12.1: Cosmological Models

orbits

Figure 141: The Ptolemaic geocentric model with epicycles that su ced to explain the observational data of retrograde motion. The Copernican geocentric model also explained the data and was somewhat simpler. To determine which was correct required the use of parallax to determine distances as well as angles.

Early western (Greek) cosmology was both geocentric, with fixed stars “lamps” or “windows” on a big solid bowl, the moon and sun and planets orbiting a fixed, stationary Earth in the center. Plato represented the Earth (approximately correctly) as a sphere and located it at the center of the Universe. Astronomical objects were located on transparent “spheres” (or circles) that rotated uniformly around the Earth at di erential rates. Euxodus and then Aristotle (both students of Plato) elaborated on Plato’s original highly idealized description, adding spheres until the model “worked” to some extent, but left a number of phenomena either unexplained or (in the case of e.g. lunar phases) not particularly believably explained.

The principle failure of the Aristotelian geocentric model is that it fails to explain retrograde motion of the planets, where for a time they seem to go backwards against the fixed stars in their general orbits. However, in the second century Claudius Ptolemaeus constructed a somewhat simpler geocentric model that is currently known as the Ptolemaic model that still involved Plato’s circular orbits with stars embedded on an outer revolving sphere, but added to this the notion of epicycles – planets orbiting in circles around a point that was itself in a circular orbit around the Earth. The model was very complex, but it actually explained the observational data including retrograde motion well enough that – for a variety of political, psychological, and religious reasons – it was adopted as the “o cial” cosmology of Western Civilization, endorsed and turned into canonical dogma by the Catholic Church as geocentrism agreed (more or less) with the cosmological assertions of the Bible.

In this original period – during which the Greeks invented things like mathematics and philosophy and the earliest rudiments of physics – geocentrism was not the only model. The Pythogoreans, for example, postulated that the earth orbited a “great circle of fire” that was always beneath one’s feet in a flat-earth model, while the sun, stars, moon and so on orbited the whole thing. An “anti-Earth” was supposed to orbit on the far side of the great fire, where we cannot see it. All one can say is gee, they must have had really good recreational/religious hallucinogenic drugs back then...212. Another

212Which in fact, they did...

be true on observational grounds.

Galileo’s telescope – which was little more powerful than an ordinary pair of hand-held binoculars today – was su cient to provide that proof. Galileo’s instrument clearly revealed that the moon was a planetoid object, a truly massive ball of rock that orbited the Earth, so large that it had its own mountains and “seas”. It revealed that Jupiter had not one, but four similar moons of its own that orbited it in similar manner (moons named “The Galilean Moons” in his honor). He observed the phases of Venus as it orbited the sun, and correctly interpreted this as positive evidence that Venus, too, was a huge world orbiting the sun as the Earth orbits the sun while revolving and being orbited by its own moon. He was one of the first individuals in modern times to observe sunspots (although he incorrectly interpreted them as Mercury in transit across the Sun) and set the stage for centuries of solar astronomical observations and sunspot counts that date from roughly this time. His (independent) observations on gravity even helped inspire Newton to develop gravity as the universal cause of the observed orbital motions.

However, the publication of his own observations defending Copernicus corresponded almost exactly with the Church finally taking action to condemn the work of Copernicus and ban his book describing the model. In 1600 the Roman Inquisition had found Catholic priest, freethinker, and philosopher Giordano Bruno217 guilty of heresy and burned him at the stake, establishing a dangerous precedent that put a damper on the development of science everywhere that the Roman church held sway.

Bruno not only embraced the Copernican theory, he went far beyond it, recognizing that the Sun is a star like other stars, that there were far, far more stars than the human eye could see without help, and he even asserted that many of those stars have planets like the Earth and that those planets were likely to be inhabited by intelligent beings. While Galileo was aided in his assertions by the use of the telescope, Bruno’s were all the more remarkable because they preceded the invention of the telescope. Note well that the human eye can only make out some 3500 stars altogether unaided on the darkest, clearest nights. This leap from 3500 to “infinity”, and the other inferences he made to accompany them, were quite extraordinary. His guess that the stars are e ectively numberless was validated shortly afterwards by means of the very first telescopes, which revealed more and more stars in the gaps between the visible stars as the power of the telescopes was systematically increased.

