Download or read book General Relativity for Planetary Navigation written by James Miller and published by Springer. This book was released on 2021-09-01 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief approaches General Relativity from a planetary navigation perspective, delving into the unconventional mathematical methods required to produce computer software for space missions. It provides a derivation of the Einstein field equations and describes experiments performed on the Near Earth Asteroid Rendezvous mission, spanning General Relativity Theory from the fundamental assumptions to experimental verification. The software used for planetary missions is derived from mathematics that use matrix notation. An alternative is to use Einstein summation notation, which enables the mathematics to be presented in a compact form but makes the geometry difficult to understand. In this book, the relationship of matrix notation to summation notation is shown. The purpose is to enable the reader to derive the mathematics used in the software in either matrix notation or summation notation. This brief is a useful tool for advanced students and young professionals embarking on careers in planetary navigation.

Download or read book General Relativity for Planetary Navigation written by James Miller and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief approaches General Relativity from a planetary navigation perspective, delving into the unconventional mathematical methods required to produce computer software for space missions. It provides a derivation of the Einstein field equations and describes experiments performed on the Near Earth Asteroid Rendezvous mission, spanning General Relativity Theory from the fundamental assumptions to experimental verification. The software used for planetary missions is derived from mathematics that use matrix notation. An alternative is to use Einstein summation notation, which enables the mathematics to be presented in a compact form but makes the geometry difficult to understand. In this book, the relationship of matrix notation to summation notation is shown. The purpose is to enable the reader to derive the mathematics used in the software in either matrix notation or summation notation. This brief is a useful tool for advanced students and young professionals embarking on careers in planetary navigation.

Download or read book General Relativity for Planetary Navigation written by James Miller and published by Springer Nature. This book was released on 2021-08-31 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief approaches General Relativity from a planetary navigation perspective, delving into the unconventional mathematical methods required to produce computer software for space missions. It provides a derivation of the Einstein field equations and describes experiments performed on the Near Earth Asteroid Rendezvous mission, spanning General Relativity Theory from the fundamental assumptions to experimental verification. The software used for planetary missions is derived from mathematics that use matrix notation. An alternative is to use Einstein summation notation, which enables the mathematics to be presented in a compact form but makes the geometry difficult to understand. In this book, the relationship of matrix notation to summation notation is shown. The purpose is to enable the reader to derive the mathematics used in the software in either matrix notation or summation notation. This brief is a useful tool for advanced students and young professionals embarking on careers in planetary navigation.

Download or read book Planetary Spacecraft Navigation written by James Miller and published by Springer. This book was released on 2025-01-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new edition, the authors James Miller and Connie Weeks dive deeper into how computer programming has assisted with planetary spacecraft navigation; evaluating real-world results and relying on complex mathematical theory to observe advancements made in this rapidly accelerating field. This textbook introduces the theories and practical procedures used in planetary spacecraft navigation. Written by a former member of NASA's Jet Propulsion Laboratory (JPL) navigation team with his co-author, it delves into the mathematics behind modern digital navigation programs, as well as the numerous technological resources used by JPL as a key player in the field. In addition, the text offers an analysis of navigation theory application in recent missions, with the goal of showing students the relationship between navigation theory and the real-world orchestration of mission operations.

Download or read book Planetary Spacecraft Navigation written by James Miller and published by Springer. This book was released on 2018-09-03 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the theories and practical procedures used in planetary spacecraft navigation. Written by a former member of NASA's Jet Propulsion Laboratory (JPL) navigation team, it delves into the mathematics behind modern digital navigation programs, as well as the numerous technological resources used by JPL as a key player in the field. In addition, the text offers an analysis of navigation theory application in recent missions, with the goal of showing students the relationship between navigation theory and the real-world orchestration of mission operations.

Download or read book Applied General Relativity written by Michael H. Soffel and published by Springer Nature. This book was released on 2019-09-23 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late 20th and beginning 21st century high-precision astronomy, positioning and metrology strongly rely on general relativity. Supported by exercises and solutions this book offers graduate students and researchers entering those fields a self-contained and exhaustive but accessible treatment of applied general relativity. The book is written in a homogenous (graduate level textbook) style allowing the reader to understand the arguments step by step. It first introduces the mathematical and theoretical foundations of gravity theory and then concentrates on its general relativistic applications: clock rates, clock sychronization, establishment of time scales, astronomical references frames, relativistic astrometry, celestial mechanics and metrology. The authors present up-to-date relativistic models for applied techniques such as Satellite LASER Ranging (SLR), Lunar LASER Ranging (LLR), Globale Navigation Satellite Systems (GNSS), Very Large Baseline Interferometry (VLBI), radar measurements, gyroscopes and pulsar timing. A list of acronyms helps the reader keep an overview and a mathematical appendix provides required functions and terms.

