Kevin T. Kelly
Department of Philosophy
Carnegie Mellon University
Spherical Earth: ships sink on the horizon, circular shadows in lunar eclipses. Eratosthenes (c. 280 B.C.) measured the diameter of the Earth using shadows of two vertical stakes planted a known north-south distance apart . 1600 years later, Columbus used a bad estimate 1/3 too small. That's why he thought that India was across the Atlantic! The "superstitious skeptics" knew Eratosthenes' measurement and the current capabilities of sailing ships! Fortunately, North America was in the way.
Celestial sphere: stars seem to be glued to a sphere enveloping the Earth. The pole of the celestial sphere goes through the poles of the Earth. The equator of the celestial sphere is cut by a plane through the Earth's equator.
Diurnal (daily) motion: The celestial sphere rotates daily on its axis from east to west. The Earth is stationary, of course.
Annual motion of the sun: The sun backslides about a degree per day against the fixed stars along a great circle inclined to the celestial Equator at about 23+1/3 degrees. This path is called the Ecliptic. The distance of the sun above or below the celestial equator determines day length and hence the seasons. The lengths of the seasons are not the same, Winter being shorter than Summer. The point at which the sun rises above the celestial equator is called the vernal equinox and the other intersection is called the autumnal equinox. The high point on the ecliptic above the equator is the summer solstice and the low point below the equator is called the winter solstice.
Dividing the year into days and months so that the calendar remains in sync with the sun year after year was a major astronomical problem up to Copernicus. The problem was particularly pressing with regards to religious feast days and planting. This was the primary practical duty of astronomy. The Julian calendar (45 B.C.) measured the year at 365+1/4 days. This is actually a bit short, lagging behind the true value by one day in 128 years. Pope Gregory had to reform the calendar again in 1582 when the vernal equinox came ten days early!
It was hard to plot the sun against the fixed stars because the two are not visible at the same time. The sun's position in the sky at a givent ime can be fixed by looking at shadows, but this position must be projected onto where the fixed stars would be at that time. But time could only be measured by a water clock at the time, so solar measurements were very inaccurate. Nonetheless, Hipparchus painstakingly discovered the precession of the equinoxes: a very slow revolution of the equinoxes along the celestial equator .
Planets (wanderers) are stars observed to move on orbits slightly inclined to the ecliptic from west to east at different rates. The points where a planet's orbit cuts the ecliptic are called nodes. Each circuit of the orbit is a revolution in longitude. The planets with periods equal to that of the sun are said to be inferior (excluding the moon) and those with periods greater than the sun are called superior.
Occasionally, all the planets except the sun and the moon move backwards (east to west). This is called retrograde motion. A complete retrograde backwards and forwards loop is called a cycle of anomaly. Mars and Venus retrograde more than the other planets.
Inferior planets:
Superior planets
Monthly motion of the moon: The moon circles the earth nearly once a month, which results in a cyclic pattern of illumination by the sun, which is referred to as the phases of the moon. The connection of this obvious celestial phenomenon with menstruation and tides gave rise to the inescapable hypothesis that our destiny is tied to planetary motions. This hypothesis is the scientific basis of astrology.
Eclipses: Solar eclipses occur at new (dark) moon and Lunar eclipses occur at full moon. Eclipses can only occur when the moon is near one of its nodes, since this is the only time the sun, Earth and moon can be collinear.
Pythagoras (c. 600 B.C.) discovered that the notes of the Greek musical scale correspond to simple ratios of whole numbers. In the enthusiastic spirit of the age, he got the idea that perhaps everything else could be explained with such ratios. The discovery that the square root of two (the hypotenuse of a right triangle with unit sides) cannot be expressed as such a ratio was a great impediment to this program! Pythagoras originated the idea that the stars are attached to a crystalline sphere and that the planets ride around on spheres nested inside of it. This accounts for the crude phenomenon that the planets slowly backslide against the fixed stars throughout the year. Their spheres revolve a bit more slowly than the sphere carrying the fixed starts. Each sphere was supposed to emit a musical note due to its motion. Pythagoras hoped that ratios among these notes would account for the rotational rates of the planets.
Philolaus (c. 500 B.C.): a follower of Pythagoras proposed that the Eartha nd all the planets revolve around a central fire. He was quoted by Copernicus in his Preface to the De Revolutionibus. Other Pythagoreans were said to hold the same view.
Plato (c. 400 B.C.): Earth-centered universe based on concentric wheels. He proposed the research problem of accounting for the planetary motions using only uniform circular motion.
Eudoxus, Calippus(c. 400 B.C), Carried out Plato's program to a good approximation with the theory of homocentric spheres.
Rejected in antiquity because it did not explain the increased brightness of the planets during retrograde. If it were a qualitative feature of the planet, rather than variation in distance, the planets would not be immutable. But that would undercut the reason for using circles in the first place!
Aristotle (c. 400 B.C.) made homocentric spheres a feature of his physics. He wasn't an astronomer himself and at the time Eudoxus' approach was the best. After Aristotle, cosmologists kept referring to the spheres even though they didn't fit with the new astronomical theories.
Alexandria: After Aristotle, the center of astronomy and Greek thought moved to Alexandria, where Greek Ptolemies built the library and fostered learning.
Aristarchus of Samos c.300 B.C, Seleucus of Selucia c. 200 B.C. proposed geometrical sun-centered astronomies, but these theories had little influence prior to Copernicus. Aristarchus also found the ratio of the distances of the sun and the moon. At half moon, there is a right angle at the moon between the sun and the Earth (since we see the moon exactly half illuminated). On Earth, we can measure the angle between the Sun and the Moon. Two angles fix the triangle and hence the ratios of the sides.
