To Explain the World: The Discovery of Modern Science (22 page)

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 for 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: