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Planetary Systems from the Ancient Greeks to Kepler - Theodor S. Jacobsen

Planetary Systems from the Ancient Greeks to Kepler

Hardcover

Published: 1st September 1999
For Ages: 22+ years old
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However deficient by modern standards was the astronomical knowledge of most early astronomers, one never ceases to wonder at the completeness and precision of some of their results, derived as they were from inaccurate observations made with the naked eye or with crude instruments. The main results of astronomy that could be discovered by the naked eye actually were discovered by the best ancient observers. "Planetary Systems from the Ancient Greeks to Kepler" describes the detailed technical models whereby astronomers prior to Newton accounted for their observations. Unlike histories of science that focus on the influence of great ideas, this book presents the actual substance of those ideas and details their elaboration and development. The exposition is as geometrical as possible, reflecting the original style of the ancients. The first chapter presents the general body of observational astronomy known to the ancients and forming the subject of their explanatory endeavors. Each of the following chapters concentrates on the work of a single astronomer - Eudoxus, Hipparchus, Ptolemy, Copernicus, Tycho, and Kepler - and provides biographical details, a detailed exposition of his astronomical system, and some evaluation of the astronomer's role in the history of astronomy. Theodor S. Jacobsen is professor emeritus of astronomy at the University of Washington.

List of Figuresp. x
Forewordp. xv
Introductionp. 3
Astronomical Knowledge of the Ancient Greeksp. 6
Knowledge of the Sun's, the Moon's, and the Planets' Apparent Motionsp. 6
The Aspects, Stations, and Retrograde Motions of the Planetsp. 8
The Periods of the Planetsp. 9
Apparent Planetary Loops and Zigzagsp. 13
The Elements of a Planetary Orbitp. 15
Orbit Computationp. 22
Concepts of Some Early Greek Philosophersp. 23
Thales of Miletus (c. 624-546 B.C.)p. 23
Anaximander (c. 611-545 B.C.)p. 23
Anaximenes of Miletus (c. 585-528 B.C.)p. 24
Anaxagoras of Clazomenae (c. 500-428 B.C.)p. 25
Pythagoras of Samos (c. 580-500 B.C.)p. 25
Philolaus, the Pythagorean (c. 470-400 B.C.)p. 26
Hicetas of Syracuse (c. 350 B.C.)p. 26
Ecphantus of Syracuse (c. 325 B.C.)p. 26
Xenophanes of Colophon (c. 530 B.C.)p. 27
Heraclitus of Ephesus (c. 500 B.C.)p. 27
Empedocles of Agrigentum (c. 450 B.C.)p. 27
Leukippus of Abdera (c. 450 B.C.)p. 28
Democritus of Abdera (c. 400 B.C.)p. 29
Metrodorus of Chios (c. 400 B.C.)p. 29
Plato of Samos (427-347 B.C.)p. 29
Aristotle of Stagira (384-322 B.C.)p. 30
Heracleides of Pontus (c. 350 B.C.)p. 32
Aristarchus of Samos (c. 310-230 B.C.)p. 32
Eudoxus (408-355 B.C.)p. 34
Eudoxus's Lunar Theoryp. 35
Eudoxus's Solar Theoryp. 35
Eudoxus's Planetary Theoryp. 37
The Systems of Spheresp. 40
Hipparchus (fl. 146-126 B.C.)p. 41
Hipparchus's Main Astronomical Contributionsp. 42
Hipparchus's Solar Theoryp. 42
The Apparent Nonuniform Motion of the Sun in the Eclipticp. 42
Hipparchus's Method of Finding the Line of Apsides and the Eccentricity of the Sun's Orbit (Considered as an Eccentric Circle)p. 45
Hipparchus's Method of Predicting the Sun's Place at Any Instantp. 47
Equivalence of Epicyclic and Eccentric Motionp. 49
Hipparchus's Lunar Theoryp. 51
Hipparchus's Method of Finding the Line of Apsides and Eccentricity of the Moon's Orbitp. 53
Hipparchus's Method of Predicting the Moon's Place at Any Timep. 56
Hipparchus's (Abortive) Theory of Planetary Motionp. 60
