Planetary Systems from the Ancient Greeks to Kepler [E-Book]
Saved in:
Full text |
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Personal Name(s): | Jacobsen, Theodor S., author |
Imprint: |
Seattle :
University of Washington Press,
2018
|
Physical Description: |
1 online resource (274 pages) |
Note: |
englisch |
ISBN: |
9780295978215 9780295997599 |
- 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.
- 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" τ 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).
- 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.