This textbook provides students with a solid introduction to the techniques of approximation commonly used in data analysis across physics and astronomy. The choice of methods included is based on their usefulness and educational value, their applicability to a broad range of problems and their utility in highlighting key mathematical concepts. Modern astronomy reveals an evolving universe rife with transient sources, mostly discovered - few predicted - in multi-wavelength observations. Our window of observations now includes electromagnetic radiation, gravitational waves and neutrinos. For the practicing astronomer, these are highly interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle physics and data-analysis. The book is organized to be largely self-contained, starting from basic concepts and techniques in the formulation of problems and methods of approximation commonly used in computation and numerical analysis. This includes root finding, integration, signal detection algorithms involving the Fourier transform and examples of numerical integration of ordinary differential equations and some illustrative aspects of modern computational implementation. Some of the topics highlighted introduce the reader to selected problems with comments on numerical methods and implementation on modern platforms including CPU-GPU computing. Developed from lectures on mathematical physics in astronomy to advanced undergraduate and beginning graduate students, this book will be a valuable guide for students and a useful reference for practicing researchers. To aid understanding, exercises are included at the end of each chapter. Furthermore, some of the exercises are tailored to introduce modern symbolic computation.

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes-regions of space in which space and time are distorted in such a way that nothing, not even light, can escape-as an end-state for massive stars. There is evidence that such stellar black holes as well as more massive varieties of black hole are responsible for the intense radiation emitted by certain types of astronomical objects such as active galactic nuclei or microquasars.

'The whole text is written in a clear and light scientific style. It is fully referenced to scientific publications and supported by numerous figures, mainly in full colour ... The present book can be recommended to any interested reader with a background in physics and/or astronomy, in particular to undergraduate and graduate students within astronomy and related fields, possibly being also of interest to scientists in (evolutionary) biology.'Contemporary PhysicsThe search for exoplanets and habitable objects in general is one of the fastest growing and most prominent fields in modern astrophysics. This book provides an overview on habitability on exoplanets. Habitability is strongly dependent on stellar activity. Therefore, space weather effects on objects in the solar system as well as on exoplanets are discussed.The concept of the book is to introduce the topics and then discuss actual scientific papers so that the interested reader has access to most recent research. Therefore the book is valuable to undergraduate students as well as to graduate students and researchers.

This textbook treats Celestial Mechanics as well as Stellar Dynamics from the common point of view of orbit theory making use of the concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian Mechanics and ends with the dynamics of chaotic motions. The book is meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry. Volume 1 begins with classical mechanics and a thorough treatment of the 2-body problem, including regularization, followed by an introduction to the N-body problem with particular attention given to the virial theorem. Then the authors discuss all important non-perturbative aspects of the 3-body problem. A final chapter deals with integrability of Hamilton-Jacobi systems.

'The content is presented in a colloquial style that is easy to understand and interesting to read. It is supported by numerous colour figures and pictures. Thanks to the excellent quality of the paper and the print, the pictures are indeed pleasing to look at ... The text is self-contained as much as possible. It can be recommended to any scientifically interested reader who wants an overview of the universe, what is in it, and of the methods and instruments in use for the investigations science undertakes to acquire this knowledge.'Contemporary PhysicsThis popular science book offers a glimpse into a plethora of extreme cosmic phenomena in which the theories of modern physics, particularly quantum mechanics and general relativity, play a key role. Despite their vastly different appearances, these cosmic phenomena have much in common: they are all powered by exotic stars - black holes, neutron stars and white dwarfs - collectively called compact objects.The book describes, in accessible language, the physics underlying these phenomena, the historical background that led to their discovery, and the various observational techniques used by astronomers for their exposure. The book contains many spectacular photographs taken with modern telescopes around the world and satellites of different space agencies, as well as illustrations specially prepared by the author to enhance the reading experience.

In February 2016, physicists announced the breakthrough discovery of the gravitational waves, which were predicted by Albert Einstein in his century-old theory of General Relativity. These gravitational waves were emitted as a result of the collision of two massive black holes that happened about 1.3 billion years ago. They were discovered at the Laser Interferometer Gravitational-Wave Observatory (LIGO) in the United States and thus marked a new milestone for physics. However, it remains unclear to physicists how the gravitational interaction can be included in the Standard Theory of particle physics which describes the electroweak and the strong interactions in our universe.In this volume are the lectures, given by the speakers at the conference on cosmology and particle physics. The discussed topics range from gravitational waves to cosmology, dark matter, dark energy and particle physics beyond the Standard Theory.