Hipparchus's Method of Finding the Stationary Points and Arcs of Retrogression of a Planet (a Method Originally Due to Apollonius)p. 60
Hipparchus's Eclipse Method of Finding the Actual Distances and Diameters of the Sun and Moonp. 62
Hipparchus's Discovery of the Precession of the Equinoxesp. 65
Hipparchus's Discussion of Errorsp. 66
Ptolemy (fl. 125-150)p. 67
Ptolemy's Main Contributions to Astronomyp. 67
Contents of the Almagestp. 69
Ptolemy's Solar Theoryp. 72
Ptolemy's Work on the Lunar Orbitp. 72
Ptolemy's View of the Regression of the Nodes and the Advance of the Apsides of the Lunar Orbitp. 73
Ptolemy's Preliminary Derivation of the Elements of the Lunar Orbitp. 73
The Motions in Ptolemy's Lunar Orbitp. 77
The Effects of Evectionp. 77
Ptolemy's Explanation of the Evectionp. 80
Ptolemy's Determination of the Evection at the Quartersp. 82
The Prosneusisp. 82
Ptolemy's Computation of the Prosneusis and an Example of His Prediction of the Moon's True Longitudep. 84
Approximate Elementary Derivation of the Longitude Correction to the Moon's Position Caused by the Prosneusisp. 87
Introduction to Ptolemy's Planetary Theoryp. 90
Ptolemy's Planetary Theoryp. 91
Ptolemy's Reason for Introducing an Equant Point in All Planetary Orbitsp. 93
Example of Ptolemy's Prediction of a Superior Planet's Celestial Longitudep. 93
Ptolemy's Determination of the Equant Point's Positionp. 94
Ptolemy's Theory of the Celestial Latitudes of the Planetsp. 97
The Superior Planetsp. 97
The Inferior Planetsp. 99
Copernicus (1473-1543)p. 103
Copernicus's Main Astronomical Contributionsp. 109
The Copernican System of the Sun, Moon, and Planetsp. 110
Copernicus's Solar Theoryp. 114
Elementary Considerationsp. 114
Simple Method of Finding the Earth's Orbitp. 114
Copernicus's (Improved) Method for Finding Eccentricity and Aphelion of the Earth's Orbitp. 117
Copernicus's Orbit of the Earthp. 120
Notes on Some Elementary Methods of Finding the Relative Distances in the Planetary Systemp. 122
The Precession of the Equinoxes and the Trepidationp. 127
The Precession of the Equinoxesp. 127
The Trepidationp. 128
Copernicus's Treatment of Precession and Trepidationp. 130
Copernicus's Lunar Theoryp. 133
Copernicus's Orbit of Venusp. 133
Copernicus's Orbit of Mercuryp. 136
Copernicus's Orbit of a Superior Planetp. 138
Copernicus's Theory of the Celestial Latitudes of the Superior Planetsp. 141
Copernicus's Obliquationp. 141
A Mechanical Model of the Obliquationp. 143
Some Special Observational Factsp. 143
Copernicus's Theory of the Celestial Latitudes of the Inner Planets, Involving Both Obliquation and Deviationp. 147
Tycho Brahe (1546-1601)p. 150
Tycho's Main Astronomical Contributionsp. 152
The Tychonic Systemp. 153
Note on Reymers's Systemp. 155
Tycho's Solar Theoryp. 156
Tycho's Orbit of Saturn: An Example of an Outer Planetp. 157
Tycho's Lunar Theoryp. 157
Tycho's Method of Predicting the Moon's Placep. 163
Modern Development of Tycho's Method into a Series Involving the Mean Anomaly M[subscript 1] and Solar Phase Angle Dp. 166
Change from Tycho's "Mean Solar Time" [tau] to Modern Mean Solar Time tp. 167
Analytical Comparison between Tycho's Expression and the Modern Expression for the Moon's Longitudep. 168
Numerical Example of Predicting the Moon's Place at Any Time in Tycho's Systemp. 169
Wittich's Formulap. 171
The Elliptic Termsp. 171
Kepler (1571-1630)p. 172
Highlights of Kepler's Most Important Astronomical Booksp. 173
Mysterium Cosmographicum (1596)p. 173
Astronomia Nova, Based on Celestial Physics with a Commentary on the Motion of Mars (1609)p. 175
Harmonice Mundi (1619)p. 175
Astronomiae Copernicanae (In Parts: 1618, 1620, 1621)p. 175
Tabulae Rudolphinae (1627)p. 176
Shorter Books and Pamphletsp. 177
A Brief View of Kepler's Accomlishmentsp. 177
