Download or read book The First Law of Mechanics in General Relativity Isochrone Orbits in Newtonian Gravity written by Paul Ramond and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis tackles two distinct problems of great interest in gravitational mechanics - one relativistic and one Newtonian. The relativistic one is concerned with the "first law of binary mechanics", a remarkably simple variational relation that plays a crucial role in the modern understanding of the gravitational two-body problem, thereby contributing to the effort to detect gravitational-wave signals from binary systems of black holes and neutron stars. The work reported in the thesis provides a mathematically elegant extension of previous results to compact objects that carry spin angular momentum and quadrupolar deformations, which more accurately represent astrophysical bodies than mere point particles. The Newtonian problem is concerned with the isochrone problem of celestial mechanics, namely the determination of the set of radial potentials whose bounded orbits have a radial period independent of the angular momentum. The thesis solves this problem completely in a geometrical way and explores its consequence on a variety of levels, in particular with a complete characterisation of isochrone orbits. The thesis is exceptional in the breadth of its scope and achievements. It is clearly and eloquently written, makes excellent use of images, provides careful explanations of the concepts and calculations, and it conveys the author's personality in a way that is rare in scientific writing, while never sacrificing academic rigor.
Download or read book The First Law of Mechanics in General Relativity Isochrone Orbits in Newtonian Gravity written by Paul Ramond and published by Springer Nature. This book was released on 2023-06-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis tackles two distinct problems of great interest in gravitational mechanics — one relativistic and one Newtonian. The relativistic one is concerned with the "first law of binary mechanics", a remarkably simple variational relation that plays a crucial role in the modern understanding of the gravitational two-body problem, thereby contributing to the effort to detect gravitational-wave signals from binary systems of black holes and neutron stars. The work reported in the thesis provides a mathematically elegant extension of previous results to compact objects that carry spin angular momentum and quadrupolar deformations, which more accurately represent astrophysical bodies than mere point particles. The Newtonian problem is concerned with the isochrone problem of celestial mechanics, namely the determination of the set of radial potentials whose bounded orbits have a radial period independent of the angular momentum. The thesis solves this problem completely in a geometrical way and explores its consequence on a variety of levels, in particular with a complete characterisation of isochrone orbits. The thesis is exceptional in the breadth of its scope and achievements. It is clearly and eloquently written, makes excellent use of images, provides careful explanations of the concepts and calculations, and it conveys the author’s personality in a way that is rare in scientific writing, while never sacrificing academic rigor.
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 Gravitation written by U. Kivi and published by BoD - Books on Demand. This book was released on 2020-09-04 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: The presentation of the book leans heavily on mathematics, and good understanding of some parts of the book require skills in ground level university mathematics. You manage rather well also with high school mathematics and positive attitude (or maybe also with pure positive attitude). Both classical gravitation theory and general relativity theory are treated using easier mathematics than in standard presentations. The basic structure of the theories is presented clearly in the book. Some new results with relation to planet orbits are presented in the book.
Download or read book From Newton s Laws to Einstein s Theory of Relativity written by Lizhi Fang and published by World Scientific. This book was released on 1987 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to introduce to the reader the main thread of development from Newton's laws to Einstein's theory of relativity. Limited by its scope and avoiding as much as possible the use of mathematical apparatus, the authors try to clarify the most fundamental ideas and concepts. Both authors hold a deep reverence for Galileo and Einstein, and this book is dedicated to these two great scientists.
Download or read book Space Time and Gravitation An Outline of the General Relativity Theory written by Arthur Eddington and published by Moulton Press. This book was released on 2011-04 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book In The Grip Of The Distant Universe The Science Of Inertia written by Peter Graneau and published by World Scientific. This book was released on 2006-06-01 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about the history of the science of inertia. Nobody denies the existence of the forces of inertia, but they are branded as “fictitious” because they do not fit smoothly into modern physics. Named by Kepler and given mathematical form by Newton, the force of inertia remains aloof because it has no obvious local cause. At the end of the 19th century, Ernst Mach bravely claimed that the inertia of an object was the result of its instantaneous interaction with all matter in the universe.Many other well-known physicists, including Aristotle, Galileo, Descartes and Einstein, are shown to have tackled this difficult subject. The book also concentrates on inertia research in the 20th century, taking place under the shadow of general relativity, which is seen as uncomfortable with Mach's principle. A Newtonian paradigm, based on action-at-a-distance forces, is discussed throughout the book, allowing the revival of Mach's principle as the only coherent explanation of the inertia forces which play such an important role in the laboratory and in the cosmos.