Since several decades, comets have been considered as key witnesses of solar system formation. Their nature has been explored using the modern arsenal of Earth- and space-based observations, and they hold a central place as dynamical arbiters of the planetary system in the new paradigm of solar system evolution known as the Nice Model. Thus, they have the potential to test the various ideas, using the detailed data recently gathered by the ESA/Rosetta mission. This requires an understanding of their origin and evolution, which form the subject of the present book. All the relevant issues are covered, describing both the background and the current frontiers of research.

This book is an attempt to demystify the activities of a celestial object such as the Sun appealing to basic physics already available to high school students. Building on simple logic, the contents begin with measurements of the gross properties of the Sun like size (volume) and mass from which the average density of solar material is shown to be almost equal to water's density. Then the temperature is obtained using the colour of sunlight, and the gravitational force is discussed to indicate how the solar material is compressed at the centre of the Sun leading to heating which further causes nuclear reactions. The roles of all the forces of nature, viz. strong, weak, electromagnetic and gravitation are shown in the construction of the Sun. The generation of magnetic fields by solar rotation and the eruptions of solar atmospheric material are also included.To further demystify the methods of obtaining all such facts about the Sun, a chapter is solely devoted to the different kinds of solar telescopes operating at different wavelengths and also at different locations ranging from outer space to deep underground, where solar neutrino flux is measured. The entire discussion is interspersed with historical encounters between giants of science to show the human face of scientific research.

This is a revisit of a radical theory of cometary panspermia and cosmic life that was first proposed by Chandra Wickramasinghe and the late Sir Fred Hoyle in 1982. In its earliest form the theory of cosmic life started off as a speculation in 1974 after the first discovery of complex organic molecules and polymeric dust in interstellar space. The speculation soon developed into a serious scientific theory, predictions of which were available to be verified or falsified. Over four decades there have been a multitude of tests and predictions of the theory being positive in vindicating the proposition of life as a cosmic rather than a purely terrestrial phenomenon. A paradigm shift of enormous magnitude and significance is to be expected.The ideas and theories described in this book would have a far-reaching influence affecting the future development of diverse branches of science.

The chief argument of this book, first published in 1990, is that Ibn al-Haytham's On the Configuration of the World is a non-technical expose of basic astronomical teachings: it was written in particular for those whose main interests were in the areas of philosophy and natural science and who, accordingly, had an interest in relating the mathematical devices employed by professional astronomers to the heavenly bodies mentioned in the philosophical literature. However, the primary reason for this publication is not the advancement of this thesis, but rather the presentation of the medieval texts themselves, normally so inaccessible to scholars and students alike.

Whoever wants to understand the genesis of modern Science has to follow three lines of development, all starting in antiquity, which were brought together in the work of ISAAC NEWTON, namely 1. Ancient Mathematics => DESCARTES 2. Ancient Astronomy => COPERNICUS : ~~~~ I=> NEWTON 3. Ancient Mechanics => GALILEO => HUYGENS In Science Awakening I (Dutch edition 1950, first Eng1ish edition 1954, second 1961, first German edition 1956, second 1965) I have followed the first 1ine, giving an outline of the development of Mathematics in Egypt, Babylonia, and Greece. Volume II, dealing with Egyptian and Baby1onian Astronomy first appeared in German under the title 'Die Anfange der Astronomie' (Noordhoff, Groningen 1965 and Birkhau- ser, Basel 1968). The volume was written in collaboration with PETER HUBER (Swiss Federal School of Technology, Zurich). HUBER has written considerable parts of Chap- ters 3 and 4, in particular all transcriptions of cuneiform texts in these chapters. I also had much help from ERNST WEIDNER (Graz), MARTIN VERMASEREN (Amsterdam), JOSEF JANSEN (Leiden) and MANU LEUMANN (Zurich).

