In today’s blog we talk to Dr. Andre’ Goddu, PhD in history from the University of California Los Angeles, Professor of History and Philosophy of Science in the Department of Physics and Astronomy at Stonehill College, on when and why heliocentrism was accepted.

**David**: Is there a clear line that can be drawn connecting Copernicus’s mathematical constructs in De revolutionibus to scholars that came before him?

**Andre’**: Copernicus's mathematics is nearly identical to Ptolemy's: the axiom of uniform circular motions; the use of eccentric and epicycle models. There are some scholars who believe that Copernicus copied models from Islamic authors (these involve double-epicycle devices, the use of rotating spheres to account for the motion of the center of a circle on a straight line as in his Mercury model and also in precession of the equinoxes), but so far no one has found a sketch that he could have copied. It seems likelier that he heard about these devices and may have been familiar with only verbal descriptions of them. In any case, he adapted the ideas concerning these models for his heliocentric or rather heliostatic models. Copernicus also seems to have known of tables for the latitudes of planets devised by Giovanni Bianchini, some of which are decimal trigonometric tables. He may also have been familiar with the trigonometry of an Arabic author, Geber ibn Afflah. It is by and large Polish scholars familiar with the teaching of astronomy at Cracow in the 15th century who have discovered and published this material. In short, all of his mathematics was derivative, and I can't think of anything in his mathematics that anyone today considers his original creation except for the adaptation of basically geocentric mathematics to a heliostatic arrangement.

**David**: Given that the circle is a special case of a conic section, did Copernicus or other thinkers prior to him consider conic sections in trying to fit the data?

**Andre’**: Authors had some familiarity with conic sections, but to my knowledge no one prior to Kepler came to the realization that an eccentric point was the focus of an ellipse, and it took even Kepler quite some time to realize it himself. Everyone was obsessed with circles for a variety of reasons: perfection of the circle, the belief that celestial bodies move uniformly, and for those who thought the planets were attached to spheres (like Copernicus) there were additional physical or mechanical reasons for thinking that the planets moved uniformly.

The fact that observation of non-uniform motion of planets was anomalous did not lead them to reject the belief but rather to construct eccentric models, and, then, in the cases of the Moon and planets to suppose (as Ptolemy did) that there was yet a third point (the so-called equant) around which a body moved uniformly. Several Arabic authors criticized Ptolemy's solution as a violation of the principle of uniform, circular motion, and they devised other geocentric models (double epicycles) to replace the equant model. Now Copernicus himself testified that it was the equant model that first led him to question Ptolemy's solutions, but because Copernicus's models actually have an equant point (hidden in his models), then most scholars do not think that his criticism of the model led him to heliocentrism.

It is my view that in his first heliocentric system, Copernicus realized that not only the equant but also the eccentric was illegitimate. He knew, however, that the annual motion of the Sun was non-uniform (unequal length of time from vernal to autumnal equinox and from autumnal equinox to vernal equinox), so this would require finding a single center for the motions of the planets. I suspect at this point that he speculated if the Earth moved around an eccentric point, then all the remaining planets could be centered on Earth's eccentric point. In other words, he arrived at a quasi-homocentric (a common center of motion) arrangement. But this required him to put all the planets on double epicycles, just like his lunar model.

Some years later (probably between 1512 and 1523) he realized that he could not eliminate eccentrics from the planetary models, restored eccentrics, and modified his epicycle models. He retained Earth's annual motion probably because of a number of results that I will describe in answering your next question. He eliminated the double epicycles (except from the lunar model), reduced the sizes of the epicycles, and eliminated them with some compensating models for Mercury and Venus. Notice here that with Venus and Mercury between Sun and Earth, there was no reason for them to be on epicycles to account for bounded elongation. Nevertheless, he still had to resort to a kind of double eccentric model (eccentreccentric) to make the models work, and there were other problems with Mercury that complicated that model even more.

**David**: Is it fair to conclude that since the heliocentric model did little to improve the match between theory and observations, Copernicus based his worldview on intuition? Given the revolution in science he inspired, is this not a lesson for modern times in which intuition is often discouraged in science?

