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EB

ONLINE

Seattle : University of Washington Press, 2018

1 online resource (274 pages)

ISBN 9780295997599 (electronic bk.)

ISBN 9780295978215

Print version: Jacobsen, Theodor S. Planetary Systems from the Ancient Greeks to Kepler Seattle : University of Washington Press,c2018 ISBN 9780295978215

Cover -- Planetary Systems from the Ancient Greeks to Kepler -- Title -- Copyright -- Contents -- List of Figures -- Foreword -- Introduction -- I. Astronomical Knowledge of the Ancient Greeks -- Knowledge of the Sun’s, the Moon’s, and the Planets’ Apparent Motions -- The Aspects, Stations, and Retrograde Motions of the Planets -- The Periods of the Planets -- Apparent Planetary Loops and Zigzags -- The Elements of a Planetary Orbit -- Orbit Computation -- Concepts of Some Early Greek Philosophers -- Thales of Miletus (c. 624-546 B.C.) -- Anaximander (c. 611-545 B.C.) -- Anaximenes of Miletus (c. 585-528 B.C.) -- Anaxagoras of Clazomenae (c. 500-428 B.C.) -- Pythagoras of Samos (c. 580-500 B.C.) -- Philolaus, the Pythagorean (c. 470-400 B.C.) -- Hicetas of Syracuse (c. 350 B.C.) -- Ecphantus of Syracuse (c. 325 B.C.) -- Xenophanes of Colophon (c. 530 B.C.) -- Heraclitus of Ephesus (c. 500 B.C.) -- Empedocles of Agrigentum (c. 450 B.C.) -- Leukippus of Abdera (c. 450 B.C.) -- Democritus of Abdera (c. 400 B.C.) -- Metrodorus of Chios (c. 400 B.C.) -- Plato of Samos (427-347 B.C.) -- Aristotle of Stagira (384-322 B.C.) -- Heracleides of Pontus (c. 350 B.C.) -- Aristarchus of Samos (c. 310-230 B.C.) -- II. Eudoxus (408-355 B.C.) -- Eudoxus’s Lunar Theory -- Eudoxus’s Solar Theory -- Eudoxus’s Planetary Theory -- The Systems of Spheres -- III. Hipparchus (fl. 146-126 B.C.) -- Hipparchus’s Main Astronomical Contributions -- Hipparchus’s Solar Theory -- The Apparent Nonuniform Motion of the Sun in the Ecliptic -- Hipparchus’s Method of Finding the Line of Apsides and the Eccentricity of the Sun’s Orbit (Considered as an Eccentric Circle) -- Hipparchus’s Method of Predicting the Sun’s Place at Any Instant -- Equivalence of Epicyclic and Eccentric Motion -- Hipparchus’s Lunar Theory.

Hipparchus’s Method of Finding the Line of Apsides and Eccentricity of the Moon’s Orbit -- Hipparchus’s Method of Predicting the Moon’s Place at Any Time -- Hipparchus’s (Abortive) Theory of Planetary Motion -- Hipparchus’s Method of Finding the Stationary Points and Arcs of Retrogression of a Planet (a Method Originally Due to Apollonius) -- Hipparchus’s Eclipse Method of Finding the Actual Distances and Diameters of the Sun and Moon -- Hipparchus’s Discovery of the Precession of the Equinoxes -- Hipparchus’s Discussion of Errors -- IV. Ptolemy (fl. 125-150) -- Ptolemy’s Main Contributions to Astronomy -- Contents of the Almagest -- Ptolemy’s Solar Theory -- Ptolemy’s Work on the Lunar Orbit -- Ptolemy’s View of the Regression of the Nodes and the Advance of the Apsides of the Lunar Orbit -- Ptolemy’s Preliminary Derivation of the Elements of the Lunar Orbit -- The Motions in Ptolemy’s Lunar Orbit -- The Effects of Evection -- Ptolemy’s Explanation of the Evection -- Ptolemy’s Determination of the Evection at the Quarters -- The Prosneusis -- Ptolemy’s Computation of the Prosneusis and an Example of His Prediction of the Moon’s True Longitude -- Approximate Elementary Derivation of the Longitude Correction to the Moon’s Position Caused by the Prosneusis -- Introduction to Ptolemy’s Planetary Theory -- Ptolemy’s Planetary Theory -- Ptolemy’s Reason for Introducing an Equant Point in All Planetary Orbits -- Example of Ptolemy’s Prediction of a Superior Planet’s Celestial Longitude -- Ptolemy’s Determination of the Equant Point’s Position -- Ptolemy’s Theory of the Celestial Latitudes of the Planets -- The Superior Planets -- The Inferior Planets -- V. Copernicus (1473-1543) -- Copernicus’s Main Astronomical Contributions -- The Copernican System of the Sun, Moon, and Planets -- Copernicus’s Solar Theory -- Elementary Considerations.

