5. The apparent daily motion of the stars around the Earth arises entirely from the Earth’s rotation on its axis.
6. The apparent motion of the Sun arises jointly from the rotation of the Earth on its axis and the Earth’s revolution (like that of the other planets) around the Sun.
7. The apparent retrograde motion of the planets arises from the Earth’s motion, occurring when the Earth passes Mars, Jupiter, or Saturn, or is passed in its orbit by Mercury or Venus.
Copernicus could not claim in the Commentariolus that his scheme fitted observation better than that of Ptolemy. For one thing, it didn’t. Indeed, it couldn’t, since for the most part Copernicus based his theory on data he inferred from Ptolemy’s Almagest, rather than on his own observations.3 Instead of appealing to new observations, Copernicus pointed out a number of his theory’s aesthetic advantages.
One advantage is that the motion of the Earth accounted for a wide variety of apparent motions of the Sun, stars, and the other planets. In this way, Copernicus was able to eliminate the “fine-tuning” assumed in the Ptolemaic theory, that the center of the epicycles of Mercury and Venus had to remain always on the line between the Earth and the Sun, and that the lines between Mars, Jupiter, and Saturn and the centers of their respective epicycles had to remain always parallel to the line between the Earth and the Sun. In consequence the revolution of the center of the epicycle of each inner planet around the Earth and the revolution of each outer planet by a full turn on its epicycle all had to be fine-tuned to take precisely one year. Copernicus saw that these unnatural requirements simply mirrored the fact that we view the solar system from a platform revolving about the Sun.
Another aesthetic advantage of the Copernican theory had to do with its greater definiteness regarding the sizes of planetary orbits. Recall that the apparent motion of the planets in Ptolemaic astronomy depends, not on the sizes of the epicycles and deferents, but only on the ratio of the radii of the epicycle and deferent for each planet. If one liked, one could even take the deferent of Mercury to be larger than the deferent of Saturn, as long as the size of Mercury’s epicycle was adjusted accordingly. Following the lead of Ptolemy in Planetary Hypotheses, astronomers customarily assigned sizes to the orbits, on the assumption that the maximum distance of one planet from the Earth equals the minimum distance from the Earth of the next planet outward. This fixed the relative sizes of planetary orbits for any given choice of the order of the planets going out from the Earth, but that choice was still quite arbitrary. In any case, the assumptions of Planetary Hypotheses were neither based on observation nor confirmed by observation.
In contrast, for the scheme of Copernicus to agree with observation, the radius of every planet’s orbit had to have a definite ratio to the radius of the Earth’s orbit.* Specifically, because of the difference in the way that Ptolemy had introduced epicycles for the inner and outer planets (and leaving aside complications associated with the ellipticity of the orbits), the ratio of the radii of the epicycles and deferents must equal the ratio of the distances from the Sun of the planets and Earth for the inner planets, and equal the inverse of this ratio for the outer planets. (See Technical Note 13.) Copernicus did not present his results this way; he gave them in terms of a complicated “triangulation scheme,” which conveyed a false impression that he was making new predictions confirmed by observation. But he did in fact get the right radii of planetary orbits. He found that going out from the Sun, the planets are in order Mercury, Venus, Earth, Mars, Jupiter, and Saturn; this is precisely the same as the order of their periods, which Copernicus estimated to be respectively 3 months, 9 months, 1 year, 2½ years, 12 years, and 30 years. Though there was as yet no theory that dictated the speeds of the planets in their orbits, it must have seemed to Copernicus evidence of cosmic order that the larger the orbit of a planet, the more slowly it moves around the Sun.4
The theory of Copernicus provides a classic example of how a theory can be selected on aesthetic criteria, with no experimental evidence that favors it over other theories. The case for the Copernican theory in the Commentariolus was simply that a great deal of what was peculiar about the Ptolemaic theory was explained at one blow by the revolution and rotation of the Earth, and that the Copernican theory was much more definite than the Ptolemaic theory about the order of the planets and the sizes of their orbits. Copernicus acknowledged that the idea of a moving Earth had long before been proposed by the Pythagoreans, but he also noted (correctly) that this idea had been “gratuitously asserted” by them, without arguments of the sort he himself was able to advance.