A Common Popular (Under) statement of Kepler's Workp. 177
A More Detailed List of Kepler's Contributionsp. 177
Semipopular Statement of Kepler's Work on Mars's Orbitp. 178
The Vicarious Hypothesisp. 180
The First Ovalp. 181
The "Auxiliary Ellipse"p. 181
The "Orbital Ellipse"p. 182
Kepler's Work on the Lunar Theoryp. 182
Kepler's Solar Theoryp. 183
Kepler's Determination of the Equant Point of the Earth's Orbitp. 184
Some Further Determinations of the Equant Position in the Earth's Orbitp. 188
Kepler's Preliminary Work on the Orbit of Marsp. 189
Kepler's Vicarious Hypothesisp. 189
Estimate of the Accuracy of the Vicarious Hypothesis in Longitudep. 193
Kepler's First Refutation of the Vicarious Hypothesis (from the Latitudes)p. 196
Estimate of the Accuracy of the Vicarious Hypothesis in Latitudep. 196
Kepler's Estimate of Mars's Orbital Eccentricity (from the Latitudes)p. 199
Kepler's Second Refutation of the Vicarious Hypothesis (from the Longitudes)p. 201
The Bisection of Eccentricity Hypothesisp. 205
Kepler's Improvement of the Earth's Orbit by Bisecting Its Eccentricityp. 205
Bisection of the Eccentricity for Mars's Orbitp. 206
Suspicion of a Law: Estimate of the Accuracy of the Bisection of Eccentricity Hypothesisp. 206
Direct Determination of the Distances of Mars from the Sun by Tycho's Observations (1602)p. 207
Three of Kepler's Efforts to Retain an Epicycle and a Deferent: Kepler's "Ovoid" Orbitp. 208
First Construction of Kepler's Ovoid Orbitp. 208
Geometrical Estimate of the Sagitta of Kepler's Ovoid Orbitp. 212
Replacement of the Ovoid by an Epicycle and Deferentp. 212
Sagitta of the Ovoid Constructionp. 216
Why Kepler Considered the Ovoid Theory to Be a Physical Theoryp. 216
Kepler's First, or Auxiliary, Ellipse: Its Eccentricity and Propertiesp. 216
Some of Kepler's Further Attempts with Ovals or Combination Orbitsp. 220
Kepler's Further Experiments with Circular Uniform Motionsp. 222
Kepler's Construction of an Empirical Orbit of Mars Directly from Tycho's Observationsp. 225
Kepler's Check of His Ovoid Theory by 40 of Tycho's Observationsp. 229
Kepler's Rejection of His Ovoid Theoryp. 230
Kepler's Accidental Discovery of His Second, or Final, Ellipsep. 230
Construction of Kepler's Final Ellipse by Diametral Distancesp. 231
Kepler's Search for a Physical Cause of Elliptic Motion: His First Magnetic Orbitp. 233
Kepler's Law of Libration for the Magnetic Orbitp. 235
Kepler's Law of Total Libration for the Magnetic Orbitp. 236
Kepler's Proof That the Magnetic Orbit Is an Ellipsep. 236
Kepler's Construction of an Ellipse from Its Total Libration on the Radius of Its Major Auxiliary Circlep. 238
Kepler's Abandonment of His Epicylic First Magnetic Orbitp. 240
First Application of the Areal Law to the Final Ellipsep. 240
Another Attempt with the Areal Law on an Exact Ellipsep. 240
Astronomy with the Final Ellipse: Kepler's Equationp. 241
Confirmation of Kepler's Final Elliptic Orbit by Celestial Latitudes of Marsp. 241
Kepler's Second Magnetic Orbitp. 243
Comparison between the Shapes of Some of Kepler's Ovals and the True Ellipsep. 247
Kepler's Correction of His Law of Linear Orbital Velocityp. 248
Some Curiosities Found in Kepler's Worksp. 252
Kepler's "Proof" of His Third Lawp. 252
Kepler's Views on Stellar Distancesp. 252
Kepler's "Proof" That Mars Has Just Two Moonsp. 253
Concluding Remarksp. 253
Bibliographyp. 255
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780295978215
ISBN-10: 029597821X
Audience: Professional
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 304
Published: 1st September 1999
Publisher: University of Washington Press
Country of Publication: US
Dimensions (cm): 28.0 x 21.6  x 2.21
Weight (kg): 0.97