Download or read book Gravitation and Cogravitation written by Oleg D. Jefimenko and published by . This book was released on 2006 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newtons theory of gravitation is the grandest and the most enduring physical theory ever created. Today, more than 300 years after it was first conceived, Newton''s theory of gravitation is still the basic working theory of astronomers and of all the scientists dealing with space exploration and celestial mechanics. However, Newton''s theory of gravitation has serious defects: it is incapable of accounting for certain fine details of planetary motion; it does not provide any information on the temporal aspect of gravitational interactions; it cannot be reconciled with the principle of causality and with the law of conservation of momentum when it is applied to time-dependent gravitational systems.This book extends and generalizes Newton''s theory of gravitation, makes it free from the above defects, makes it fully applicable to all possible gravitational systems, and provides a large variety of methods for calculating gravitational interactions between moving or stationary bodies of all shapes, sizes and configurations.The starting point of the generalization of Newton''s theory of gravitation developed in this book is the idea that gravitational interactions are mediated by two force fields: the gravitational field proper created by all masses and acting upon all masses, and the "cogravitational" field created by moving masses only and acting upon moving masses only. In accordance with the principle of causality, the two fields are represented by retarded field integrals, which, for static or slowly-varying gravitational systems, yield the ordinary Newtonian gravitational field.An immediate consequence of the generalized Newtonian theory of gravitation developed on this basis is that gravitational interactions normally involve at least five different forces associated with velocities, accelerations and rotations of interacting bodies. The effects of these forces are quite remarkable. Some examples: a fast-moving mass passing a spherically-symmetric body causes the latter to rotate; a mass moving with rapidly-decreasing velocity exerts both an attractive and a repulsive force on neighboring bodies; a rotating mass that is suddenly stopped causes neighboring bodies to rotate; the differential rotation of the Sun is caused by the planets orbiting around it.The generalized theory of gravitation is fully compatible with the laws of conservation of energy and momentum. A very important result of this compatibility is the definitive explanation of the process of conversion of gravitational field energy into the kinetic energy of bodies moving under the action of gravitational fields.The generalized theory of gravitation predicts the existence of gravitation-cogravitational waves and explains how such waves can be generated.The generalized theory of gravitation also indicates the existence of antigravitational (repulsive) fields and mass formations. A cosmological consequence of such fields and mass formations is a periodic expansion and contraction of the Universe. Another consequence is that the actual mass of the Universe may be much larger than the mass revealed by an analysis of gravitational attraction in the galaxies.It is natural to compare the various consequences of the generalized theory of gravitation with the consequences of the general relativity theory. In this regard the following three remarks should be made.First, there are no observable gravitational effects revealed by the general relativity theory that do not have their counterparts in the generalized theory of gravitation.Second, the generalized theory of gravitation describes a vastly larger number of gravitational effects than those described by the general relativity theory.Third, numerical values for gravitational effects predicted by the general relativity theory are usually different from the corresponding values predicted by the generalized theory of gravitation; the difference is almost always a consequence of greater complexity and depth of gravitational interactions revealed by the generalized theory of gravitation.Although this book presents the results of original research, it is written in the style of a textbook and contains numerous illustrative examples demonstrating various applications of the generalized Newtonian theory of gravitation developed in the book.
