From Eudoxus to Einstein: a history of mathematical astronomy

C. M. Linton0521827507, 9780521827508, 9780511216466

Since man first looked towards the heavens, a great deal of effort has been put into trying to predict and explain the motions of the sun, moon, and planets. Developments in man’s understanding have been closely linked to progress in the mathematical sciences. Whole new areas of mathematics, such as trigonometry, were developed to aid astronomical calculations, and on numerous occasions throughout history, breakthroughs in astronomy have only been possible because of progress in mathematics. This book describes the theories of planetary motion that have been developed through the ages, beginning with the homocentric spheres of Eudoxus and ending with Einstein’s general theory of relativity. It emphasises the interaction between progress in astronomy and in mathematics, showing how the two have been inextricably linked since Babylonian times. This valuable text is accessible to a wide audience, from amateur astronomers to professional historians of astronomy.

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Table of contents :
Half-title……Page 2
Title……Page 4
Copyright……Page 5
Dedication……Page 6
Contents……Page 8
Preface……Page 10
Basic astronomical phenomena……Page 14
Babylonian astronomy……Page 23
Early Greek astronomy……Page 27
Eudoxus’ system of concentric spheres……Page 38
Aristotle……Page 45
Developments in mathematics……Page 49
Aristarchus……Page 51
Eccentric circles and epicycles……Page 58
Hipparchus……Page 64
The distances of the Sun and Moon……Page 66
The motion of the Sun and precession……Page 68
The motion of the Moon……Page 70
Ptolemy and the Almagest……Page 73
Mathematics in the Almagest……Page 77
Solar theory……Page 82
Lunar theory……Page 85
Planetary theory……Page 88
The Handy Tables and the Planetary Hypotheses……Page 94
Astronomy in India……Page 98
Islamic astronomy……Page 100
Technical modifications to Ptolemaic astronomy……Page 102
Developments in trigonometry……Page 105
Criticisms of Ptolemy……Page 109
The Maragha School……Page 113
The revival of learning in Western Europe……Page 121
Scholasticism……Page 126
Peurbach and Regiomontanus……Page 129
Copernicus……Page 132
The Commentariolus……Page 135
On the Revolutions……Page 138
The motion of the Earth……Page 142
The motion of the Moon……Page 150
Copernicus’ planetary theory……Page 151
The reception of Copernicus’ theory……Page 159
Tycho Brahe……Page 166
Tycho’s world system……Page 172
Tycho’s lunar theory……Page 178
Kepler……Page 181
The Secret of the Universe……Page 183
Tycho’s assistant……Page 187
The New Astronomy, and the first two laws of planetary motion……Page 190
The Harmony of the World and the third law……Page 206
Galileo……Page 214
The Epitome of Copernican Astronomy……Page 229
The Rudolphine Tables and their impact……Page 233
Transits of Mercury and Venus……Page 241
Horrocks’ lunar theory……Page 247
The contributions of Kepler and Galileo……Page 248
The Cartesian vortex theory……Page 252
Pre-Newtonian conceptions of gravity……Page 256
Isaac Newton and the Principia……Page 263
Newton’s laws and orbital motion……Page 275
Universal gravitation……Page 283
Lunar theory and perturbations……Page 288
The reception of Newton’s theory……Page 295
The demise of the vortex theory……Page 301
Analytic developments……Page 304
Clairaut, Euler, and d’Alembert……Page 305
The motion of the lunar apogee……Page 311
Halley’s comet……Page 317
Aberration and nutation……Page 319
Two remaining problems……Page 322
Transits of Venus and the solar parallax……Page 328
Lagrange and Laplace……Page 330
The libration of the Moon……Page 332
Exact solutions to the three-body problem……Page 336
Planetary and lunar perturbations……Page 340
Variation of orbital parameters……Page 348
The shape of the Earth and its effect……Page 351
Probability and statistics……Page 354
The System of the World and the stability of the Solar System……Page 359
Celestial Mechanics……Page 363
The Titius–Bode law of planetary distances……Page 368
The Georgian planet……Page 370
The search for a planet between Mars and Jupiter……Page 374
Orbit determination……Page 378
Problems with Uranus……Page 385
Adams and Leverrier……Page 388
Neptune……Page 395
Pluto……Page 402
Patterns and resonances……Page 410
Hamilton and Jacobi……Page 414
Perturbation theory in the nineteenth century……Page 417
Lunar theory……Page 420
The circular restricted three-body problem……Page 426
Tisserand’s criterion, and Hill curves……Page 428
Poincaré……Page 429
King Oscar’s sixtieth birthday competition……Page 432
New Methods of Celestial Mechanics……Page 434
The stability of the Solar System……Page 440
The n-body problem and its solution……Page 445
Chaos in the Solar System……Page 447
The anomalous advance of the perihelion of Mercury……Page 450
Vulcan……Page 454
Alternative hypotheses……Page 458
Einstein……Page 463
Special relativity……Page 464
General relativity……Page 471
A final thought……Page 485
References……Page 488
Index……Page 516