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7. The Copernican Theory: Toward a New Astronomy

 

Reading Assignment

Koestler, Parts 3 and 4; Kuhn, Chapter 5; Drake, "The Starry Messenger," including the introduction. Encyclopedia article on Copernicus.

 

Objectives

- To learn the basic features of Copernican astronomy

- To understand the significance of each of Galileo's telescopic discoveries for Aristotelian cosmology and Ptolemaic astronomy

- To learn about Tycho's alternative model of the universe

Key Concepts

- Eccentric
- Equant
- Copernican system 
- Tychonic system
- Phases of Venus
- Galileo's theory of the tides

Discussion

In the last lesson I tried to show how well Aristotle's theory of the elements and their motions fit in with Ptolemy's quantitative astronomical theory, which predicted where each of the seven principal heavenly bodies would be at any time of any year.

You may well wonder why anyone would ever challenge the combined system, especially given all of the arguments against the motion of the earth. Yet Copernicus did just that, despite the fact that he couldn't explain why people didn't fly off the earth like mud off a wagon wheel. (Why don't we fly off, by the way?)

 

Our task in this lesson is to understand why Copernicus was dissatisfied with the Ptolemaic system-and how Galileo's telescopic discoveries made over 60 years later provided additional evidence against the old astronomy.

DIFFICULTIES WITHIN THE PTOLEMAIC RESEARCH PROGRAM

 

Although Ptolemy's idea of epicycles showed great promise in accounting for the motion of the planets, when later astronomers tried to make the system more precise they ran into small, but persistent, difficulties.

 

We now know (thanks to Kepler) that the simplest mathematical description of a planet's motion is an ellipse with the sun at one focus. It is therefore not surprising that the attempt to describe their motion with
deferents and epicycles centered on the earth ran into problems.

 

To bring the predictions of the model into closer agreement with astronomical observations, Ptolemy's followers tried various devices. First, they just added epicycles on top of epicycles. (You can perhaps imagine how difficult it would be to calculate the resultant path of the planets.)

 

Secondly, they tried using eccentric circles--they would place the center of the deferent not in the middle of the earth but off to the side some place. The resultant path better simulates an ellipse, but even this device did not give accurate enough predictions. (It was somewhat disturbing not to have the center of motion of the universe coincide with the center of the earth.) Some even tried using eccentric epicycles on top of eccentric deferents.

Thirdly, Ptolemaists, had recourse to a mathematical device known as the equant. Here the geometric center of the deferent is located on the earth, but the center of uniform motion., i.e., the point around which the angular velocity is constant (called the equant point) is off to the side.

 

Copernicus thought the whole system was getting too junked up! He especially disliked the idea of the equant. Surely the universe could not have been designed in such an inelegant manner, he thought. On a more practical plane, there was also the fact that Ptolemy's astronomical tables, which had been really quite accurate in his day, had gotten progressively worse, so bad that it was -even difficult to calculate when Easter should be.

Kuhn, Figure 45, p. 234 shows The Basic Copernican System

Copernican Astronomy

 

Historians do not fully understand the path which led Copernicus to his new heliocentric model of the universe (some believe he had mystical ideas about the power of the sun), but we do know why he didn't like Ptolemy's system (see above) and why he was impressed with his own.

The main advantage Copernicus cited for the heliocentric model was the very simple straightforward qualitative account it gave of retrograde motion. You will recall that Ptolemy had to use an epicycle for each planet to account for this phenomena. However, by merely placing the sun in the center and assuming that bodies farther away from the sun moved with slower angular velocity, the Copernican system automatically predicted the phenomenon of retrograde motion. As the earth passed the outer planets, they would appear for a time to be moving backwards. And as the inner planets passed us, when viewed against the constellations, they would also appear to be going backwards.

Kuhn's Figure 32, p. 166, illustrates the Copernican explanation of retrograde motion for (a) outerplanets and (b) inner planets. In each diagram, the earth moves steadily -on its orbit from El to E7 and the planet moves from P1
to P7. Simultaneously, the planet's apparent position against
the stellar sphere shifts eastward from 1 to 7, but as the two
planets pass there is a brief westward retrogression from 3 to 5.

There were lots of other simplifications. Instead of having the whole universe whirl around us every 24 hours, it certainly seemed more economical just to let the earth rotate under the sky instead.

And whereas Ptolemy had to stipulate that the center of the epicycles of Venus and Mars moved in a straight line with the sun in order to explain why these planets are always seen close to the sun (i.e., close to the horizon at dusk or dawn), Copernicus could explain these facts very naturally. Since the orbits of Mercury and Venus were smaller than that of the earth, of course they would always appear at a small angle from the sun.

There were significant advantages to Copernicus' astronomy, if you didn't worry about why we weren't all blown off of the earth's surface. And, of course, it was in sharp conflict with Aristotle's theory of the five elements and their natural place in the cosmos.