Download or read book Origin of Inertia written by Amitabha Ghosh and published by . This book was released on 2002 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Newton s Gravity written by Douglas W. MacDougal and published by Springer Science & Business Media. This book was released on 2012-12-16 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Newton’s Gravity” conveys the power of simple mathematics to tell the fundamental truth about nature. Many people, for example, know the tides are caused by the pull of the Moon and to a lesser extent the Sun. But very few can explain exactly how and why that happens. Fewer still can calculate the actual pulls of the Moon and Sun on the oceans. This book shows in clear detail how to do this with simple tools. It uniquely crosses disciplines – history, astronomy, physics and mathematics – and takes pains to explain things frequently passed over or taken for granted in other books. Using a problem-based approach, “Newton’s Gravity” explores the surprisingly basic mathematics behind gravity, the most fundamental force that governs the movements of satellites, planets, and the stars. Author Douglas W. MacDougal uses actual problems from the history of astronomy, as well as original examples, to deepen understanding of how discoveries were made and what they mean. “Newton’s Gravity” concentrates strongly on the development of the science of orbital motion, beginning with Galileo, Kepler, and Newton, each of whom is prominently represented. Quotes and problems from Galileo’s Dialogs Concerning Two New Sciences and particularly Newton’s Principia help the reader get inside the mind of those thinkers and see the problems as they saw them, and experience their concise and typically eloquent writing. This book enables students and curious minds to explore the mysteries of celestial motion without having to know advanced mathematics. It will whet the reader’s curiosity to explore further and provide him or her the tools (mathematical or physical) to do so.
Download or read book Newton s Principia written by Isaac Newton and published by Independently Published. This book was released on 2020-06-05 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was Isaac Newton's Principia that founded the law of universal gravitation on 5th July 1687. It is the same principia that inspired Albert Einstein into formulating the Einstein field equations (the general relativity theory). It is still the same principia, I believe, will lead us to the quantum theory of gravity (Quantum gravity) According to Newton's Principia, the force of gravity governs the movement of bodies in the solar system. It is this simple mathematical law which determines the motion of bodies. The force of gravity accurately predicts the planetary orbits, it was used to put the first man on the moon, it predicts the return of comets, the rotation of galaxies, the solar eclipses, artificial satellites, satellite communications and television, the GPS and interplanetary probes. I almost forgot, it is why NASA was established in the first place. The book has an active table of contents for readers to access each chapter, LIFE OF SIR ISAAC NEWTONxivBOOK I.1THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY.1AXIOMS, OR LAWS OF MOTION.20OF THE MOTION OF BODIES.43SECTION II.65Of the Invention of Centripetal Forces.65SECTION III.91Of the motion of bodies in eccentric conic sections.91SECTION IV.110Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given.110SECTION V.123How the orbits are to be found when neither focus is given.123SECTION VI.171How the motions are to be found in given orbits.171SECTION VII.183Concerning the rectilinear ascent and descent of bodies.183SECTION VIII.202Of the invention of orbits wherein bodies will revolve, being acted upon by any sort of centripetal force.202SECTION IX.212Of the motion of bodies in moveable orbits; and of the motion of the apsides.212SECTION X.230Of the motion of bodies in given superficies, and of the reciprocal motion of funependulous bodies.230SECTION XI.255Of the motions of bodies tending to each other with centripetal forces.255SECTION XII.300Of the attractive forces of sphærical bodies.300SECTION XIII.333Of the attractive forces of bodies which are not of a sphærical figure.333SECTION XIV.353Of the motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body.353BOOK II.365OF THE MOTION OF BODIES.365SECTION I.365Of the motion of bodies that are resisted in the ratio of the velocity.365SECTION II.381Of the motion of bodies that are resisted in the duplicate ratio of their velocities.381SECTION III.421Of the motions of bodies which are resisted partly in the ratio of the velocities, and partly in the duplicate of the same ratio.421SECTION IV.436Of the circular motion of bodies in resisting mediums.436SECTION V.449Of the density and compression of fluids; and of hydrostatics.449SECTION VI.469Of the motion and resistance of funependulous bodies.469SECTION VII.507Of the motion of fluids, and the resistance made to projected bodies.507SECTION VIII.571Of motion propagated through fluids.571SECTION IX.600Of the circular motion of fluids.600BOOK III.619RULES OF REASONING IN PHILOSOPHY.621PHÆNOMENA OR APPEARANCES.625PROPOSITIONS634OF THE MOTION OF THE MOON'S NODES.724END OF THE MATHEMATICAL PRINCIPLES.863THE SYSTEM OF THE WORLD.865
