The Kepler Problem

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The Kepler Problem

Author : Bruno Cordani
Publisher : Birkhäuser
ISBN 13 : 3034880510
Total Pages : 454 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Kepler Problem by : Bruno Cordani

Download or read book The Kepler Problem written by Bruno Cordani and published by Birkhäuser. This book was released on 2012-12-06 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of the correspondences existing among all levels of reality, truths pertaining to a lower level can be considered as symbols of truths at a higher level and can therefore be the "foundation" or support leading by analogy to a knowledge of the latter. This confers to every science a superior or "elevating" meaning, far deeper than its own original one. - R. GUENON, The Crisis of Modern World Having been interested in the Kepler Problem for a long time, I have al ways found it astonishing that no book has been written yet that would address all aspects of the problem. Besides hundreds of articles, at least three books (to my knowledge) have indeed been published al ready on the subject, namely Englefield (1972), Stiefel & Scheifele (1971) and Guillemin & Sternberg (1990). Each of these three books deals only with one or another aspect of the problem, though. For example, En glefield (1972) treats only the quantum aspects, and that in a local way. Similarly, Stiefel & Scheifele (1971) only considers the linearization of the equations of motion with application to the perturbations of celes tial mechanics. Finally, Guillemin & Sternberg (1990) is devoted to the group theoretical and geometrical structure.

An Introduction to the Mathematics and Methods of Astrodynamics

Author : Richard H. Battin
Publisher : AIAA
ISBN 13 : 9781600860263
Total Pages : 840 pages
Book Rating : 4.8/5 (62 download)

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Book Synopsis An Introduction to the Mathematics and Methods of Astrodynamics by : Richard H. Battin

Download or read book An Introduction to the Mathematics and Methods of Astrodynamics written by Richard H. Battin and published by AIAA. This book was released on 1999 with total page 840 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Key to Newton's Dynamics

Author : J. Bruce Brackenridge
Publisher : Univ of California Press
ISBN 13 : 0520916859
Total Pages : 316 pages
Book Rating : 4.5/5 (29 download)

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Book Synopsis The Key to Newton's Dynamics by : J. Bruce Brackenridge

Download or read book The Key to Newton's Dynamics written by J. Bruce Brackenridge and published by Univ of California Press. This book was released on 1996-02-29 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: While much has been written on the ramifications of Newton's dynamics, until now the details of Newton's solution were available only to the physics expert. The Key to Newton's Dynamics clearly explains the surprisingly simple analytical structure that underlies the determination of the force necessary to maintain ideal planetary motion. J. Bruce Brackenridge sets the problem in historical and conceptual perspective, showing the physicist's debt to the works of both Descartes and Galileo. He tracks Newton's work on the Kepler problem from its early stages at Cambridge before 1669, through the revival of his interest ten years later, to its fruition in the first three sections of the first edition of the Principia.

Solving Kepler's Equation Over Three Centuries

Author : Peter Colwell
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Solving Kepler's Equation Over Three Centuries by : Peter Colwell

Download or read book Solving Kepler's Equation Over Three Centuries written by Peter Colwell and published by . This book was released on 1993 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Kepler Problem in the Presence of Dark Energy, and the Cosmic Local Flow

Author : Alexander Silbergleit
Publisher : Springer Nature
ISBN 13 : 3030367525
Total Pages : 73 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Kepler Problem in the Presence of Dark Energy, and the Cosmic Local Flow by : Alexander Silbergleit

Download or read book Kepler Problem in the Presence of Dark Energy, and the Cosmic Local Flow written by Alexander Silbergleit and published by Springer Nature. This book was released on 2019-11-29 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book derives and analyzes all solutions to the Kepler problem with dark energy (DE), presenting significant results such as: (a) all radial infinite motions obey Hubble’s law at large times; (b) all orbital infinite motions are asymptotically radial and obey Hubble’s law; (c) infinite orbital motions strongly dominate the finite ones. This clearly shows the effect of repulsive DE: In the classical Kepler problem, all orbital motions are finite for negative energies and infinite in the opposite case. Another DE effect is spatial localization of bounded orbits: mostly, they are within the equilibrium sphere, where the attractive Newtonian force outbalances the repulsive force of DE. This problem is of particular current interest due to recent studies of the local flows of galaxies showing domination of DE in their dynamics; the book discusses this observation in detail.

