Glossary

A posteriori a type of reasoning, from observation to theory, from facts or particulars to general principles, from effects to causes synonymous with inductive and empirical. See regular solids. A priori a type of reasoning, from theory or principles without prior observations. See regular solids. Anomaly a violation of expectation a discovery for which an investigator's paradigm has not prepared him or her. Anthropocentric universe centered on human interests. The Copernican revolution saw a...

Symmetry A Human and Scientific Value

Another difficulty with equant points, in addition to their sheer physical improbability, was that Mercury's equant point was located differently than were the equant points for all the other planets. The epicycles were borne with uniform motion on circles the same size as the eccentric circles but with other centers. Ptolemy wrote And these centers, in the case of all except Mercury, bisect the straight lines between the centers of the eccentrics . . . and the center of the ecliptic. But in...

Observat Sidereae

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Mental Exercises Conjunction Opposition and Retrograde Motion

Would you expect retrograde motion for a superior planet to occur, if it does occur, when the planet is near opposition or near conjunction Why Would you expect retrograde motion for an inferior planet to occur, if it does occur, when the planet is near opposition or near conjunction Why Can an inferior planet ever be in conjunction In opposition Why or why not The problem of the planets was difficult, and Ptolemy warned his readers that he might be forced to use something contrary to the...

Eccentrics And Epicycles

Plato initiated the paradigm of uniform circular motion. Working within the paradigm, Eudoxus devised combinations of concentric spheres. The combined motions were intended to mimic observed planetary motions. Combinations of concentric spheres, however, cannot produce changing distances from the Earth. Next, schemes that could do so were developed, though not in Athens. Not long after Plato and Eudoxus flourished in Athens, the center of scientific activity in the Greek intellectual world...

The Hypothetico Deductive Method

Scientific theories can be tested by the hypothetico-deductive method. First, a hypothesis is postulated that the Earth orbits around the Sun. Then, a prediction is deduced from the hypothesis the motion of the Earth will be revealed in a stellar parallax. Then the test is a stellar parallax found In this historical case, the answer was no and the logic of the method dictated that the original hypothesis was thus refuted the Copernican theory was false. Or an auxiliary hypothesis had been...

Galileo Experiments the Leaning Tower of Pisa and Pendulums

According to biographical notes made by a disciple, companion, and pupil of Galileo for the three years immediately preceding his death in 1642 and published a dozen years later T o the great confusion of all the philosophers, very many conclusions of Aristotle himself about the nature of motion, which had been theretofore held as most clear and indubitable, were convicted of falseness by means of experiments and by sound demonstrations and discourses as among others, that the velocity of...

P

Optical Property Ellipse

An ellipse is defined as the collection of all points for which the sum of R1 and R2 is a constant. Also, an ellipse is the closed curve generated by the point P (the locus of the points P) moving in such a way that the sum of its distances from two fixed points, the foci (O' and O), is a constant. The planet is at P. The Sun is at one focus point, either O' or O. AB is the major axis. The minor axis is perpendicular to AB and intersects it at its midpoint, midway between...

Primary Sources

Stocks, trans., in W. D. Ross, ed., The Works of Aristotle, vol. 2 (Oxford Clarendon Press, 1930), reprinted, with mild emendations, in Jonathan Barnes, ed., The Complete Works of Aristotle, vol. I (Princeton Princeton University Press, 1984). In On the Heavens Aristotle develops ideas raised in his Physics. Aristotle, Metaphysics newly translated as a postscript to natural science, with an analytical index of technical terms, by Richard Hope (New York Columbia...

Saving The Phenomena Quantitatively

Modern scientists try to quantify scientific theories and models, seemingly automatically, without thinking about why they are quantifying or even if they should quantify. A folklorist or an anthropologist looking for and identifying recurring general themes in the preoccupations of scientists might liken their quantitative disposition to a knee-jerk reaction or to the salivating of Pavlov's psychologically conditioned dogs when a bell rang. But if every time they talk or write scientists don't...