Download or read book Inertia and Gravitation written by Herbert Pfister and published by Springer. This book was released on 2015-02-24 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the phenomena of inertia and gravitation, one objective being to shed some new light on the basic laws of gravitational interaction and the fundamental nature and structures of spacetime. Chapter 1 is devoted to an extensive, partly new analysis of the law of inertia. The underlying mathematical and geometrical structure of Newtonian spacetime is presented from a four-dimensional point of view, and some historical difficulties and controversies - in particular the concepts of free particles and straight lines - are critically analyzed, while connections to projective geometry are also explored. The relativistic extensions of the law of gravitation and its intriguing consequences are studied in Chapter 2. This is achieved, following the works of Weyl, Ehlers, Pirani and Schild, by adopting a point of view of the combined conformal and projective structure of spacetime. Specifically, Mach’s fundamental critique of Newton’s concepts of ‘absolute space’ and ‘absolute time’ was a decisive motivation for Einstein’s development of general relativity, and his equivalence principle provided a new perspective on inertia. In Chapter 3 the very special mathematical structure of Einstein’s field equations is analyzed, and some of their remarkable physical predictions are presented. By analyzing different types of dragging phenomena, Chapter 4 reviews to what extent the equivalence principle is realized in general relativity - a question intimately connected to the ‘new force’ of gravitomagnetism, which was theoretically predicted by Einstein and Thirring but which was only recently experimentally confirmed and is thus of current interest.
Download or read book On the Free Motion of Points and on Universal Gravitation Including the Principal Propositions of Books I and III of the Principia written by William Whewell and published by . This book was released on 1836 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Genesis of General Relativity written by Jürgen Renn and published by Springer Science & Business Media. This book was released on 2007-06-17 with total page 2072 pages. Available in PDF, EPUB and Kindle. Book excerpt: This four-volume work represents the most comprehensive documentation and study of the creation of general relativity. Einstein’s 1912 Zurich notebook is published for the first time in facsimile and transcript and commented on by today’s major historians of science. Additional sources from Einstein and others, who from the late 19th to the early 20th century contributed to this monumental development, are presented here in translation for the first time. The volumes offer detailed commentaries and analyses of these sources that are based on a close reading of these documents supplemented by interpretations by the leading historians of relativity.
Download or read book Philosophi Naturalis Principia Mathematica Revision IV written by Keith Dixon-Roche and published by . This book was released on 2019-07 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Colour Images: This publication is a complete descriptive and mathematical explanation of why Isaac Newton was correct and Einstein and Bohr were both wrong. It includes; orbital motion, planetary spin, core pressure, earth's magnetic field, the atom along with mathematical descriptions for heat electricity, gravity, mass, all the physical constants. It defines Newton's gravitational constant (G) for the first time together with the true meaning of E=mc2. It also disproves; quantum theory, relativity, the singularity and dark matter, explains the size of the universe and how it works, identifies its source of its energy and explains how the stars and the planets generate their heat. It also explains that 'black-holes' are actually just inactive bodies of matter.
Download or read book The Theory of Space Time and Gravitation written by Vladimir Aleksandrovich Fok and published by . This book was released on 1959 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory and Experiment in Gravitational Physics written by Clifford M. Will and published by CUP Archive. This book was released on 1985-01-25 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1985 text offers a comprehensive survey of research and testing conducted in general relativity. As background it introduces the important principles of gravitational theory and develops the mathematical formalism necessary to carry out specific computations in order to compare theoretical predictions with experimental findings. The survey of experimental results includes not only Einstein's classical tests but also solar-system tests, never envisioned by Einstein, that make use of the high-precision space technology of the 1960s and 1970s. It also gives a systematic account of the remarkable 'binar pulsar' PSP 1913 16, the first evidence of gravitational waves. This volume will be a useful point of reference for any reader interested in the empirical underpinnings of one of the great theories of the twentieth century.
