Thursday Evening Astronomy Lecture, 9/15/05 Summary of the Apparent Motion of the Planets The Ptolemaic (Geocentric) Model Weaknesses of the Ptolemaic Model Copernicus’ Innovation Examples of the Predictive Power of the Copernican Model Weakness of the Copernican Model Red Sections are not yet completed.

Summary of the Apparent Motion of the Planets Planet Time to Cycle Zodiac Elongation Restrictions Retrograde Periodicity Angular distance behind the Stars per Day Moon27.3 daysNoneNever 13  Sun daysNoneNever 0.98  Mercury days 28  Max. Elong. 116 days 0.98  avg Venus days 45  Max. Elong. 584 days 0.98  avg Mars687 daysNone, Brightest at Opp.780 days 0.52  avg Jupiter  12 years None, Brightest at Opp.399 days 0.08  avg Saturn  29 years None, Brightest at Opp.378 days 0.03  avg The properties of the planets listed above, that we have studied for the last few weeks, must be part of any model that explains their apparent motion. We will first review the Aristotelian/Ptolemaic Model of the Univerese.

The sketch to the right illustrates the basic model of the Universe as envisioned by Aristotle. The outer sphere is the celestial sphere that carries the stars and is the home of the gods. Within this stellar sphere, the planets are located on concentric nested spheres centered on the Earth. How was the order of the planets determined?

Aristotle set the order of the planets using the apparent sidereal periods (Time to cycle to the Zodiac.) Notice that Saturn the planet farthest from the Earth is the one with the longest time period to cycle the zodiac. Which of the planets is missing on this diagram?

Ptolemy (See the Monday Class notes for his history) devised a geocentric model of the Universe which closely followed the principles of Aristotle. In particular, Ptolemy devised a clever model where by the planets moved at constant speed on perfect circles as Aristotle required, but they moved on two circles simultaneously; the smaller epicycle carried the planet and the center of the epicycle followed the deferent each at a constant rate. This simple model was too simple to explain the variable and complex motions of the real planets. To try to improve the fit to the positions of the planets, many complications had been added

Astronomers had moved the earth slightly off the center of the solar system to avoid needing have the planets move at varying speeds along their orbits. had used a different type of epicycle to explain the motions of Mercury and Venus than were used for Mars, Jupiter, and Saturn. The model got extremely complex for Mercury (and Mars). The figure to the right shows Mercury riding on an epicycle on an epicycle on an epicycle with constant speed measured from a point well off-center! (From Scientific American)

The following excerpt from John Milton’s Paradise Lost expresses the degree of complexity that the Ptolemaic model grew to just prior to its rejection by Copernicus. “Hereafter, when they come to model Heav'n, And calculate the Stars, How will they wield The mighty frame, how build, unbuild, contrive, To save appearances, how grid the Sphere With Centric and Eccentric scribbl'd o'er, Cycle and Epicycle, Orb in Orb.”

Problems with the Copernican Model 1.No Proof that the Earth moved. Scientists and philosophers of the time argued that Copernicus’ proposal that Earth moved was as ridiculous as a person on a ship proposing that it was the ocean, and not the ship, that moved. No one could believe a mass as large as the Earth could move as Copernicus proposed. A simple calculation using the radius of the Earth (6,378 km) and the approximate rotation period of the Earth (24 hours), indicates that a person on the Earth’s equator is in fact moving at 1,670 km/hr or about 1,000 mph. This high a velocity without visual effects like the blowing down of buildings was unbelievable at that time. In addition, in the Old Testament book of Joshua (10:13) scripture seemed to clearly indicate that the Sun moved, not the Earth, as inferred from this description of God’s intervention in Israel’s battle against the Amorites “And the sun stood still, and the moon stayed... So the sun stood still in the midst of heaven, and hasted not to go down about a whole day.” 2.No mechanism by which the planets (Earth included) maintained a circular motion around the Sun. Aristotelian philosophers argued that the Earth was at rest in the center of the Universe because of it’s “heaviness” drew it there. There was no physical theory that could account for the Earth being maintained in constant circular motion away from this special location (the center). The concept of gravity did not exist at this time nor would it for another 100 years.

Problems with the Copernican Model 3. Challenged Deeply Held religious beliefs. Kuhn wonderfully describes the impact of the Copernican model in his work The Copernican Revolution. I quote from Kuhn directly. “ When taken seriously, Copernicus’s proposal raised many gigantic problems for the believing Christian. If, for example, the Earth were merely one of six planets, how were the stories of the Fall and of the Salvation, with their immense bearing on Christian life, to be preserved? If there were other bodies essentially like the Earth, God’s goodness would surely necessitate that they too be inhabited. But if there were men on other planets, how could they have inherited the original sin, which explains Man’s otherwise incomprehensible travail on an Earth made for him by a good and omnipotent deity? Again, how could men on other planets know of the Savior who opened for them the possibility of eternal life? Or, if the Earth is a planet and therefore a celestial body located away from the center of the Universe, what becomes of Man’s intermediate but focal position between the devils and the angels? If the Earth, as a planet, participates in the nature of celestial bodies, it cannot be a sink of iniquity from which man will long to escape to the divine purity of the heavens. Nor can the heavens be a suitable abode for God if they participate in the evils and imperfection so clearly visible on a planetary Earth. Worst of all, if the Universe is infinite, as many of the later Copernicans thought, where can God’s Throne be located? In an infinite Universe, how is man to find God or God man? (Kuhn’s The Copernican Revolution, pg 193.)

Problems with the Copernican Model 4. Copernicus’ original heliocentric model did not predict the positions of the planets any better than Ptolemy’s geocentric model Copernicus could not complete shake off the influence of Aristotle even as he made the revolutionary proposal that the Earth was a planet. He held fast to the Aristotelian tenets that the planets moved on circles at constant speeds. There is a common misconception that the Copernican model did away with the need for epicycles. This is not true, because Copernicus was able to rid himself of the long-held notion that the Earth was the center of the Solar system, but he did not question the assumption of uniform circular motion. Thus, in the Copernican model the Sun was at the center, but the planets still executed uniform circular motion about it. As we shall see later, the orbits of the planets are not circles, they are actually ellipses. As a consequence, the Copernican model, with it assumption of uniform circular motion, still could not explain all the details of planetary motion on the celestial sphere without epicycles. The difference was that the Copernican system required many fewer epicycles than the Ptolemaic system because it moved the Sun to the center.

This presentation is unfinished at this time. I’ll be back at it as soon as I’m able. I hope to have it finished by Friday evening. In the meantime, please study the assigned text reading ( pg ) and the reserve reading in Kuhn.