There was something else about the Ptolemaic theory that Copernicus did not like, besides its fine-tuning and its uncertainty regarding the sizes and order of planetary orbits. True to Plato’s dictum that planets move on circles at constant speed, Copernicus rejected Ptolemy’s use of devices like the equant to deal with the actual departures from circular motion at fixed speed. As had been done by Ibn al-Shatir, Copernicus instead introduced more epicycles: six for Mercury; three for the Moon; and four each for Venus, Mars, Jupiter, and Saturn. Here he made no improvement over the Almagest.
This work of Copernicus illustrates another recurrent theme in the history of physical science: a simple and beautiful theory that agrees pretty well with observation is often closer to the truth than a complicated ugly theory that agrees better with observation. The simplest realization of the general ideas of Copernicus would have been to give each planet including the Earth a circular orbit at constant speed with the Sun at the center of all orbits, and no epicycles anywhere. This would have agreed with the simplest version of Ptolemaic astronomy, with just one epicycle for each planet, none for the Sun and Moon, and no eccentrics or equants. It would not have precisely agreed with all observations, because planets move not on circles but on nearly circular ellipses; their speed is only approximately constant; and the Sun is not at the center of each ellipse but at a point a little off-center, known as the focus. (See Technical Note 18.) Copernicus could have done even better by following Ptolemy and introducing an eccentric and equant for each planetary orbit, but now also including the orbit of the Earth; the discrepancy with observation would then have been almost too small for astronomers of the time to measure.
There is an episode in the development of quantum mechanics that shows the importance of not worrying too much about small conflicts with observation. In 1925 Erwin Schrödinger worked out a method for calculating the energies of the states of the simplest atom, that of hydrogen. His results were in good agreement with the gross pattern of these energies, but the fine details of his result, which took into account the departures of the mechanics of special relativity from Newtonian mechanics, did not agree with the fine details of the measured energies. Schrödinger sat on his results for a while, until he wisely realized that getting the gross pattern of the energy levels was a significant accomplishment, well worth publishing, and that the correct treatment of relativistic effects could wait. It was provided a few years later by Paul Dirac.
In addition to numerous epicycles, there was another complication adopted by Copernicus, one similar to the eccentric of Ptolemaic astronomy. The center of the Earth’s orbit was taken to be, not the Sun, but a point at a relatively small distance from the Sun. These complications approximately accounted for various phenomena, such as the inequality of the seasons discovered by Euctemon, which are really consequences of the fact that the Sun is at the focus rather than the center of the Earth’s elliptical orbit, and the Earth’s speed in its orbit is not constant.
Another of the complications introduced by Copernicus was made necessary only by a misunderstanding. Copernicus seems to have thought that the revolution of the Earth around the Sun would give the axis of the Earth’s rotation each year a 360° turn around the direction perpendicular to the plane of the Earth’s orbit, somewhat as a finger at the end of the outstretched arm of a dancer executing a pirouette would undergo a 360° turn around the vertical direction f
or each rotation of the dancer. (He may have been influenced by the old idea that the planets ride on solid transparent spheres.) Of course, the direction of the Earth’s axis does not in fact change appreciably in the course of a year, so Copernicus was forced to give the Earth a third motion, in addition to its revolution around the Sun and its rotation around its axis, which would almost cancel this swiveling of its axis. Copernicus assumed that the cancellation would not be perfect, so that the Earth’s axis would swivel around over very many years, producing the slow precession of the equinoxes that had been discovered by Hipparchus. After Newton’s work it became clear that the revolution of the Earth around the Sun in fact has no influence on the direction of the Earth’s axis, aside from tiny effects due to the action of the gravity of the Sun and Moon on the Earth’s equatorial bulge, and so (as Kepler argued) no cancellation of the sort arranged by Copernicus is actually necessary.
With all these complications, the theory of Copernicus was still simpler than that of Ptolemy, but not dramatically so. Though Copernicus could not have known it, his theory would have been closer to the truth if he had not bothered with epicycles, and had left the small inaccuracies of the theory to be dealt with in the future.
