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This accessible text on classical celestial mechanics, the principles governing the motions of bodies in the Solar System, provides a clear and concise treatment of virtually all of the major features of solar system dynamics. Building on advanced topics in classical mechanics such as rigid body rotation, Langrangian mechanics and orbital perturbation theory, this text has been written for advanced undergraduates and beginning graduate students in astronomy, physics, mathematics and related fields. Specific topics covered include Keplerian orbits, the perihelion precession of the planets, tidal interactions between the Earth, Moon and Sun, the Roche radius, the stability of Lagrange points in the three-body problem and lunar motion. More than 100 exercises allow students to gauge their understanding and a solutions manual is available to instructors. Suitable for a first course in celestial mechanics, this text is the ideal bridge to higher level treatments.

Celestial mechanics --- Mécanique céleste --- Celestial mechanics. --- Astronomy. --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics

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The Ballet of the Planets unravels the beautiful mystery of planetary motion, revealing how our understanding of astronomy evolved from Archimedes and Ptolemy to Copernicus, Kepler, and Newton. Mathematician Donald Benson shows that ancient theories of planetary motion were based on the assumptions that the Earth was the center of the universe and the planets moved in a uniform circular motion. Since ancient astronomers noted that occasionally a planet would exhibit retrograde motion--would seem to reverse its direction and move briefly westward--they concluded that the planets moved in epicyc

Planetary theory --- Celestial mechanics. --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Planets, Theory of --- Celestial mechanics --- History. --- History --- Planetary theory - History

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This volume contains the detailed text of the major lectures delivered during the I-CELMECH Training School 2020 held in Milan (Italy). The school aimed to present a contemporary review of recent results in the field of celestial mechanics, with special emphasis on theoretical aspects. The stability of the Solar System, the rotations of celestial bodies and orbit determination, as well as the novel scientific needs raised by the discovery of exoplanetary systems, the management of the space debris problem and the modern space mission design are some of the fundamental problems in the modern developments of celestial mechanics. This book covers different topics, such as Hamiltonian normal forms, the three-body problem, the Euler (or two-centre) problem, conservative and dissipative standard maps and spin-orbit problems, rotational dynamics of extended bodies, Arnold diffusion, orbit determination, space debris, Fast Lyapunov Indicators (FLI), transit orbits and answer to a crucial question, how did Kepler discover his celebrated laws? Thus, the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.

Celestial mechanics. --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Mecànica celeste --- Relativitat general (Física) --- Astrometria --- Física matemàtica --- Celestial mechanics

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These original essays explore the philosophical implications of Newton's work. They address a wide range of topics including Newton's influence on his contemporaries and successors such as Locke and Kant, and his views on the methodology of science, on absolute space and time, and on the Deity. Howard Stein compares Newton's refusal to lock natural philosophy into a preexisting system with the more rigid philosophical predilections of his near-contemporaries Christian Huygens and John Locke. Richard Arthur's commentary provides a useful gloss on Stein's essay. Lawrence Sklar puzzles over Newton's attempts to provide a unified treatment of the various real quantities: absolute space, time, and motion. According to Phillip Bricker's responding essay, however, the distinctions Sklar draws do not go to the heart of the debate between realists and representationalists. J.E. McGuire and John Carriero debate Newton's views of the relationship between the Deity and the nature of time and space. Peter Achinstein looks at the tension between Newton's methodological views and his advocacy of a corpuscular theory of light; he suggests that Newton could justify the latter by a weak inductive inference, but R.I.G. Hughes believes that this inference involves an induction Newton would be unwilling to make. Immanuel Kant's critique of Newton's view of gravity is discussed and amplified by Michael Friedman In response, Robert DiSalle raises a number of problems for Friedman's analysis. Errol Harris and Philip Grier extend the discussion to the present day and look at the ethical implications of Newton's work.

Mechanics --- Celestial mechanics --- Science --- Engineering & Applied Sciences --- Applied Mathematics --- Natural science --- Natural sciences --- Science of science --- Sciences --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Early works to 1800 --- Philosophy --- Newton, Isaac,

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Vladimir Arnold is one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics, and KAM theory.

Celestial mechanics. --- Mathematics. --- Mathematics --- Celestial mechanics --- Mathematics - General --- Mathematical Theory --- Calculus --- Physical Sciences & Mathematics --- Math --- Gravitational astronomy --- Mechanics, Celestial --- Algebra. --- Partial differential equations. --- Functions of real variables. --- Physics. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Real Functions. --- Science --- Astrophysics --- Mechanics --- Differential equations, partial. --- Mathematical analysis --- Partial differential equations --- Mathematical physics. --- Real variables --- Functions of complex variables --- Physical mathematics --- Physics