We only discovered positive evidence of the first confirmed exoplanet218 in 1988 and are still in the process of searching for evidence that might yet validate his further hypothesis of life spread throughout the Universe, some of it (other than our own) intelligent. Galileo had written a letter to Kepler in 1597, a mere three years before Bruno’s ritualized murder, stating his belief in the Copernican system (which was not, however, the direct cause of Bruno’s conviction for heresy). The stakes were indeed high, and piled higher still with wood.

Against this background, Galileo developed a careful and observationally supported argument in favor of the Copernican model and began cautiously to publish it within the limited circles of philosophical discourse available at the time, proposing it as a “theory” only, but arguing that it did not contradict the Bible. This finally attracted the attention of the church. Cardinal and Saint Robert Bellarmine wrote a famous letter to Galileo in 1615219 explaining the Church’s position on the matter. This letter should be required reading for all students, and since if you are reading this textbook you are, in a manner of speaking, my student, please indulge me by taking a moment and following the link to read the letter and some of the commentary following.

In it Bellarmine makes the following points:

217Wikipedia: http://www.wikipedia.org/wiki/Giordano Bruno. Bruno is, sadly, almost unknown as a philosopher and early scientist for all that he was braver and more honest in his martyrdom that Galileo in his capitulation.

218Wikipedia: http://www.wikipedia.org/wiki/Extrasolar planet. As of today, some 851 planets in 670 systems have

been discovered, with more being discovered almost every day using a dazzling array of sophisticated techniques. 219http://www.fordham.edu/halsall/mod/1615bellarmine-letter.asp

•If Copernicus (and Galileo, defending Copernicus and advancing the theory in his own right) are correct, the heliocentric model “is a very dangerous thing, not only by irritating all the philosophers and scholastic theologians, but also by injuring our holy faith and rendering the Holy Scriptures false.”

In other words, if Galileo is correct, the holy scriptures are incorrect. Bellarmine correctly infers that this would reduce the degree of belief in the infallibility of the holy scriptures and hence the entire basis of belief in the religion they describe.

•Furthermore, Bellarmine continues, Galileo is disagreeing with established authorities with his hypothesis, who “...all agree in explaining literally (ad litteram) that the sun is in the heavens and moves swiftly around the earth, and that the earth is far from the heavens and stands immobile in the center of the universe. Now consider whether in all prudence the Church could encourage giving to Scripture a sense contrary to the holy Fathers and all the Latin and Greek commentators. Nor may it be answered that this is not a matter of faith, for if it is not a matter of faith from the point of view of the subject matter, it is on the part of the ones who have spoken.”

•Finally, Bellarmine concludes that “if there were a true demonstration that the sun was in the center of the universe and the earth in the third sphere, and that the sun did not travel around the earth but the earth circled the sun, then it would be necessary to proceed with great caution in explaining the passages of Scripture which seemed contrary, and we would rather have to say that we did not understand them than to say that something was false which has been demonstrated.” He goes on to assert that “the words ’the sun also riseth and the sun goeth down, and hasteneth to the place where he ariseth, etc.’ were those of Solomon, who not only spoke by divine inspiration but was a man wise above all others and most learned in human sciences and in the knowledge of all created things, and his wisdom was from God.”

Interested students are invited to play Logical Fallacy Bingo220 with the text of the entire document. Opinion as fact, appeal to consequences, wishful thinking, appeal to tradition, historian’s fallacy, argumentum ad populum, thought-terminating cliche, and more. The argument of Bellarmine boils down to the following:

•If the heliocentric model is true, the Bible is false where that model contradicts it.

•If the Bible is false anywhere, it cannot be trusted everywhere and Christianity itself can legitimately be doubted.

•The Bible and Christianity are true. Even if they appear to be false they are still true, but don’t worry, they don’t even appear to be false.

•Therefore, while it is all very well to show how a heliocentric model could mathematically, or hypothetically explain the observational data, it must be false.

