rosetta and Dawn, have led to major advances in this field over the last decade. This transdisciplinary volume presents an authoritative overview of the latest in our understanding of the processes of planet formation. Combining meteorite, asteroid and icy body observations with theory and modelling of accretion and orbital dynamics, this text also provides insights into the exoplanetary system and the search for habitable worlds. This is an essential reference for those interested in planetary formation, solar system dynamics, exoplanets and planetary habitability.

Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, in the formalism of Minkowski's four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein field equation, as well as many modern cosmological subjects, from primordial inflation and cosmic microwave anisotropy to the dark energy that propels an accelerating universe.
The author presents the subject with an emphasis on physical examples and simple applications without the full tensor apparatus. The reader first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, precession of Mercury's perihelion, black holes, and cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Many modern topics in cosmology are discussed in this book: from inflation, cosmic microwave anisotropy to the "dark energy" that propels an accelerating universe.
Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own.

What is time? How has our relationship to time changed through history and how does time structure our social lives?

In this lively introduction, Barbara Adam explores the changing ways in which time has been understood and how this knowledge is embedded in cultural practices. She takes the reader on a journey of discovery that extends from ancient mythology and classical philosophy to the contemporary social world of high-speed computer networks and globalized social relations.

The book poses key questions about the nature of time, how it is conceptualized, what it means in practice and how the parameters set by nature have been transcended across the ages by the human quest for time know-how and control. It provides the reader with a good basis for understanding the role of time in contemporary social life.

This book assumes no previous knowledge. Through its broad perspective and transdisciplinary approach it provides an accessible and wide-ranging introduction for students and teachers across the social sciences.

The modern Persian word for cosmology is "Keyhan-shenakht," which is also the title of a Persian book written more than 800 years ago. The same term can also be found in Old Persian. In spite of this old tradition, modern cosmology is a new omer within the scientific disciplines in Iran. The cosmology community' is small and not yet well established. Given the spectacular recent advances in observational and theoretical cosmology, the large amount of new observational data which will become available in the near future, and the rapid expansion of the international cosmology community, it was realized that Iran should play a more active role in the exciting human endeavour which cosmology constitutes. This was the main motivation to establish a School on Cosmology in Iran. The plan is to hold a cosmology school every three years somewhere in Iran. The focus of this First School on Cosmology was chosen to be structure formation, a rapidly evolving cornerstone of modern cosmology. The topics of the school were selected in order to give both a broad overview of the current status of cosmological structure formation, and an in-depth dis cussion of the key issues theory of cosmological perturbations and analysis of cosmic microwave anisotropies. The lectures by Blanchard and Sarkar give an overview of homogeneous cosmological models and standard big bang cosmology. In his contribution, Padmanabhan presents a comprehen sive discussion of the growth of cosmological perturbations."

This Open Access book gives a comprehensive account of both the history and current achievements of molecular beam research. In 1919, Otto Stern launched the revolutionary molecular beam technique. This technique made it possible to send atoms and molecules with well-defined momentum through vacuum and to measure with high accuracy the deflections they underwent when acted upon by transversal forces. These measurements revealed unforeseen quantum properties of nuclei, atoms, and molecules that became the basis for our current understanding of quantum matter. This volume shows that many key areas of modern physics and chemistry owe their beginnings to the seminal molecular beam work of Otto Stern and his school. Written by internationally recognized experts, the contributions in this volume will help experienced researchers and incoming graduate students alike to keep abreast of current developments in molecular beam research as well as to appreciate the history and evolution of this powerful method and the knowledge it reveals.

This book presents two important new findings. First, it demonstrates from first principles that turbulent heating offers an explanation for the non-adiabatic decay of proton temperature in solar wind. Until now, this was only proved with reduced or phenomenological models. Second, the book demonstrates that the two types of anisotropy of turbulent fluctuations that are observed in solar wind at 1AU originate not only from two distinct classes of conditions near the Sun but also from the imbalance in Alfven wave populations. These anisotropies do not affect the overall turbulent heating if we take into account the relation observed in solar wind between anisotropy and Alfven wave imbalance. In terms of the methods used to obtain these achievements, the author shows the need to find a very delicate balance between turbulent decay and expansion losses, so as to directly solve the magnetohydrodynamic equations, including the wind expansion effects.

In an expanding world with limited resources, optimization and uncertainty quantification have become a necessity when handling complex systems and processes. This book provides the foundational material necessary for those who wish to embark on advanced research at the limits of computability, collecting together lecture material from leading experts across the topics of optimization, uncertainty quantification and aerospace engineering. The aerospace sector in particular has stringent performance requirements on highly complex systems, for which solutions are expected to be optimal and reliable at the same time. The text covers a wide range of techniques and methods, from polynomial chaos expansions for uncertainty quantification to Bayesian and Imprecise Probability theories, and from Markov chains to surrogate models based on Gaussian processes. The book will serve as a valuable tool for practitioners, researchers and PhD students.

This book collects together the lecture courses and seminars given at the Les Houches Summer School 2008 on Long-Range Interacting Systems. Leading scientists in different fields of mathematics and physics present their views on this fast growing and interdisciplinary field of research, by venturing upon fundamental problems of probability, transport theory, equilibrium and non-equilibrium statistical mechanics, condensed matter physics, astrophysics and cosmology, physics of plasmas, and hydrodynamics. The thermodynamic and dynamical properties of systems with long-range interactions were poorly understood until a few years ago. Substantial progress has been made only recently by realizing that the lack of additivity induced by long-range interactions does not hinder the development of a consistent thermodynamic formalism. This book reviews the state-of-the-art developments in this field and provides an essential background to future studies. All chapters are written from a pedagogical perspective, making the book accessible to masters and PhD students and all researchers wishing to enter this field.

At the XXIX IAU General Assembly held in Honolulu from 3-14 August 2015, the meetings known as Special Sessions and Joint Discussions were replaced by new 'Focus Meetings'. Astronomy in Focus XXIXA presents the most relevant contributions from the Focus Meetings together with summaries of all the accepted papers and posters. It covers the meetings on the following areas: dynamical problems in extrasolar planet science; astronomical heritage; scholarly publishing in astronomy; statistics and exoplanets; the exploration of small worlds; ground and space astrophysics and heliophysics; laboratory astrophysics; brightness variations of the Sun and Sun-like stars; astronomy for development; and mitigating the threats of light pollution and radio frequency interference. The publications Astronomy in Focus XXIXA (together with its companion, XXIXB), the proceedings of the six main Scientific Symposia and Reports on Astronomy: Commission Legacy Reports, fully cover the XXIX IAU General Assembly.