Geometric Methods in Physics XXXVII

Author : Piotr Kielanowski
Publisher : Springer Nature
ISBN 13 : 3030340724
Total Pages : 260 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Geometric Methods in Physics XXXVII by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXVII written by Piotr Kielanowski and published by Springer Nature. This book was released on 2019-11-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles based on the XXXVII Białowieża Workshop on Geometric Methods in Physics, 2018. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. This edition of the workshop featured a special session dedicated to Professor Daniel Sternheimer on the occasion of his 80th birthday. The previously unpublished papers present cutting-edge current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past seven years, the Białowieża Workshops have been complemented by a School on Geometry and Physics comprising a series of advanced lectures for graduate students and early-career researchers. The book also includes abstracts of the five lecture series that were given at the seventh school.

Variations on a Theme by Kepler

Author : Victor Guillemin
Publisher : American Mathematical Soc.
ISBN 13 : 082184184X
Total Pages : 88 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Variations on a Theme by Kepler by : Victor Guillemin

Download or read book Variations on a Theme by Kepler written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 2006 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the Colloquium Lectures presented by Shlomo Sternberg in 1990. The authors delve into the mysterious role that groups, especially Lie groups, play in revealing the laws of nature by focusing on the familiar example of Kepler motion: the motion of a planet under the attraction of the sun according to Kepler's laws. Newton realized that Kepler's second law--that equal areas are swept out in equal times--has to do with the fact that the force is directed radially to the sun. Kepler's second law is really the assertion of the conservation of angular momentum, reflecting the rotational symmetry of the system about the origin of the force. In today's language, we would say that the group $O(3)$ (the orthogonal group in three dimensions) is responsible for Kepler's second law. By the end of the nineteenth century, the inverse square law of attraction was seen to have $O(4)$ symmetry (where $O(4)$ acts on a portion of the six-dimensional phase space of the planet). Even larger groups h The remainder of the book is aimed at specialists.It begins with a demonstration that the Kepler problem and the hydrogen atom exhibit $O(4)$ symmetry and that the form of this symmetry determines the inverse square law in classical mechanics and the spectrum of the hydrogen atom in quantum mechanics. The space of regularized elliptical motions of the Kepler problem (also known as the Kepler manifold) plays a central role in this book. The last portion of the book studies the various cosmological models in this same conformal class (and having varying isometry groups) from the viewpoint of projective geometry. The computation of the hydrogen spectrum provides an illustration of the principle that enlarging the phase space can simplify the equations of motion in the classical setting and aid in the quantization problem in the quantum setting. The authors provide a short summary of the homological quantization of constraints and a list of recent applications to many interesting finite-dimensional set

The Kepler Conjecture

Author : Jeffrey C. Lagarias
Publisher : Springer Science & Business Media
ISBN 13 : 1461411297
Total Pages : 456 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis The Kepler Conjecture by : Jeffrey C. Lagarias

Download or read book The Kepler Conjecture written by Jeffrey C. Lagarias and published by Springer Science & Business Media. This book was released on 2011-11-09 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of three-dimensional Euclidean space by equal spheres is attained by the “cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published in 2006 in a special issue of Discrete & Computational Geometry. Further supporting material is also presented: a follow-up paper of Hales et al (2010) revising the proof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales that indicate his original approach to the conjecture. The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work.

APlusPhysics

Author : Dan Fullerton
Publisher : Silly Beagle Productions
ISBN 13 : 0983563306
Total Pages : 300 pages
Book Rating : 4.9/5 (835 download)

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Book Synopsis APlusPhysics by : Dan Fullerton

Download or read book APlusPhysics written by Dan Fullerton and published by Silly Beagle Productions. This book was released on 2011-04-28 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: APlusPhysics: Your Guide to Regents Physics Essentials is a clear and concise roadmap to the entire New York State Regents Physics curriculum, preparing students for success in their high school physics class as well as review for high marks on the Regents Physics Exam. Topics covered include pre-requisite math and trigonometry; kinematics; forces; Newton's Laws of Motion, circular motion and gravity; impulse and momentum; work, energy, and power; electrostatics; electric circuits; magnetism; waves; optics; and modern physics. Featuring more than five hundred questions from past Regents exams with worked out solutions and detailed illustrations, this book is integrated with the APlusPhysics.com website, which includes online question and answer forums, videos, animations, and supplemental problems to help you master Regents Physics essentials. "The best physics books are the ones kids will actually read." Advance Praise for APlusPhysics Regents Physics Essentials: "Very well written... simple, clear engaging and accessible. You hit a grand slam with this review book." -- Anthony, NY Regents Physics Teacher. "Does a great job giving students what they need to know. The value provided is amazing." -- Tom, NY Regents Physics Teacher. "This was tremendous preparation for my physics test. I love the detailed problem solutions." -- Jenny, NY Regents Physics Student. "Regents Physics Essentials has all the information you could ever need and is much easier to understand than many other textbooks... it is an excellent review tool and is truly written for students." -- Cat, NY Regents Physics Student