The Commentariolus did not give much in the way of technical details. These were supplied in his great work De Revolutionibus Orbium Coelestium,5 commonly known as De Revolutionibus, finished in 1543 when Copernicus was on his deathbed. The book starts with a dedication to Alessandro Farnese, Pope Paul III. In it Copernicus raised again the old argument between the homocentric spheres of Aristotle and the eccentrics and epicycles of Ptolemy, pointing out that the former do not account for observations, while the latter “contradict the first principles of regularity of motion.” In support of his daring in suggesting a moving Earth, Copernicus quoted a paragraph of Plutarch:
Some think that the Earth remains at rest. But Philolaus the Pythagorean believes that, like the Sun and Moon, it revolves around the fire in an oblique circle. Heraclides of Pontus and Ecphantus the Pythagorean make the Earth move, not in a progressive motion, but like a wheel in a rotation from west to east about its own center.
(In the standard edition of De Revolutionibus Copernicus makes no mention of Aristarchus, but his name had appeared originally, and had then been struck out.) Copernicus went on to explain that since others had considered a moving Earth, he too should be permitted to test the idea. He then described his conclusion:
Having thus assumed the motions which I ascribe to the Earth later 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.
As in the Commentariolus, Copernicus was appealing to the fact that his theory was more predictive than Ptolemy’s; it dictated a unique order of planets and the sizes of their orbits required to account for observation, while Ptolemy’s theory left these undetermined. Of course, Copernicus had no way of confirming that his orbital radii were correct without assuming the truth of his theory; this had to wait for Galileo’s observations of planetary phases.
Most of De Revolutionibus is extremely technical, fleshing out the general ideas of the Commentariolus. One point worth special mention is that in Book 1 Copernicus states an a priori commitment to motion composed of circles. Thus Chapter 1 of Book I begins:
First of all, we must note that the universe is spherical. The reason is either that, of all forms, the sphere is the most perfect, needing no joint and being a complete whole, which can neither be increased nor diminished [here Copernicus sounds like Plato]; or that it is the most capacious of figures, best suited to enclose and retain all things [that is, it has the greatest volume for a given surface area]; or even that all the separate parts of the universe, I mean the Sun, Moon, planets and stars are seen to be of this shape [how could he know anything about the shape of the stars?]; or that wholes strive to be circumscribed by this boundary, as is apparent in drops of water and other fluid bodies when they seek to be self-contained [this is an effect of surface tension, which is irrelevant on the scale of planets]. Hence no one will question that the attribution of this form belongs to the divine bodies.
He then went on to explain in Chapter 4 that in consequence the movement of the heavenly bodies is “uniform, eternal, and circular, or compounded of circular motions.”
Later in Book 1, Copernicus pointed out one of the prettiest aspects of his heliocentric system: it explained why Mercury and Venus are never seen far in the sky from the Sun. For instance, the fact that Venus is never seen more than about 45° from the Sun is explained by the fact that its orbit around the Sun is about 70 percent the size of the orbit of the Earth. (See Technical Note 19.) As we saw in Chapter 11, in Ptolemy’s theory this had required fine-tuning the motion of Mercury and Venus so that the centers of their epicycles are always on the line between the Earth and the Sun. The system of Copernicus also made unnecessary Ptolemy’s fine-tuning of the motion of the outer planets, which kept the line between each planet and the center of its epicycle parallel to the line between the Earth and the Sun.
