My rating: 4 of 5 stars
And though all these things are difficult, almost inconceivable, and quite contrary to the opinion of the multitude, nevertheless in what follows we will with God’s help make them clearer than day—at least for those who are not ignorant of the art of mathematics.
The Copernican Revolution has become the prime exemplar of all the great transformations in our knowledge of the world—a symbol of scientific advance, the paradigmatic clash of reason and religion, a shining illustration of how cold logic can beat out old prejudices. Yet reading this groundbreaking book immediately after attempting Ptolemy’s Almagest—the Bible of geocentric astronomy—reveals far more similarities than differences. Otto Neugebauer was correct in calling Copernicus’s system an ingenious modification of Hellenistic astronomy, for it must be read against the background of Ptolemy in order to grasp its significance.
The most famous section of De revolutionibus was, ironically, not even written by Copernicus, but by the presumptuous Andreas Osiander, a Lutheran theologian who was overseeing the publication of the book, and who included a short preface without consulting or informing Copernicus. Knowing that Copernicus’s hypothesis could prove controversial (Luther considered it heretical), Osiander attempted to minimize its danger by asserting that it was merely a way of calculating celestial positions and did not represent physical reality: “for it is not necessary that the hypotheses should be true, or even probable; but it is enough if they provide a calculation which fits the observations.”
Though this assertion obviously contradicts the body of the work (in which Copernicus argues at length for the reality of the earth’s movement), and though Copernicus and his friends were outraged by the insertion, it did help to shield the book from censure. And arguably Osiander was being a good and true Popperian—believing that science is concerned with making accurate predictions, not in giving us “the truth.” In any case, Osiander was no doubt correct in this assertion: “For it is sufficiently clear that this art is absolutely and profoundly ignorant of the causes of the apparent irregular movements.” Neither Ptolemy nor Copernicus had any coherent explanation of what caused the orbits of the planets, which would not come until Einstein.
After this little interpolation, Copernicus himself wastes no time in proclaiming the mobility of the earth. In retrospect, it is remarkable that it took such a long stretch of history for the heliocentric idea to emerge. For it instantly explains many phenomena which, in the Ptolemaic system, are completely baffling. Why do the inner planets (Venus and Mercury) move within a fixed distance of the sun? Why does the perigee (the closest point in the orbit) of the outer planets (Mars, Jupiter, Saturn) occur when they are at opposition (i.e., when they are opposite in the sky from the sun), and why does their apogee (the farthest point) occur when they are in conjunction (when they are hidden behind the sun)? And why do the planets sometimes appear to move backwards relative to the fixed stars?
But putting the earth in orbit between Venus and Mars neatly and instantly explains all of these mysteries. Mercury and Venus always appear a fixed distance from the sun because they are orbiting within the earth’s orbital circle, and thus from our position appear to go back and forth around the sun. Mars, Jupiter, and Saturn, by contrast, can appear at any longitudinal distance from the sun because their orbits are outsider ours; but if Mars’ orbit were tracked from Jupiter, for example, it would, like Venus and Mercury, appear to go back and forth around the sun. Also note that Mars will appear to go “backwards” from earth when earth overtakes the red planet, due to our planet’s shorter orbital period. And since Mars will be closest to us when it is on the same side of the sun as earth (opposition from the sun), and furthest from us when it is on far side of the sun (conjunction with the sun), this also explains the apogee and perigee positions of the outer planets.
This allows Copernicus to collapse five circles—one for each of the planets, which were needed in the Ptolemaic system to account for these anomalies—into one circle: namely, the earth’s orbit. The advantages are palpable.
Nevertheless, while I think the benefits of putting the planets in orbit around the sun are obvious, perhaps even to a traditionalist, it is not obvious why Copernicus should put the earth in motion around the sun rather than the reverse. Indeed, this is exactly what the eminent astronomer Tycho Brahe did, several generations later. For it makes no observational difference whether the sun or the earth is in motion. And in the Aristotelian physics of the time, the former solution makes a great deal more sense, since the heavens were supposed to be constituted of the lightest elements and the earth of the heaviest elements. So how could the heavy earth move so quickly? What is more, there is no concept of inertia or gravity in Aristotelian physics, and so no explanation for why people would not fly off the earth if it were in rapid motion.