Orbital Mechanics for Engineering Students

Author : Howard D Curtis
Publisher : Elsevier
ISBN 13 : 0080887848
Total Pages : 744 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Orbital Mechanics for Engineering Students by : Howard D Curtis

Download or read book Orbital Mechanics for Engineering Students written by Howard D Curtis and published by Elsevier. This book was released on 2009-10-26 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orbital Mechanics for Engineering Students, Second Edition, provides an introduction to the basic concepts of space mechanics. These include vector kinematics in three dimensions; Newton’s laws of motion and gravitation; relative motion; the vector-based solution of the classical two-body problem; derivation of Kepler’s equations; orbits in three dimensions; preliminary orbit determination; and orbital maneuvers. The book also covers relative motion and the two-impulse rendezvous problem; interplanetary mission design using patched conics; rigid-body dynamics used to characterize the attitude of a space vehicle; satellite attitude dynamics; and the characteristics and design of multi-stage launch vehicles. Each chapter begins with an outline of key concepts and concludes with problems that are based on the material covered. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra. Graduate students, researchers, and experienced practitioners will also find useful review materials in the book. NEW: Reorganized and improved discusions of coordinate systems, new discussion on perturbations and quarternions NEW: Increased coverage of attitude dynamics, including new Matlab algorithms and examples in chapter 10 New examples and homework problems

Qualitative Analysis of the Anisotropic Kepler Problem

Author : Josefina Casasayas
Publisher : American Mathematical Soc.
ISBN 13 : 0821823094
Total Pages : 115 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Qualitative Analysis of the Anisotropic Kepler Problem by : Josefina Casasayas

Download or read book Qualitative Analysis of the Anisotropic Kepler Problem written by Josefina Casasayas and published by American Mathematical Soc.. This book was released on 1984 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Key to Newton's Dynamics

Author : J. Bruce Brackenridge
Publisher :
ISBN 13 : 9780520200654
Total Pages : 299 pages
Book Rating : 4.2/5 (6 download)

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Book Synopsis The Key to Newton's Dynamics by : J. Bruce Brackenridge

Download or read book The Key to Newton's Dynamics written by J. Bruce Brackenridge and published by . This book was released on 1995 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Key to Newton's Dynamics is lucid, important, and fills a large gap in the existing literature. Brackenridge is undoubtedly that gifted, patient teacher that one expects from a quality liberal arts college."--Alan E. Shapiro, University of Minnesota

The Wayward Comet

Author : Martin Beech
Publisher : Universal-Publishers
ISBN 13 : 1627340645
Total Pages : 218 pages
Book Rating : 4.6/5 (273 download)

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Book Synopsis The Wayward Comet by : Martin Beech

Download or read book The Wayward Comet written by Martin Beech and published by Universal-Publishers. This book was released on 2016-01-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comets have not only blazed across the celestial vault throughout human history, they have embellished the night sky since the Earth itself formed some 4.5 billion years ago. Comets were among the first-born solid bodies in the solar system, and their frozen nuclei tell of the primordial chemistry and chaos that ultimately resulted in the formation of the planets, the evolution of life and us. For all this, however, comets have long been celestial oddities: they baffled our distant ancestors, and human society continues to marvel and speculate wildly at their appearance even to the present day. Cutting against the perceived constancy of the stars, comets seemingly present themselves at random times and they are often interpreted as harbingers of terrestrial change - both good and ill. How then are we to tame the comet: where do they form, how do they move, and can their appearances be predicted? Such questions have preoccupied astronomers for centuries but comets have only gradually allowed the secrets of their wayward flight to be revealed. In this book I explore the historical struggle to understand not only the place of comets within a societal context, but also the scientific quest to make their paths amenable to mathematical certitude. The latter narrative is the more technical in content, but it took tactile form with the invention, in 1732, of the cometarium, a mechanical device to demonstrate the first two of Kepler's planetary laws. And, this development was later paralleled, in the mid to late 19th century, by the development of various mechanical devices (analog computers) to help obtain solutions to Kepler's Problem - the problem which asks, exactly where in its orbit is a given comet at some specific set time. The telling of the wayward comets story covers the past two millennia of human history, and it takes us from the phenomenological musings of Aristotle, through the exactitude of Newton's gravitational theory and calculus, to the truly incredible study of comet 67P/Churyumov-Gerasimenko, by the European Space Agency's Rosetta spacecraft, in the modern era.