Field theory is an important topic in theoretical physics, which is studied in the physical and physico-mathematical departments of universities. Therefore, lecturers are faced with the urgent task of not only providing students with information about the subject, but also to help them master the material at a deep qualitative level, by presenting the specific features of general approaches to the statement and the solution of problems in theoretical physics. One of the ways to study field theory is the practical one, where the students can deepen their knowledge of the theoretical material and develop problem-solving skills. This book includes a concise theoretical summary of the main branches of field theory and electrodynamics, worked examples, and some problems for the student to solve.The book is written for students of theoretical and applied physics, and corresponds to the curricula of the theoretical courses 'Field theory' and 'Electrodynamics' for physics undergraduates. It can also be useful for students of other disciplines, in particular, those in which physics is one of the base subjects.

In Hellenistic Astronomy: The Science in Its Contexts, new essays by renowned scholars address questions about what the ancient science of the heavens was in the ancient Near East and Mediterranean worlds, and the numerous contexts in which it was pursued. Together, these essays will enable readers not only to understand the technical accomplishments of this ancient science but also to appreciate their historical significance by locating the questions, challenges, and issues inspiring them in their political, medical, philosophical, literary, and religious contexts. Winner of the 2020 Choice Outstanding Academic Title Award

This textbook provides an introduction to gravitational lensing, which has become an invaluable tool in modern astrophysics, with applications that range from finding planets orbiting distant stars to understanding how dark matter and dark energy conspired to form the cosmic structures we see today. Principles of Gravitational Lensing begins with Einstein's prediction that gravity bends light, and shows how that fundamental idea has spawned a rich field of study over the past century. The gravitational deflection of light was first detected by Eddington during a solar eclipse in May 1919, launching Einstein and his theory of relativity into public view. Yet the possibility of using the phenomenon to unlock mysteries of the Universe seemed remote, given the technology of the day. Theoretical work was carried out sporadically over the next six decades, but only with the discovery of the system Q0957+561 in 1979 was gravitational lensing transformed from a curiosity of general relativity into a practical observational tool. This book describes how the three subfields known as strong lensing, weak lensing, and microlensing have grown independently but become increasingly intertwined. Drawing on their research experience, Congdon and Keeton begin with the basic physics of light bending, then present the mathematical foundations of gravitational lensing, building up to current research topics in a clear and systematic way. Relevant background material from physics and mathematics is included, making the book self-contained. The derivations and explanations are supplemented by exercises designed to help students master the theoretical concepts as well as the methods that drive current research. An extensive bibliography guides those wishing to delve more deeply into particular areas of interest. Principles of Gravitational Lensing is ideal for advanced students and seasoned researchers looking to penetrate this thriving subject and even contribute research of their own.

Beginning with the famous Olber's paradox, paradoxes such as the missing mass, dark energy, baryon to photon ratio and cosmic zero-point energy are examined in detail. The Heisenberg-Lemaitre's units, based on the total enormous but finite mass of the Universe, are introduced and rigorous solutions of Einstein's cosmological equations for an open Universe with cosmological constant are obtained. Energy conservation after the Big Bang is consistently required.This book discusses such paradoxes in depth with physical and logical content and historical perspective, and has not too technical content in order to serve a wide audience. In the second edition, the content is updated and new sections are added.

Beginning with the famous Olber's paradox, paradoxes such as the missing mass, dark energy, baryon to photon ratio and cosmic zero-point energy are examined in detail. The Heisenberg-Lemaitre's units, based on the total enormous but finite mass of the Universe, are introduced and rigorous solutions of Einstein's cosmological equations for an open Universe with cosmological constant are obtained. Energy conservation after the Big Bang is consistently required.This book discusses such paradoxes in depth with physical and logical content and historical perspective, and has not too technical content in order to serve a wide audience. In the second edition, the content is updated and new sections are added.

Stoicheiosis Astronomike ('Elements of Astronomy') is a late Byzantine comprehensive introduction to Astronomy. It was written by an outstanding figure in Byzantine culture and politics, who served also as prime minister. This volume makes available for the first time a large part of its astronomical contents, offering the original text with an English translation, accompanied by an introduction and analysis.This book describes the celestial spheres, the rotation of the planets, and especially the apparent trajectory of the sun with its uniform and anomalous rotations, which are used to determine the length of the year. Metochites proposed a new starting date for the calendar (6th of October 1283) specifying the position of the sun on that date. The work revived the interest in studies of Ptolemaic astronomy as attested by numerous annotations in the margins of the manuscripts.Besides its astronomical content there are statements on the epistemological method and other issues elucidating the spirit of that age. It will be of interest as an introduction to Byzantine astronomy for historians of science and philosophy, for astronomers, and those interested in the development of calendars.