The Copernican system ran into opposition from religious leaders, beginning even before publication of De Revolutionibus. This conflict was exaggerated in a famous nineteenth-century polemic, A History of the Warfare of Science with Theology in Christendom by Cornell’s first president, Andrew Dickson White,6 which offers a number of unreliable quotations from Luther, Melanchthon, Calvin, and Wesley. But a conflict did exist. There is a record of Martin Luther’s conversations with his disciples at Wittenberg, known as Tischreden, or Table Talk.7 The entry for June 4, 1539, reads in part:
There was mention of a certain new astrologer who wanted to prove that the Earth moves and not the sky, the Sun, and the Moon. . . . [Luther remarked,] “So it goes now. Whoever wants to be clever must agree with nothing that others esteem. He must do something of his own. This is what that fool does who wishes to turn the whole of astronomy upside down. Even in these things that are thrown into disorder I believe in the Holy Scriptures, for Joshua commanded the Sun to stand still and not the Earth.”8
A few years after the publication of De Revolutionibus, Luther’s colleague Philipp Melanchthon (1497–1560) joined the attack on Copernicus, now citing Ecclesiastes 1:5—“The Sun also rises, and the Sun goes down, and hastens to his place where he rose.”
Conflicts with the literal text of the Bible would naturally raise problems for Protestantism, which had replaced the authority of the pope with that of Scripture. Beyond this, there was a potential problem for all religions: man’s home, the Earth, had been demoted to just one more planet among the other five.
Problems arose even with the printing of De Revolutionibus. Copernicus had sent his manuscript to a publisher in Nuremberg, and the publisher appointed as editor a Lutheran clergyman, Andreas Osiander, whose hobby was astronomy. Probably expressing his own views, Osiander added a preface that was thought to be by Copernicus until the substitution was unmasked in the following century by Kepler. In this preface Osiander had Copernicus disclaiming any intention to present the true nature of planetary orbits, as follows:9
For it is the duty of an astronomer to compose the history of the [apparent] celestial motions through careful and expert study. Then he must conceive and devise the causes of these motions or hypotheses about them. Since he cannot in any way attain to the true cause, he will adopt whatever suppositions enable the motions to be computed correctly from the principles of geometry for the future as well as for the past.
Osiander’s preface concludes:
So far as hypotheses are concerned, let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas
conceived for another purpose, and depart from this study a greater fool than when he entered it.
This was in line with the views of Geminus around 70 BC (quoted here in Chapter 8), but it was quite contrary to the evident intention of Copernicus, in both the Commentariolus and De Revolutionibus, to describe the actual constitution of what is now called the solar system.
Whatever individual clergymen may have thought about a heliocentric theory, there was no general Protestant effort to suppress the works of Copernicus. Nor did Catholic opposition to Copernicus become organized until the 1600s. The famous execution of Giordano Bruno by the Roman Inquisition in 1600 was not for his defense of Copernicus, but for heresy, of which (by the standards of the time) he was surely guilty. But as we will see, the Catholic church did in the seventeenth century put in place a very serious suppression of Copernican ideas.
What was really important for the future of science was the reception of Copernicus among his fellow astronomers. The first to be convinced by Copernicus was his sole pupil, Rheticus, who in 1540 published an account of the Copernican theory, and who in 1543 helped to get De Revolutionibus into the hands of the Nuremberg publisher. (Rheticus was initially supposed to supply the preface to De Revolutionibus, but when he left to take a position in Leipzig the task unfortunately fell to Osiander.) Rheticus had earlier assisted Melanchthon in making the University of Wittenberg a center of mathematical and astronomical studies.
The theory of Copernicus gained prestige from its use in 1551 by Erasmus Reinhold, under the sponsorship of the duke of Prussia, to compile a new set of astronomical tables, the Prutenic Tables, which allow one to calculate the location of planets in the zodiac at any given date. These were a distinct improvement over the previously used Alfonsine Tables, which had been constructed in Castile in 1275 at the court of Alfonso X. The improvement was in fact due, not to the superiority of the theory of Copernicus, but rather to the accumulation of new observations in the centuries between 1275 and 1551, and perhaps also to the fact that the greater simplicity of heliocentric theories makes calculations easier. Of course, adherents of a stationary Earth could argue that De Revolutionibus provided only a convenient scheme for calculation, not a true picture of the world. Indeed, the Prutenic Tables were used by the Jesuit astronomer and mathematician Christoph Clavius in the 1582 calendar reform under Pope Gregory XIII that gave us our modern Gregorian calendar, but Clavius never gave up his belief in a stationary Earth.
To Explain the World: The Discovery of Modern Science Page 16
