The First Law of Mechanics in General Relativity & Isochrone Orbits in Newtonian Gravity PDF Download
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Author: Paul Ramond
Publisher:
ISBN: 9783031179655
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Paul Ramond
Publisher:
ISBN: 9783031179655
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Paul Ramond
Publisher: Springer Nature
ISBN: 3031179641
Category : Science
Languages : en
Pages : 408
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Book Description
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.
Author: Sir Arthur Stanley Eddington
Publisher:
ISBN:
Category : General relativity (Physics).
Languages : en
Pages : 240
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Book Description
Author: U. Kivi
Publisher: BoD - Books on Demand
ISBN: 9528091172
Category : Science
Languages : en
Pages : 82
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Book Description
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.
Author: Lizhi Fang
Publisher: World Scientific
ISBN: 9789971978365
Category : Science
Languages : en
Pages : 128
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Book Description
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.
Author: Arthur Eddington
Publisher: Moulton Press
ISBN: 1447402243
Category : Science
Languages : en
Pages : 226
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Book Description
Author: Peter Graneau
Publisher: World Scientific
ISBN: 9814478164
Category : Science
Languages : en
Pages : 287
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Book Description
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.
Author: Oleg D. Jefimenko
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 388
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Book Description
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.
Author: Amitabha Ghosh
Publisher:
ISBN:
Category : Celestial mechanics
Languages : en
Pages : 172
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Book Description
Author: Isaac Newton
Publisher: Independently Published
ISBN:
Category :
Languages : en
Pages : 708
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Book Description
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
