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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.
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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