Download or read book Gravity from the Ground Up written by Bernard Schutz and published by Cambridge University Press. This book was released on 2003-12-04 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book invites the reader to understand our Universe, not just marvel at it. From the clock-like motions of the planets to the catastrophic collapse of a star into a black hole, gravity controls the Universe. Gravity is central to modern physics, helping to answer the deepest questions about the nature of time, the origin of the Universe and the unification of the forces of nature. Linking key experiments and observations through careful physical reasoning, the author builds the reader's insight step-by-step from simple but profound facts about gravity on Earth to the frontiers of research. Topics covered include the nature of stars and galaxies, the mysteries of dark matter and dark energy, black holes, gravitational waves, inflation and the Big Bang. Suitable for general readers and for undergraduate courses, the treatment uses only high-school level mathematics, supplemented by optional computer programs, to explain the laws of physics governing gravity.

Download or read book A Mathematical Journey to Relativity written by Wladimir-Georges Boskoff and published by Springer Nature. This book was released on 2020-06-01 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.

Download or read book A Mathematical Introduction To General Relativity written by Amol Sasane and published by World Scientific. This book was released on 2021-08-10 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.

Download or read book Relativistic Celestial Mechanics of the Solar System written by Sergei Kopeikin and published by John Wiley & Sons. This book was released on 2011-10-25 with total page 897 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic reference frames, the celestial mechanics of N-body systems, and high-precision astrometry, navigation, and geodesy, which are then treated in the following five chapters. The final chapter provides an overview of the new field of applied relativity, based on recent recommendations from the International Astronomical Union. The book is suitable for teaching advanced undergraduate honors programs and graduate courses, while equally serving as a reference for professional research scientists working in relativity and dynamical astronomy. The authors bring their extensive theoretical and practical experience to the subject. Sergei Kopeikin is a professor at the University of Missouri, while Michael Efroimsky and George Kaplan work at the United States Naval Observatory, one of the world?s premier institutions for expertise in astrometry, celestial mechanics, and timekeeping.

Download or read book Space Time and Gravitation written by Sir Arthur Stanley Eddington and published by . This book was released on 1920 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Relativity Gravitation and GPS written by Clive A. Redwood and published by Createspace Independent Pub. This book was released on 2012-03-15 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamentals of the science of general relativity and gravitation (GR) and the principles of application of this science in the technology of the Global Positioning System (GPS). Of the science of GR, the topics covered include: tensor analysis, including the development of the metric tensor, tensor calculus and the Riemann-Christoffel tensor; the geodesic equation; the equations of gravitational fields in the absence and in the presence of matter; the generally covariant reformulation of Maxwellian electromagnetism; development of the energy tensors of fluids and of the electromagnetic field; relativising physical relationships; the Newtonian approximation; the Schwarzschild solution; the behaviour of light in a weak gravitational field: the relativistic precession of Mercury's orbit; and the Schwarzschild black hole. In the section on GPS, the topics covered include: the structure of the GPS; the synchronization of clocks in an Earth-Centered Earth-Fixed (ECEF) coordinate system; the setup and behaviour of clocks on satellites in the Space Segment; frequency shifts of signals from satellite-based clocks; the pseudorange and its relativistic and other sources of errors; and the principles of the determination of local time and position by receiver. The book seeks to provide a full development of basic GR principles and their application in the technology of GPS. The presentation is integral and self-sufficient. That is, for the prepared reader, there should be no need to refer to other works in order to assimilate the material presented. Therefore, several concepts and methods, that elsewhere may not be discussed or are axiomatically presented, are here developed in a logically satisfactory manner. An appendix includes a review of Kleperian kinematics of orbits that informs the basic model of the GPS and develops interpolation techniques used by GPS receivers in correcting the raw data received from GPS satellites.

Download or read book Gravity written by Eric Poisson and published by Cambridge University Press. This book was released on 2014-05-29 with total page 795 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique graduate textbook that develops powerful approximation methods and their applications to real-life astrophysical systems.