Copernicus takes a brief stab at answering these obvious counterarguments, even offering a primitive notion of inertia: “As a matter of fact, when a ship floats on over a tranquil sea, all the things outside seem to the voyagers to be moving in a movement which is the image of their own, and they think on the contrary that they themselves and all the things with them are at rest.” Even so, it is obvious that such a brief example does not suffice to refute the entire Aristotelian system. Clearly, a whole new concept of physics was needed if the earth was to be in motion, one which did not arrive until Isaac Newton, born nearly two hundred years after Copernicus. It took a certain amount of boldness, or obtuseness, for Copernicus to proclaim the earth’s motion without at all being able to explain how the heaviest object in the universe—or so they believed—could hurtle through space.
In structure and content, De revolutionibus follows the Algamest pretty closely: beginning with mathematical preliminaries, onward to the orbits of the sun (or, in this case the earth), the moon, and the planets—with plenty of tables to aid calculation—as well as a description of his astronomical instruments and a chart of star locations, and finally ending with deviations in celestial latitude (how far the planets deviate north and south from the ecliptic in their orbits). Copernicus was even more wedded than Ptolemy to the belief that celestial objects travel in perfect circles, which leads him to repudiate Ptolemy’s use of the equant (the point around which a planet moves at a constant speed). The use of the equant upset Copernicus’s sense of elegance, you see, since its center is different from the planet’s actual center of orbit, thus requiring two overlapping circles.
Copernicus’s own solution was an epicyclet, which revolves twice westward (clockwise, from the celestial north pole) for each rotation eastward on the deferent. And so, ironically, though Ptolemy is sometimes mocked for using epicycles, Copernicus followed the same path. I also find it amusing that the combined effect of these circular motions, in both Ptolemy and Copernicus, added up to a non-circular orbit; clearly nature had different notions of elegance than these astronomers. In any case, it would have to wait until Kepler that it was realized that the planets actually follow an ellipse.
Perhaps the greatest irony is that Copernicus’s book is not any easier to use than Ptolemy’s as a recipe book for planetary positions. Now, it is far beyond my powers to even attempt such a calculation. But in his Very Short Introduction to Copernicus (which I recommend), Owen Gingerich takes the reader through the steps to calculation the position of Mars on Copernicus’s birthday: February 19, 1473. To do this you needed the radix, which is a root position of the planet recorded at a specified time; and you also need the planet’s orbital speed (the time needed for one complete orbit, in this case 687 days). The year must be converted into sexigesimal (base 60) system, and then converted in elapsed Egyptian years (which lack a leap year), in order to calculate the time elapsed since the date of the radix’s position (in this case is January 1st, 1 AD). Then this sexigesimal number can be looked up in Copernicus’s tables; but this only gives us the location of Mars with respect to the sun. To find out where it will appear in the sky, we also need the location of earth, which is another tedious process. You get the idea.
I read the bulk of this book while I was on vacation in rural Canada. Faced with the choice between relaxation or self-torture, I naturally chose the latter. While most of my time was spent scratching my head and helplessly scratching the page with a pencil, the experience was enough to show me—as if I needed more demonstration after Ptolemy—that astronomy is not for the faint of heart, but requires intelligence, patience, and care.
There was one advantage to reading the book on vacation. For it is the only time of year when I am in a place without light pollution. The stars, normally hiding behind street lights and apartment buildings, shone in the hundreds. I would have seen even more were it not for the waxing moon. But this did give me the opportunity to get out an old telescope—bought as a birthday present for a cousin, over a decade ago—and examine the moon’s pitted surface. It is humbling to think that even such basic technology was years ahead of Copernicus’s time.
Looking at the brilliant grey circle, surrounded by a halo of white light, I felt connected to the generations of curious souls who looked at the same moon and the same stars, searching for answers. So Copernicus did not, in other words, entirely spoil my vacation.