**Andre’**: Copernicus based his worldview on a number of assumptions. First, he believed that the universe is a whole, finite sphere. (I know that absence of parallax suggests an infinite or at least indefinite universe, and Copernicus leaves the question with respect to 'heaven' open, but he otherwise referred to a stationary sphere of stars and a stationary Sun as the center of the universe). Second, he rejected Aristotle's arguments about a central Earth as fallacious. Aristotle argued from a part (Earth) to the whole (the universe), but Copernicus relied on a logical doctrine in this case that argued from the whole to the part. If a house exists, then we may infer the existence of a wall. But from the existence of a wall, we cannot validly infer the existence of the house. Suppose a case where only a wall is left standing. So, in effect, Copernicus claimed that we first had to know the structure of the whole before we could decide on the existence and location of a part.

I think that you could call that an intuition, but it is one that is dependent on a critique and a form of logical argumentation that was well known to him as a student in Cracow. But I suspect that he developed such an argument after he arrived at his theory. As I mentioned above he criticized Ptolemy on the equant model. He also objected to a feature of geocentrism that had never been resolved. Geocentrists could not agree on the linear order of the planets. To Copernicus this was a major flaw. Most followed Ptolemy, but for arbitrary reasons: the symmetry between superior planets and inferior planets including the Moon with the Sun in the middle of that arrangement, moving around a central Earth. After he came up with the idea of a single eccentric for Earth with all planets including Earth moving around that center, then the ordering of the planets became clear along with an explanation for bounded elongation and for the observation of retrograde planetary motions. Even though he modified those solutions later, those results, I believe, convinced him that he must be right. And so, when he realized that he could not eliminate eccentrics, he did not return to a geocentric arrangement, but revised his first theory.

I would be inclined to agree that intuition should not be overlooked, but clearly this calls for an elaboration of what intuition is and how it works. I imagine that there is a lot of psychological literature on the topic, and I don't know whether you have engaged with it. It's surely a daunting topic in itself.

**David**: How do we understand the relatively quick acceptance of heliocentrism post 1550 compared to previous attempts at heliocentrism dating back over one thousand years?

**Andre’**: Because of several circumstances after 1550, heliocentrism became accepted gradually. Without putting these in any particular order, we have to consider the following: Osiander's "letter to the Reader" at the very beginning of De revolutionibus caused a lot of confusion. For a long time many people thought that Copernicus himself had written it, which in turn encouraged some people to study his mathematics and adapt it to their geocentric solutions. The tables generated were somewhat better than earlier ones, and the sense that more accurate observations were needed became more pressing. These are perhaps negative reasons, if you will, that is, reasons why heliocentrism was not condemned altogether and completely rejected.

The early critiques of Copernicus by theologians and philosophers did not lead to official condemnations, so there was a kind of toleration for Copernicus's ingenuity even as nearly everyone rejected the theories about Earth's motions. Then there is the fact that with Copernicus we had a more or less completely worked out heliocentric system, albeit one that in a way remained geocentric, that is, it retained residues of Ptolemaic geocentrism, so it could be looked on as a kind of reform of Ptolemy. There were, as you know, heliocentric ideas and theories but no complete version with models.

Copernicus's solution to the problem of linear planetary ordering according to sidereal periods, explanations of bounded elongation and retrograde motion, along with his criticisms of Ptolemy and geocentrists and his questions about Aristotle were almost certainly the features that impressed the few who did follow him, accept him, or try to improve on what he had started.

It is virtually certain that Galileo was convinced by the results mentioned above along with Galileo's criticisms of Aristotle, especially in his analysis of falling bodies. Galileo understood that it required an enormous exercise of imagination to change one's perspective from stationary to moving. Galileo fundamentally questioned the Aristotelian assumption that we can arrive at an understanding of nature through simple observation on the further assumption that since we negotiate our way through the world so successfully then it follows that nature is not constructed so as to deceive us and mislead us. Now everyone was familiar with sensory deception, but these illusions were almost all easily explicable. Here, at last, was a theory where we could not rely on ordinary experience but had to imagine ourselves in a situation that generated exactly the same observational experience.

It is striking as well how clearly Galileo understood the mathematics of conic sections in his analysis of falling and projectile bodies. But, amazingly, he too was obsessed with circles in the heavens, and either rejected Kepler's solution or perhaps could never bring himself to consider heavenly motions as anything other than circular.

Perhaps what I've collected here were reasons not to accept heliocentrism, yet most astronomers did not reject Copernicus's work or book altogether. Their allowance of it to the extent that Copernicus's book and theories were taught and discussed meant that it did not fall by the wayside but survived long enough to persuade others of its achievements, the results again that I mentioned above.

**David**: Thank you Professor!

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