Hipparchus (c. 300 B.C.) was the first painstaking empirical astronomer who made extensive attempts to obtain quantitative agreement with observation. The rest of Greek astronomy followed his example. His theory was based on epicycles and deferents, a consruction introduced by the celebrated mathematician Apollonius of Perga (c. 300 B.C.) Newton owed a tremendous mathematical debt to Apollonius, who worked out much of the theory of conic sections. Ironically, he was the author both of Greek astronomy and of the tools that would supercede it.
A deferent is a circle revolving uniformly about its center. An epicycle is another uniformly moving circular orbit with its center attached to the rim of the deferent. There is a carnival ride called the "scrambler" that implements this design. The seats ride on spokes attached to axles that are attached to larger spokes attached to another axle. Several kinds of motions can be produced.
Claudius Ptolemaeus (Ptolemy) (c. 200 A.D.): half a milennium after Hipparchus! Standard reference until Copernicus. Ptolemy used compositions of epicycles, eccentrics, and the equant: a circular orbit with speed uniform to an offset center. The equant violates the uniform circular motion assumption of earlier astronomers.
Planetary theory:
Problems
Copernicus was a university-educated amateur with a good reputation in the astronomical profession in Italy that preceded his later publications. He was an "insider". In 1515 the Pope invited him to reform the calendar (the major research grant of the age!), which he declined. Lectured on his system in Rome at the request of Pope Clement VII. His treatise, De Revolutionibus was handed to him on his deathbed.
Copernicus revolution was a revolution in planetary theory. It retained circles, and hence still required a basic Ptolemaic account of eccentricity and other solar and lunar anomalies.
Theory:
Inferior planets
Superior planets
From the Preface:
...those who devised the eccentrics seem thereby in large measure to have solved the problem of the apparent motions with appropriate calculations. But meanwhile they introduced a good many ideas which apparently contradict the first principles of uniform motion. Nor could they elicit or deduce from the eccentrics the principal consideration, that is, the structure of the universe and the true symmetry of its parts. On the contrary, their experience was just like some one taking from various places hands, feet, a head, and other pieces, very well depicted, it may be, but not for the representation of a single person; since these fragments would not belong to one another at all, a monster rather than a man would be put together from them.
Having thus assumed the motions which I ascribe to the earth later on in the volume, by long and intense study I finally found that if the motions of the other planets are correlated with the orbiting of the earth, and are computed for the revolution of each planet, not only do their phenomena follow therefrom but also the order and size of all the planets and spheres, and heaven itself is so linked together that in no portion of it can anything be shifted without disrupting the remaining parts and the universe as a whole.
From Chapter 1:
In the middle sits the Sun enthroned. In this most beautiful temple, could we place this luminary in any better position from which he can illuminate the whole at once? He is rightly called the Lamp,the Mind, the Ruler of the Universe; Hermes Trismegistus names him the visible God, Sophocles' Elecra calls him the All-seeing. So the Sun sits as upon a royal throne ruling his children the planets which circle round him.
So we find underlying this ordination an admirable symmetry in the Universe, and a clear bond of harmony in the motion and magnitude of the Spheres such as can be discovered in no other wise. ... All these phenomena proceed from the same cause,namely Earth's motion.
Compare:
Marcilio Ficino was a leading figure in the humanistic, Platonistic movement in Florence. He was a leading exponent of "natural magic", which was based on the astrological idea that our bodies and minds are influenced by the music of the spheres. He was much in demand as a physician, and even served as physician to the Pope. He wrote:
Nothing reveals the nature of the Good [i.e., God] more fully than the light [of the sun]. First, light is the most brilliant and clearest of sensible objects. Second, there is nothing which spreads out so easily, broadly, or rapidly as light. Third, like a caress, it penetrates all things harmlessly and gently. Fourth, the heat which accompanies it fosters and nourishes all things and is the universal generator and mover.... Similarly the Good is itself spread everywhere, and it soothes and entices all things. .... The sun can signify God himself to you, and who shall dare to say the sun is false?
Erasmus Reinhold (1511-1553) calculated a new table of planetary positiosn based on Copernicus' book called the Prutenic Tables. Practicing astronomers and astrologers regularly used these tables for practical work. Copernicus' work gained steady acceptance among astronomers.
Luther and Melanchtthon ridiculed the view six years after Copernicus' death. Protestantism was based on the idea of respect for scripture.Why would God command the sun to stop when it is the Earth that must stop? In Copernicus' world, where are heaven and hell?
Catholics were more cautious. They didn't want to have to undo Aquinas' Aristotelian synthesis if it wasn't necessary to do so. Protestant reformation also put new literalist pressure on the Catholics.
What is "harmony"? Is it a scientific consideration, an aesthetic value, or a particular prejudice of Platonistic philosophy?
Does "harmony" count as a scientific reason to believe?
Is "harmony" an indicator of truth?
What is coherence?
How do you balance coherence with background beliefs against harmony in the theory itself?
Should coherence with other accepted theories and prejudices matter?
Arthur Berry (1961) A Short History of Astronomy. New York: Dover. See especially chapters I - IV.
Clark Glymour (1981) Theory and Evidence. Princetion: Princeton University Press. See especially chapter VI.
Hugh Kearney (1981) Science and Change. New York: McGraw-Hill.
Thomas S. Kuhn (1959) The Copernican Revolution. New York: Vintage Books.