Shorter Books and Pamphlets -- A Brief View of Kepler’s Accomplishments -- A Common Popular (Under)statement of Kepler’s Work -- A More Detailed List of Kepler’s Contributions -- Semipopular Statement of Kepler’s Work on Mars’s Orbit -- The Vicarious Hypothesis -- The First Oval -- The "Auxiliary Ellipse -- The "Orbital Ellipse -- Kepler’s Work on the Lunar Theory -- Kepler’s Solar Theory -- Kepler’s Determination of the Equant Point of the Earth’s Orbit -- Some Further Determinations of the Equant Position in the Earth’s Orbit -- Kepler’s Preliminary Work on the Orbit of Mars -- Kepler’s Vicarious Hypothesis -- Estimate of the Accuracy of the Vicarious Hypothesis in Longitude -- Kepler’s First Refutation of the Vicarious Hypothesis (from the Latitudes) -- Estimate of the Accuracy of the Vicarious Hypothesis in Latitude -- Kepler’s Estimate of Mars’s Orbital Eccentricity (from the Latitudes) -- Kepler’s Second Refutation of the Vicarious Hypothesis (from the Longitudes) -- The Bisection of Eccentricity Hypothesis -- Kepler’s Improvement of the Earth’s Orbit by Bisecting Its Eccentricity -- Bisection of the Eccentricity for Mars’s Orbit -- Suspicion of a Law: Estimate of the Accuracy of the Bisection of Eccentricity Hypothesis -- Direct Determination of the Distances of Mars from the Sun by Tycho’s Observations (1602) -- Three of Kepler’s Efforts to Retain an Epicycle and a Deferent: Kepler’s "Ovoid" Orbit -- First Construction of Kepler’s Ovoid Orbit -- Geometrical Estimate of the Sagitta of Kepler’s Ovoid Orbit -- Replacement of the Ovoid by an Epicycle and Deferent -- Sagitta of the Ovoid Construction -- Why Kepler Considered the Ovoid Theory to Be a Physical Theory -- Kepler’s First, or Auxiliary, Ellipse: Its Eccentricity and Properties -- Some of Kepler’s Further Attempts with Ovals or Combination Orbits.

Kepler’s Further Experiments with Circular Uniform Motions -- Kepler’s Construction of an Empirical Orbit of Mars Directly from Tycho’s Observations -- Kepler’s Check of His Ovoid Theory by 40 of Tycho’s Observations -- Kepler’s Rejection of His Ovoid Theory -- Kepler’s Accidental Discovery of His Second, or Final, Ellipse -- Construction of Kepler’s Final Ellipse by Diametral Distances -- Kepler’s Search for a Physical Cause of Elliptic Motion: His First Magnetic Orbit -- Kepler’s Law of Libration for the Magnetic Orbit -- Kepler’s Law of Total Libration for the Magnetic Orbit -- Kepler’s Proof That the Magnetic Orbit Is an Ellipse -- Kepler’s Construction of an Ellipse from Its Total Libration on the Radius of Its Major Auxiliary Circle -- Kepler’s Abandonment of His Epicylic First Magnetic Orbit -- First Application of the Areal Law to the Final Ellipse -- Another Attempt with the Areal Law on an Exact Ellipse -- Astronomy with the Final Ellipse: Kepler’s Equation -- Confirmation of Kepler’s Final Elliptic Orbit by Celestial Latitudes of Mars -- Kepler’s Second Magnetic Orbit -- Comparison between the Shapes of Some of Kepler’s Ovals and the True Ellipse -- Kepler’s Correction of His Law of Linear Orbital Velocity -- Some Curiosities Found in Kepler’s Works -- Kepler’s "Proof’’ of His Third Law -- Kepler’s Views on Stellar Distances -- Kepler’s "Proof’’ That Mars Has Just Two Moons -- Concluding Remarks -- Bibliography.

Simple Method of Finding the Earth’s Orbit -- Copernicus’s (Improved) Method for Finding Eccentricity and Aphelion of the Earth’s Orbit -- Copernicus’s Orbit of the Earth -- Notes on Some Elementary Methods of Finding the Relative Distances in the Planetary System -- The Precession of the Equinoxes and the Trepidation -- The Precession of the Equinoxes -- The Trepidation -- Copernicus’s Treatment of Precession and Trepidation -- Copernicus’s Lunar Theory -- Copernicus’s Orbit of Venus -- Copernicus’s Orbit of Mercury -- Copernicus’s Orbit of a Superior Planet -- Copernicus’s Theory of the Celestial Latitudes of the Superior Planets -- Copernicus’s Obliquation -- A Mechanical Model of the Obliquation -- Some Special Observational Facts -- Copernicus’s Theory of the Celestial Latitudes of the Inner Planets, Involving Both Obliquation and Deviation -- VI. Tycho Brahe (1546-1601) -- Tycho’s Main Astronomical Contributions -- The Tychonic System -- Note on Reymers’s System -- Tycho’s Solar Theory -- Tycho’s Orbit of Saturn: An Example of an Outer Planet -- Tycho’s Lunar Theory -- Tycho’s Method of Predicting the Moon’s Place -- Modern Development of Tycho’s Method into a Series Involving the Mean Anomaly M1 and Solar Phase Angle D -- Change from Tycho’s "Mean Solar Time" x to Modern Mean Solar Time t -- Analytical Comparison between Tycho’s Expression and the Modern Expression for the Moon’s Longitude -- Numerical Example of Predicting the Moon’s Place at Any Time in Tycho’s System -- Wittich’s Formula -- The Elliptic Terms -- VII. Kepler (1571-1630) -- Highlights of Kepler’s Most Important Astronomical Books -- Mysterium Cosmographicum (1596) -- Astronomia Nova, Based on Celestial Physics with a Commentary on the Motion of Mars (1609) -- Harmonice Mundi (1619) -- Astronomiae Copernicanae (In Parts: 1618, 1620, 1621) -- Tabulae Rudolphinae (1627).

001905571

express

(Au-PeEL)EBL6994311

(MiAaPQ)EBC6994311

(OCoLC)1321801887