Download or read book Introducing General Relativity written by Mark Hindmarsh and published by John Wiley & Sons. This book was released on 2022-04-25 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing General Relativity An accessible and engaging introduction to general relativity for undergraduates In Introducing General Relativity, the authors deliver a structured introduction to the core concepts and applications of General Relativity. The book leads readers from the basic ideas of relativity—including the Equivalence Principle and curved space-time—to more advanced topics, like Solar System tests and gravitational wave detection. Each chapter contains practice problems designed to engage undergraduate students of mechanics, electrodynamics, and special relativity. A wide range of classical and modern topics are covered in detail, from exploring observational successes and astrophysical implications to explaining many popular principles, like space-time, redshift, black holes, gravitational waves and cosmology. Advanced topic sections introduce the reader to more detailed mathematical approaches and complex ideas, and prepare them for the exploration of more specialized and sophisticated texts. Introducing General Relativity also offers: Structured outlines to the concepts of General Relativity and a wide variety of its applications Comprehensive explorations of foundational ideas in General Relativity, including space-time curvature and tensor calculus Practical discussions of classical and modern topics in relativity, from space-time to redshift, gravity, black holes, and gravitational waves Optional, in-depth sections covering the mathematical approaches to more advanced ideas Perfect for undergraduate physics students who have studied mechanics, dynamics, and Special Relativity, Introducing General Relativity is an essential resource for those seeking an intermediate level discussion of General Relativity placed between the more qualitative books and graduate-level textbooks.

Download or read book PATHWAYS TO THE PLANETS written by John R. Strand and published by AuthorHouse. This book was released on 2004-11-05 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: When my generation grew up, we were never limited by the sky or the stars. Man had already begun to probe its mysteries. Our mothers and fathers before us had created methods, maps, and ships that would forever change their planet and the way their children would view the world. So, when our small new-media company was offered the opportunity to work with John Strand and Pathways to the Planets, we all knew that it was a chance of a lifetime to work with someone who was instrumental in helping man reach that small rock in space called the moon. We live in the new world created by those brave pioneers and today are posed new frontiers; nano-science, cyberspace, molecular medicine, etc... All afforded to us humans, at least in part, by the extraordinary people portrayed in this book. Pathways to the Planets is a unique insight into the lives of those individuals as told through the memoirs of Astrophysicist John Strand. I personally, found this book to be an affirmation for anyone who seeks adventure and welcomes challenge and certainly a must read for those who were there (on earth!) during that exciting time. What a journey producing this book has been! For more information on John Strand, Pathways to the Planets or the early days of the space program go to “http://www.pathwaystotheplanets.com/” . by Perry Berryhill - President, Panacore Corporation

Download or read book Principles Of Quantum General Relativity written by Eduard Prugovecki and published by World Scientific. This book was released on 1995-01-20 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explains and analyzes the principles of a quantum-geometric framework for the unification of general relativity and quantum theory. By taking advantage of recent advances in areas like fibre and superfibre bundle theory, Krein spaces, gauge fields and groups, coherent states, etc., these principles can be consistently incorporated into a framework that can justifiably be said to provide the foundations for a quantum extrapolation of general relativity. This volume aims to present this approach in a way which places as much emphasis on fundamental physical ideas as on their precise mathematical implementation. References are also made to the ideas of Einstein, Bohr, Born, Dirac, Heisenberg and others, in order to set the work presented here in an appropriate historical context.

Download or read book Introduction to General Relativity written by H. A. Atwater and published by Elsevier. This book was released on 2013-10-22 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to General Relativity is an introductory text on the concepts and modes of calculation used in general relativity. Topics covered range from Newton's laws of motion and the Galilean transformation to tensor analysis, equations of motion of free particles, electromagnetism, and gravitational fields and waves. Solutions of the field equations are also given. The emphasis is on the actual performance of relativistic calculations, rather than on mathematical rigor or exhaustive completeness. This volume is comprised of nine chapters and begins with an overview of the theory of relativity, which includes special relativity and general relativity. The discussion then turns to Newton's laws of motion and the Galilean transformation, electromagnetism and the Galilean transformation, and the Lorentz transformation. Subsequent chapters explore tensor analysis; equations of motion of free particles; gravitational fields and waves; relativity in cosmology; and unified theories and quantized theories of general relativity. The final chapter is devoted to Minkowski's coordinates and orthogonal transformations. This book will be a valuable resource for students of physics.