Fundamentals of Astrodynamics

Author : Roger R. Bate
Publisher : Courier Corporation
ISBN 13 : 9780486600611
Total Pages : 484 pages
Book Rating : 4.6/5 (6 download)

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Book Synopsis Fundamentals of Astrodynamics by : Roger R. Bate

Download or read book Fundamentals of Astrodynamics written by Roger R. Bate and published by Courier Corporation. This book was released on 1971-01-01 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching text developed by U.S. Air Force Academy and designed as a first course emphasizes the universal variable formulation. Develops the basic two-body and n-body equations of motion; orbit determination; classical orbital elements, coordinate transformations; differential correction; more. Includes specialized applications to lunar and interplanetary flight, example problems, exercises. 1971 edition.

Hidden Symmetries of the Kepler Problem

Author : Julia Kathryn Sheffler
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (143 download)

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Book Synopsis Hidden Symmetries of the Kepler Problem by : Julia Kathryn Sheffler

Download or read book Hidden Symmetries of the Kepler Problem written by Julia Kathryn Sheffler and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The orbits of planets can be described by solving Kepler's problem which considers the motion due to by gravity (or any inverse square force law). The solutions to Kepler's problem, for energies less then 0, are ellipses, with a few conserved quantities: energy, angular momentum and the Laplace-Runge-Lenz (LRL) vector. Each conserved quantity corresponds to symmetries of the system via N öther's theorem. Energy conservation relates to time translations and angular momentum to three dimensional rotations. The symmetry related to the LRL vector is more difficult to visualize since it lives in phase space rather than configuration space. To understand the symmetry corresponding to the LRL vector, I use tools from Hamiltonian Mechanics, including the Poisson bracket, flow parameters, and action angle variables to make a visualization of the effect of the symmetry corresponding to the LRL vector. In particular the LRL vector corresponds to four-dimensional rotations in phase space. Though it is beyond the scope of this project I hope to use the solidified understanding of the relationship between conserved quantities and symmetries to simplify the derivation of the probability distribution of semi-major axis given a single direct image of an exoplanet.

Keplerian Ellipses

Author : Bruce Cameron Reed
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1643274708
Total Pages : 72 pages
Book Rating : 4.6/5 (432 download)

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Book Synopsis Keplerian Ellipses by : Bruce Cameron Reed

Download or read book Keplerian Ellipses written by Bruce Cameron Reed and published by Morgan & Claypool Publishers. This book was released on 2019-05-10 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of man's understanding of planetary motions is the crown jewel of Newtonian mechanics. This book offers a concise but self-contained handbook-length treatment of this historically important topic for students at about the third-year-level of an undergraduate physics curriculum. After opening with a review of Kepler's three laws of planetary motion, it proceeds to analyze the general dynamics of 'central force' orbits in spherical coordinates, how elliptical orbits satisfy Newton's gravitational law, and how the geometry of ellipses relates to physical quantities, such as energy and momentum. Exercises are provided, and derivations are set up in such a way that readers can gain analytic practice by filling in the missing steps. A brief bibliography lists sources for readers who wish to pursue further study on their own.

Fundamentals of Physics I

Author : R. Shankar
Publisher : Yale University Press
ISBN 13 : 0300249586
Total Pages : 523 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Fundamentals of Physics I by : R. Shankar

Download or read book Fundamentals of Physics I written by R. Shankar and published by Yale University Press. This book was released on 2019-08-20 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: A beloved introductory physics textbook, now including exercises and an answer key, explains the concepts essential for thorough scientific understanding In this concise book, R. Shankar, a well-known physicist and contagiously enthusiastic educator, explains the essential concepts of Newtonian mechanics, special relativity, waves, fluids, thermodynamics, and statistical mechanics. Now in an expanded edition—complete with problem sets and answers for course use or self-study—this work provides an ideal introduction for college-level students of physics, chemistry, and engineering; for AP Physics students; and for general readers interested in advances in the sciences. The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics.