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BL
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| Record Number
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862697
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| Main Entry
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Capuzzo-Dolcetta, Roberto
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| Title & Author
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Classical Newtonian gravity : : a comprehensive introduction, with examples and exercises /\ Roberto A. Capuzzo Dolcetta.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2019]
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| Series Statement
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UNITEXT for Physics
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| Page. NO
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1 online resource
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| ISBN
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3030258467
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: 9783030258467
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3030258459
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9783030258450
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Preface; Introduction; Contents; Symbols; 1 Elements of Vector Calculus; 1.1 Vector Functions of Real Variables; 1.2 Limits of Vector Functions; 1.3 Derivatives of Vector Functions; 1.3.1 Geometric Interpretation; 1.4 Integration of Vector Functions; 1.5 The Formal Vector Operator; 1.5.1 Gradient and in Spherical Polar Coordinates; 1.5.2 Gradient and in Cylindrical Coordinates; 1.6 The Divergence Operator; 1.7 The Curl; 1.8 Formal Calculation of Divergence and Laplacian by the Operator; 1.8.1 Spherical Polar Coordinates; 1.8.2 Cylindrical Coordinates; 1.9 Vector Fields
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1.9.1 Lines of Force of a Vector Field1.10 The Divergence Theorem; 1.10.1 The Stokes' Theorem; 1.11 Velocity Fields; 1.12 Meaning of the Divergence of a Vector Field; 1.13 Link Between Divergence and Volume Variation; 1.14 Solenoidal Vector Fields; 1.14.1 Flux Tubes; 1.15 Further Readings; 2 Newtonian Gravitational Interaction; 2.1 Single Particle Gravitational Potential; 2.2 Motion of a Particle Gravitating in a Resisting Medium; 2.3 The Gravitational N-Body Case; 2.3.1 Potential of N Gravitating Bodies; 2.3.2 Mechanical Energy of the N Bodies; 2.4 The Scalar Virial Theorem
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2.4.1 Consequences of the Virial Theorem2.5 Continuous Distributions of Matter; 2.5.1 Poisson's and Laplace's Equations; 2.6 Gauss' Theorem; 2.7 Gravitational Potential Energy; 2.8 Newton's Theorems; 2.9 Further Readings; 3 Central Force Fields; 3.1 The Potential and Force Generated by a Spherical Matter Distribution; 3.1.1 Calculating Spherical Potentials via Poisson's Equation; 3.2 Motion in a Spherical Potential; 3.2.1 Circular Trajectories; 3.3 Potential Generated by a Homogeneous Sphere; 3.3.1 Trajectories in a Homogeneous Sphere; 3.3.2 Radial Motion in a Homogeneous Sphere
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3.4 Some Relevant Spherical Models3.4.1 The Plummer Sphere; 3.4.2 The Isochrone Potential; 3.5 Quality of Motion; 3.5.1 The Keplerian Case; 3.5.2 The Homogeneous Sphere Case; 3.6 Periods of Oscillations; 3.6.1 Radial Period in the Keplerian Potential; 3.6.2 Radial Period in the Homogeneous Sphere Potential; 3.6.3 Radial Period in the Plummer Potential; 3.6.4 Radial Period in the Isochrone Potential; 3.7 Azimuthal Period; 3.7.1 Fully Periodic Motion; 3.8 The Inverse Problem in a Central Force Field; 3.8.1 From Elliptic Trajectories to their Central Force Field; 3.9 Further Readings
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| Abstract
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This textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field.
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| Subject
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Gravity.
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| Subject
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Gravity.
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| Dewey Classification
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526.7
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| LC Classification
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QB335.C37 2019
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