In 1633, this same Bellarmine (later made into a saint of the church) prosecuted Galileo in the Inquisition. Galileo was found “vehemently suspect of heresy” for precisely the reasons laid out in Bellarmine’s original letter to Galileo. He was forced to publicly recant, his book laying out the reasons for believing the Copernican model was added along with the book of Copernicus to the list of banned books, and he was sentenced to live out his life under house arrest, praying all day for forgiveness. He died in 1642 a broken man, his prodigious and productive mind silenced by the active defenses of the locally dominant religious mythology for almost ten years.

I was fortunate enough to be teaching gravitation in the classroom on October 31, 1992, when Pope John Paul II (finally) publicly apologized for how the entire Galileo a air was handled. On

220http://lifesnow.com/bingo/ http://lifesnow.com/bingo/

Galileo’s behalf, I accepted the apology, but of course I must also point out that Bellarmine’s argument is essentially correct. The conclusions of modern science have, almost without exception, contradicted the assertions made in the holy scriptures not just of Christianity but of all faiths. They therefore stand as direct evidence that those scriptures are not, in fact, divinely inspired or perfect truth, at least where we can check them. While this does not prove that they are incorrect in other claims made elsewhere, it certainly and legitimately makes them less plausible.

12.2: Kepler’s Laws

Galileo was not, in fact, the person who made the greatest contributions to the rejection of the Ptolemaic model as the first step towards first the (better) heliocentric Copernican model, then to the invention of physics and science as a systematic methodology for successively improving our beliefs about the Universe that does not depend on authority or scripture. He wasn’t even one of the top two. Let’s put him in the third position and count up to number one.

The person in the second position (in my opinion, anyway) was Tycho Brahe221 , a wealthy Danish nobleman who in 1571, upon the death of his father, established an observatory and laboratory equipped with the most modern of contemporary instrumentation in an abbey near his ancestral castle. He then proceeded to spend a substantial fraction of his life, including countless long Danish winter nights, making and recording systematic observations of the night sky!

His observations bore almost immediate fruit. In 1572 he observed a supernova in the constellation Cassiopeia. This one observation refuted a major tenet of Aristotelian and Church philosophy

– that the Universe beyond the Moon’s orbit was immutable. A new star had appeared where none was observed before. However, his most important contributions were immense tables of very precise measurements of the locations of objects visible in the night sky, over time. This was in no small part because his own hybrid model for a mixture of Copernican and Ptolemaic motion proved utterly incorrect.

If you are a wealthy nobleman with a hobby who is generating a huge pile of data but who also has no particular mathematical skill, what are you going to do? You hire a lab rat, a flunky, an assistant who can do the annoying and tedious work of analyzing your data while you continue to have the pleasure of accumulating still more. And as has been the case many a time, the servant exceeds the master. The number one philosopher who contributed to the Copernican revolution, more important than Brahe, Bruno, Galileo, or indeed any natural philosopher before Newton was Brahe’s assistant, Johannes Kepler 222 .

Kepler was a brilliant young man who sought geometric order in the motions of the stars and planets. He was also a protestant living surrounded by Catholics in predominantly Catholic central Europe and was persecuted for his religious beliefs, which had a distinctly negative impact on his professional career. In 1600 he came to the attention of Tycho Brahe, who was building a new observatory near Prague. Brahe was impressed with the young man, and gave him access to his closely guarded data on the orbit of Mars and attempted to recruit him to work for him. Although he was was trying hard to be appointed as the mathematician of Archiduke Ferdinand, his religious and political a lations worked against him and he was forced to flee from Graz to Prague in 1601, where Brahe supported him for a full year until Brahe’s untimely death (either from possibly deliberate mercury poisoning or a bladder that ruptured from enforced continence at a state banquet – it isn’t clear which even today). With Brahe’s support, Kepler was appointed an Imperial mathematician and “inherited” at least the use of Brahe’s voluminous data. For the next eleven years he put it to very good use.

Although he was largely ignored by contemporaries Galileo and Descartes, Kepler’s work laid, as

221Wikipedia: http://www.wikipedia.org/wiki/Tycho Brahe.

222Wikipedia: http://www.wikipedia.org/wiki/Johannes Kepler.