The System of the World Pythagoras vs Ptolemy, epicycles, ellipses, Copernicus, Tyco, Galileo, Gamow, Penzias, Wilson…

Anaximander was an early Greek scholar from one of the Greek cities on the coast of Asia Minor – he lived about 500 BCE.

Summer Solstice at Stonehenge

Stonehenge is an astronomical pointer built over many decades of observation

Eratosthenes was one of the great Greek philosophers. He lived in the Hellenic city of Alexandria about the year 200 BC and was Librarian of the great Library of Alexandria. A brilliant mathematician and geometer, he accurately calculated the circumference of the Earth and the tilt of the Earth’s axis, and may have calculated the distance to the sun (a scribe who copied his writings used an ambiguous phrase – either he got it right within 1% or was off by 50% depending on how you read the passage.)

Chapter 30.—Of the Perfection of the Number Six, Which is the First of the Numbers Which is Composed of Its Aliquot Parts. These works are recorded to have been completed in six days (the same day being six times repeated), because six is a perfect number,—not because God required a protracted time, as if He could not at once create all things, which then should mark the course of time by the movements proper to them, but because the perfection of the works was signified by the number six. For the number six is the first which is made up of its own parts, i.e., of its sixth, third, and half, which are respectively one, two, and three, and which make a total of six. In this way of looking at a number, those are said to be its parts which exactly divide it, as a half, a third, a fourth, or a fraction with any denominator, e.g., four is a part of nine, but not therefore an aliquot part; but one is, for it is the ninth part; and three is, for it is the third. Yet these two parts, the ninth and the third, or one and three, are far from making its whole sum of nine. So again, in the number ten, four is a part, yet does not divide it; but one is an aliquot part, for it is a tenth; so it has a fifth, which is two; and a half, which is five. But these three parts, a tenth, a fifth, and a half, or one, two, and five, added together, do not make ten, but eight. Of the number twelve, again, the parts added together exceed the whole; for it has a twelfth, that is, one; a sixth, or two; a fourth, which is three; a third, which is four; and a half, which is six. But one, two, three, four, and six make up, not twelve, but more, viz., sixteen. So much I have thought fit to state for the sake of illustrating the perfection of the number six, which is, as I said, the first which is exactly made up of its own parts added together; and in this number of days God finished His work. And, therefore, we must not despise the science of numbers, which, in many passages of holyScripture, is found to be of eminent service to the careful interpreter. Neither has it been without reason numbered among God's praises, "You have ordered all things in number, and measure, and weight.” City of God – Book IX, Chapter 30 St Augustine of Hippo, about 400 AD

Usually, even a non-Christian knows something about the earth, the heavens, and the other elements of this world, about the motion and orbit of the stars and even their size and relative positions, about the predictable eclipses of the sun and moon, the cycles of the years and the seasons, about the kinds of animals, shrubs, stones, and so forth, and this knowledge he hold to as being certain from reason and experience. Now, it is a disgraceful and dangerous thing for an infidel to hear a Christian, presumably giving the meaning of Holy Scripture, talking nonsense on these topics; and we should take all means to prevent such an embarrassing situation, in which people show up vast ignorance in a Christian and laugh it to scorn. The shame is not so much that an ignorant individual is derided, but that people outside the household of faith think our sacred writers held such opinions, and, to the great loss of those for whose salvation we toil, the writers of our Scripture are criticized and rejected as unlearned men. If they find a Christian mistaken in a field which they themselves know well and hear him maintaining his foolish opinions about our books, how are they going to believe those books in matters concerning the resurrection of the dead, the hope of eternal life, and the kingdom of heaven, when they think their pages are full of falsehoods and on facts which they themselves have learnt from experience and the light of reason? Reckless and incompetent expounders of Holy Scripture bring untold trouble and sorrow on their wiser brethren when they are caught in one of their mischievous false opinions and are taken to task by those who are not bound by the authority of our sacred books. For then, to defend their utterly foolish and obviously untrue statements, they will try to call upon Holy Scripture for proof and even recite from memory many passages which they think support their position, although they understand neither what they say nor the things about which they make assertion. St Augustine, about 400 AD De Genesi ad litteram libri duodecim, translation by J. H. Taylor in Ancient Christian Writers, Newman Press, 1982, volume 41. “I desire to know two things only: God and the soul. And nothing more? Absolutely nothing at all.” St Augustine Soliliquies about 400 AD

Cosmas Indicopleus was a Christian scholar who lived in the 6 th Century after Christ. He rejected the use of empirical data, but believe that our knowledge of the world should come from Christian religious texts, i.e. the Bible. His reading of the Bible convinced him that the Earth was in this form.

Onservable facts: The sun rises in the East and sets in the west. The position of the sunrise varies during the year, further north in the Northern Summer until the Solstice, then further south until the Winter Solstice. On the day of the Equinox, the sun rises in the East for everyone on Earth.

Observable Facts: The moon rises about an hour earlier each day, completing a cycle in about 28 days. When the moon is waning (decreasing), it rises before the sun. As it gets closer and closer to ‘new’ moon, when it is invisible from Earth, it is also growing closer and closer to being in line with the sun. When the moon is waxing (growing larger) it is rising after the sun, so as it grows from ‘new’ to ‘full’ it is rising just after the sun, then further and further after, until it is on the opposite side of the Earth from the sun, setting as the sun is rising.

