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musielak d leonhard euler foundations celestial mechanics 2022

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Textbook in PDF format The intention of this book is to shine a bright light on the intellectual context of Euler’s contributions to physics and mathematical astronomy. Leonhard Euler is one of the most important figures in the history of science, a blind genius who introduced mathematical concepts and many analytical tools to help us understand and describe the universe. Euler also made a monumental contribution to astronomy and orbital mechanics, developing what he called astronomia mechanica. Orbital mechanics of artificial satellites and spacecraft is based on Euler’s analysis of astromechanics. However, previous books have often neglected many of his discoveries in this field. For example, orbital mechanics texts refer to the five equilibrium points in the Sun-Earth-Moon system as Lagrange points, failing to credit Euler who first derived the differential equations for the general n-body problem and who discovered the three collinear points in the three-body problem of celestial mechanics. These equilibrium points are essential today in space exploration; the James Webb Space Telescope (successor to the Hubble), for example, now orbits the Sun near L2, one of the collinear points of the Sun-Earth-Moon system, while future missions to study the universe will place observatories in orbit around Sun-Earth and Earth-Moon equilibrium points that should be properly called Euler-Lagrange points. In this book, the author uses Euler’s memoirs, correspondence, and other scholarly sources to explore how he established the mathematical groundwork for the rigorous study of motion in our Solar System. The reader will learn how he studied comets and eclipses, derived planetary orbits, and pioneered the study of planetary perturbations, and how, old and blind, Euler put forward the most advanced lunar theory of his time. Did you know? Acknowledgements Author’s Notes Prelude Euler’s Contributions to Celestial Mechanics Planetary Perturbations Lunar Theories Three-Body Problem List of Figures Euler Study of Newtonian and Cartesian Physics The Birth and Nurturing of Genius Cartesian and Newtonian Natural Philosophy A Young Scholar Earns Recognition Euler’s Grand Tour Saint Petersburg: Russian Bright Star Seeds for Euler Initiation into the Analysis of the Universe Introducing Analysis to Celestial Mechanics Euler at the St. Petersburg Observatory Euler Stellar Triangle Euler’s Mechanica, First Newtonian Physics in Analytical Form Analysis of Planetary Motion Euler’s Solution of Kepler’s Problem First Prize from the French Academy of Sciences A Theory of Tides French Academy Prize Competition for a Theory of Tides Universal Gravitation Law Euler’s Theory of Tides Elementary Analysis of Tides Leaving St. Petersburg A New Beginning in the Prussian Kingdom Theories of Motion in the Solar System The Berlin Observatory Euler’s First Astronomy Book Based on Analytical Principles Euler Lunar Tables Solar Eclipse in July 1748 Lunar Eclipse in August 1748 Research on the Motion of Celestial Bodies—Newtonian Second Law Equation Precession of the Equinoxes The Great Inequality That Links the Orbital Motions of Jupiter and Saturn Lunar Theory and Newton’s Inverse Square Law St. Petersburg Academy First Astronomy Competition in 1751 Euler Second Lunar Theory (1751) Euler and the Variation of the Moon An Intriguing Little Mystery—A Riddle from the Father? Life in the Prussian Kingdom Adieu Berlin Motion of Comets and Comet Tail Theory Comets as Objects in the Solar System The Comet of 1742 The Great Comet of 1744 Anonymous Lectures on Comets Prediction of Halley’s Comet Return in 1758 The Great Comet of 1769 Euler’s Theory of Comet Tail Formation Lexell and the Mysterious Comet What Is Known About Comets Comets and Their Place in Contemporary Space Exploration The Three-Body Problem and Lunar Theories Equations of Motion for the Three-Body System Euler’s Three-Body Problem of Two Gravitational Centers (E. 337) Euler’s Three-Body Problem in Collinear Configuration (E. 400) Euler’s Last Moon Theory Aiming to Perfect the Lunar Theory: Prize Competition in 1770 To Perfect the Lunar Theory: Last Prize Competition Equilibrium Points of a Restricted Three-Body System Euler’s Legacy to Astronautics The Personal Challenges St. Petersburg Fire, Vision and Family Loss The Triumphs Last Works Related to Celestial Mechanics Prizes from the French Academy To See Infinity Les Éloges The Scientific Legacy Euler Opera Omnia and Opera Postuma Astronomia Mechanica Euler’s Legacy for Engineering and Physics Euler’s Legacy for Observational Astronomy Legacy to Astronautics and Space Exploration Euler: Blind Mathematician, Astronomer, Engineer and Astrophysicist Appendix Prizes Related to Celestial Mechanics Awarded to Euler by the French Academy of Sciences Euler Timeline The Restricted Three-Body System

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musielak d leonhard euler foundations celestial mechanics 2022

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