Plato And Saving The Appearances

The guiding themata or paradigm of Greek planetary astronomy is attributed to Plato by the philosopher Simplicius of Athens in his commentary on Aristotle's book On the Heavens. Around a.d. 500 Simplicius wrote that Plato had set as a task for astronomers to explain the apparently irregular motions of the planets, the Sun, and the Moon as a combination of circular motions with constant speeds of rotation. To save the appearances with a system of uniform circular motions is, in the context of...

Ptolemys Exposition Of Mathematical Astronomy

Concerned With Complex

Hundreds of years of Greek geometrical astronomy was systematized and quantified with rigorous geometrical demonstrations and proofs by Claudius Ptolemaeus around a.d. 140. He did for astronomy what Euclid had done for geometry and earned a reputation as the greatest astronomer of the ancient world. Ptolemy's mathematical systematic treatise of astronomy, The Mathematical Syntaxis, soon attracted the appellation megiste, Greek for greatest. This was transliterated into Arabic and preceded by...

Secondary Sources

J., The Vortex Theory of Planetary Motions (London Macdonald & Co., 1972). On Descartes' vortex theory, the primary rival of Newton's theory of gravitation. See also B. S. Biagre, Descartes's Mechanical Cosmology, in Norriss S. Hetherington, ed., Encyclopedia of Cosmology Historical, Philosophical, and Scientific Foundations of Modern Cosmology (New York Garland Publishing, Inc., 1993), pp. 164-176. Andrade, E. N. da C., Sir Isaac Newton His Life and Work (Garden City, New York...

The Newtonian Revolution

Revolutions, scientific and social, consist of more than an initial press release followed by a victory celebration. Often, they are drawn out wars between opposing forces, with the outcome long in doubt. Copernicus declared a heliocentric system in 1543, but more than half a century later Galileo was fighting valiantly nor did he win every battle. Near the end of the seventeenth century Isaac Newton quantitatively reproduced Kepler's mathematical kinematics of the heavens with a new celestial...

Newton Astrotheology and Galaxies

Eighteenth-century belief in the orderliness of the universe made determination of that order an important theological, philosophical, and scientific endeavor for astrotheologians. William Whiston, Newton's successor in the Lucasian Chair of Mathematics at Cambridge University, from 1702 to 1710, when he was charged with heresy and dismissed from the university, argued that the system of the stars, the work of the Creator, had a beautiful proportion, even if frail man were ignorant of the...

Mental Exercise Tychos System

Orbital Chart Planets Moons

List astronomical phenomena that the Tychonic world system accounts for automatically but that the Ptolemaic system does not. Explain how the Tychonic system accounts for the phenomena. system differed from Ptolemy's was in placing Mercury, Venus, Mars, Jupiter, and Saturn in circular orbits centered on the Sun rather than on the Earth. In departing from the ancients and placing the planets in orbits centered on the Sun, Tycho gained many of the geometric advantages of the Copernican system...

Copernicus And Planetary Motions

Copernicus Stimmer

A great underlying theme dominating Western astronomy from Plato and the Greeks to the end of the Middle Ages and into the early Renaissance was a continuing and evolving struggle to represent observed planetary motions as combinations of uniform circular motions. Copernicus's De revolutionibus orbium caelestium On the Revolutions of the Celestial Spheres of 1543 is as full of epicycles and deferents as was Ptolemy's Almagest fourteen centuries earlier. Scholars have quibbled over who had more...

Physics

Astronomers labored to conform their planetary hypotheses to Plato's paradigm of uniform circular motion. Another body of beliefs, more all-encompassing and possibly even stronger than that of uniform circular motion, was Aristotle's physics. Supposedly, astronomers were not equipped as physicists were to contemplate physical causes and their effects. Nor were astronomers required to derive from the essence of bodies, or from the nature of things, explanations for why other things occurred. In...

Eudoxus And Concentric Spheres

Esferas Celeste Eudoxo

Plato encouraged a new approach to astronomy to devise a combination of uniform circular motions to reproduce the observed motions in the heavens. Whether the Platonic paradigm would die in infancy or grow in strength depended, in part, on the support it received. Greek society supported playwrights when the citizens of Athens paid to see the productions of Aeschylus, Sophocles, and Euripides and prizes were awarded at festivals to poets and musicians. No city held geometry in high regard,...