Observable Facts: In the minds of many intelligent medieval people, the ‘fixed stars’ were believed to be lights stuck in permanent positions in a solid crystal bowl – the firmament – which rotated as a whole over the world, completing a rotation each year. The firmament was quite far above the world. Beyond the firmament was, well, that’s a little vague – heaven? God? ( ps the woodcut on the previous slide is not medieval, but was done in imitation of medieval style for the French historian Flammarion in the 1880s. ) Even right up to modern times, no telescope could resolve the stars into anything but points of light. So they seemed to be tiny (singularities?) and were clearly far away. They moved completely predictably and did not change their relative positions. So, they are a mystery.

Observable Facts: But, some stars did NOT maintain permanent positions compared to other stars - these were seen to change their positions in a predictable, but rather odd way. The ancient Greeks called them ‘planetes’ meaning ‘wanderers.’ The path that planets followed in the sky is known as “apparent retrograde motion.” and it is a big problem if you are trying to explain the System of the World.

Observable Facts: The planets move in relationship to the fixed stars. They move Eastward. That means that over time, a planet will be to the westward of one of the fixed stars, and after a while it will move so that it is to the east, and gradually the planets move entirely around the entire circle of the sky from one constellation of fixed starts to the next most eastward one, and then to the next, and the next. Some planets move quite rapidly around the sky to complete this cycle, and others move more slowly. The real puzzler, though, is retrograde motion – the planets appear to move eastward against the stars, and then periodically they reverse and move westward for a while! What the hey!!!!

Observable Facts If you traced the progress of a planet across the sky relative to the fixed stars, the tracing you would get would look like this: Wo!

Retrograde motion of Mars Oct 1996 to July 1997 from website of Dr Ted Snow, Univ of Colorado – Boulder Link to animation of Mars retrograde motion Alternative Link to Original Animation at U Colorado

So, any System of the World that you want to use to explain how the Earth and planets operate, will have to account for all these facts… 1.Sun motion 2.Moon motion 3.Fixed stars 4.Planet motion, especially, apparent retrograde motion 5.And also, the relative sizes and distances of the different elements. 6.And, possibly, a cosmography of the way in which the elements came into existence and came into the relationship with each other that we observe. But I think the really tough one to explain is the retrograde motion…. If planets are big rocky items, how can they stop, go backwards, and then go forward again???

Ptolemy’s explanation works like this…

Geocentric model of retrograde motion using epicycles

If you are not too particular, and don’t care about long term results, then Ptolemy’s model is good enough. It predicts what will happen with a certain degree of accuracy. But, if you need better accuracy, and you want to predict the motion of the planets over long time periods, then there are a lot of problems that show up… these were blamed on faulty observations. To work things out and really figure out what’s going on, you need a set of very good observations of the movement of the stars and planets. That was done by Tyco Brahe.

Tyco and Kepler Tyco Brahe was born in Denmark/Sweden in 1546 to an important political family. He was raised by an uncle who was an Admiral and an important advisor to the king. In 1560 there was a predicted eclipse of the Sun. The 13 year old Tyco was stunned by the idea that events such as this could be predicted - just three months later on Nov 30 he bought a copy of Ptolemy’s Almagest at the local bookseller’s for $2 (and wrote the price and date on the flyleaf.) He began studying astronomy but soon found that things were not as solid as he had believed. He noted several astronomical events where the predictions were off by days, or even in one important case, by a whole month. He decided to dedicate his life to getting the best possible observations over a long period of time. After a long complicated life, he settled down on a small island, Hveen, near Copenhagen. There he carried out 20 years of observations including very accurate observations of the planets and sun, and a series of comet observations that were a big breakthrough. Since telescopes hadnt been invented, all the observations were made with naked eye observations using large scale instruments that he designed himself. Tyco’s work really wasn’t completed until he began work with a brilliant young mathematician, Johannes Kepler. The younger man used Tyco’s painstaking calculations to work out the exact way in which the planets moved around the Sun – in elliptical orbits with the Sun at one of the foci of the ellipse. This was the resolution of the whole planet problem and convincingly completed the arguments which Copernicus had raised many years earlier in favor of a Heliocentric System of the World.

How retrograde motion works in a Sun centered System of the World link to Animation of Earth and Mars motion around the sun from U Colorado

Sidereus Nuncius 1610 “The Starry Messenger” In which Galileo recounts how he heard about the telescope, built his own, and began his observations.

SIDEREAL MESSENGER unfolding great and very wonderful sights and displaying to the gaze of everyone, but especially philosophers and astronomers, the things that were observed by GALILEO GALILEI, Florentine patrician and public mathematician of the University of Padua, with the help of a spyglass lately devised by him, about the face of the Moon, countless fixed stars, the Milky Way, nebulous stars, but especially about four planets flying around the star of Jupiter at unequal intervals and periods with wonderful swiftness; which, unknown by anyone until this day, the first author detected recently and decided to name MEDICEAN STARS (trans. A. van Helden, p. [26])

(Summary by D.C. Toedt )

It was the “afterglow” of microwave radiation that Penzias and Wilson found, as described in the Bryson chapter. They shared the Nobel Prize in George Gamow would probably have received a portion of the prize as well, but he had died some years earlier and Nobel Prizes are only given to living researchers.