Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Introduction -- Basic astronomical phenomena -- Babylonian astronomy -- Early Greek astronomy -- 2 Spheres and circles -- Eudoxus' system of concentric spheres -- Aristotle -- Developments in mathematics -- Aristarchus -- Eccentric circles and epicycles -- 3 The Ptolemaic universe -- Hipparchus -- The distances of the Sun and Moon -- The motion of the Sun and precession -- The motion of the Moon -- The motion of the planets -- Ptolemy and the Almagest -- Mathematics in the Almagest -- Solar theory -- Lunar theory -- Planetary theory -- The Handy Tables and the Planetary Hypotheses -- 4 Developments in geocentric astronomy -- Astronomy in India -- Islamic astronomy -- Technical modifications to Ptolemaic astronomy -- Developments in trigonometry -- Criticisms of Ptolemy -- The Maragha School -- The revival of learning in Western Europe -- Scholasticism -- Peurbach and Regiomontanus -- 5 The heliocentric universe -- Copernicus -- The Commentariolus -- On the Revolutions -- The motion of the Earth -- The motion of the Moon -- Copernicus' planetary theory -- The reception of Copernicus' theory -- 6 Tycho Brahe, Kepler, and the ellipse -- Tycho Brahe -- Tycho's world system -- Tycho's lunar theory -- Kepler -- The Secret of the Universe -- Tycho's assistant -- The New Astronomy, and the first two laws of planetary motion -- The Harmony of the World and the third law -- 7 Galileo, the telescope, and Keplerian astronomy -- Galileo -- The Epitome of Copernican Astronomy -- The Rudolphine Tables and their impact -- Transits of Mercury and Venus -- Horrocks' lunar theory -- The contributions of Kepler and Galileo -- 8 The universal theory of gravitation -- The Cartesian vortex theory -- Pre-Newtonian conceptions of gravity -- Isaac Newton and the Principia.

Newton's laws and orbital motion -- Universal gravitation -- Lunar theory and perturbations -- The reception of Newton's theory -- The demise of the vortex theory -- 9 Celestial mechanics -- Analytic developments -- Clairaut, Euler, and d'Alembert -- The motion of the lunar apogee -- Halley's comet -- Aberration and nutation -- Two remaining problems -- Transits of Venus and the solar parallax -- Lagrange and Laplace -- The libration of the Moon -- Exact solutions to the three-body problem -- Planetary and lunar perturbations -- Variation of orbital parameters -- The shape of the Earth and its effect -- Probability and statistics -- The System of the World and the stability of the Solar System -- Celestial Mechanics -- 10 The asteroids and the outer planets -- The Titius-Bode law of planetary distances -- The Georgian planet -- The search for a planet between Mars and Jupiter -- Orbit determination -- Problems with Uranus -- Adams and Leverrier -- Neptune -- Pluto -- 11 New methods -- Patterns and resonances -- Hamilton and Jacobi -- Perturbation theory in the nineteenth century -- Lunar theory -- The circular restricted three-body problem -- Tisserand's criterion, and Hill curves -- Poincaré -- King Oscar's sixtieth birthday competition -- New Methods of Celestial Mechanics -- The stability of the Solar System -- The n-body problem and its solution -- Chaos in the Solar System -- 12 Mercury and relativity -- The anomalous advance of the perihelion of Mercury -- Vulcan -- Alternative hypotheses -- Einstein -- Special relativity -- General relativity -- A final thought -- References -- Index.