Galileo's Telescopic Discoveries

 

According to Copernican theory, the earth was just another planet moving around the sun--there was no sharp distinction between celestial matter and terrestial matter as Aristotle had claimed. All Galileo's discoveries gave support to this view. The moon had mountains just like the earth. Jupiter had moons which shone by reflected light just like the earth did. The sun had spots on it so it was not perfect and unchangeable as Aristotle had supposed.

 

But his most striking discovery was that Venus had phases somewhat similar to those of our moon. This phase behavior was important for two reasons. First of all it showed that Venus shone by reflected light--it was not a star at all. This strengthened the possibility that the earth was not categorically different from the planets.

 

Secondly, detailed observations of the phases of Venus showed that the Ptolemaic system could not be right. Instead, the sizes and shapes observed were exactly what would be expected if the Copernican theory were correct.

Kuhn, Figure 44, p.223 shows

the phases of Venus as predicted by (a) the Ptolemaic system (b) the Copernican system, and (c) as observed with a low-power telescope.

 

To understand this, look at the relative positions of the sun, earth, and Venus in diagram (a) above. According to Ptolemy, from the earth one would never see Venus in a full moon phase because its illuminated side is always away from us.

However, according to Copernicus, one should see a full moon phase (diagram (b) above). Furthermore, Venus in the full moon phase should appear smaller than when it is crescent shaped because of its greater distance in the former case. Galileo's actual observations are reproduced in diagram (c).

 

This is as pretty a refutation as one sees in the history of science. There aren't even any auxiliary hypotheses to blame. (Unless one is willing to claim that Venus shines by her own light, which is crescent shaped and waxes and wanes--but this would be a hopelessly contrived response.)

 

So Ptolemy is refuted, but this doesn't mean that Copernicus is proved correct. There was a third alternative waiting in the wings.

The Tychonic System

 

In 1588 Tycho Brahe, a great observational astronomer, had proposed a sort of hybrid structure for the universe. The earth was stationary in the center and the sun revolved around it (as in Ptolemy's system), but all of the planets orbited around the sun (as in Copernicus' model).

The Basic Tychonic System is illustrated in Kuhn, Figure 37, p.202.

 

After Galileo's discovery of the phases of Venus, the Tychonic system became very popular. It was consistent with both Aristotelian physics and Galileo's new telescopic discoveries.

There was one obvious way to decide between Tycho's and Copernicus' system--look for stellar parallax. According to Tycho, the earth did not move relative to the fixed stars during the year. (Of course, each night the stars made a complete circuit around the earth.) According to the Copernican model, on the other hand, the angle of a particular star, as viewed from the earth, should change during the year as the earth revolved around the sun.

 

As you probably know, there was no observable parallax. Adherents of Tycho said the Copernican theory was thereby refuted. Galileans concluded that the stars must be farther away than previously believed. Because there was no good way to compute stellar distances (and because the discovery of the composition of the Milky Way showed that some stars were very far away), this was not an unreasonable position to adopt. (Of course, if stellar parallax had been observed, Galileo would have been quite willing to conclude the stars were closer!)

 

Unable to detect stellar parallax, Galileo desperately searched for other ways of disproving the Tychonic compromise and proving that the earth moved.

For a while he thought the phenomena of sun spots would be helpful. Maybe their apparent movement across the face of the sun is really due to the rotation of the earth -- but this idea didn't work out.

Then he turned to the subject of the tides. For a long time people had realized that tidal behavior was correlated with the positions of the heavenly bodies. Some people even thought the moon caused the tides, but Galileo rejected this idea as astrological nonsense. He had a much more sophisticated idea. He thought tides were caused by the movement of the earth and since it is the earth's motion which makes the heavenly bodies appear to move, it is not surprising that a correlation exists.

 

His detailed theory went as follows. (Note the geometrical similarity to Ptolemy's account of retrograde motion.

Let us look down at the earth from the North Pole. At noon, a certain point (say Venice) is at and its rapid daily motion is opposed to the slow yearly motion. At midnight, however, Venice is opposite the sun at and the two motions add up. Galileo believed that this periodic acceleration and deceleration caused the oceans to slosh. The fact that there are two high tides a day and that high tide is not always at the same hour of the day, Galileo attributed to imperfections in the seabed.

 

The main problem with Galileo's theory of the tides, however, is that he fails to establish a difference in motion between the earth and the water. Viewed from the sun, both the sea and seabed appear to speed up and slow down. Viewed from the North Pole, neither do. But Galileo never realized this fallacy in his analysis and what is even more surprising, neither his disciples nor opponents caught the error either! Everyone of course realized that the predictions from his theory of the tides did not fit observations of tidal behavior.

 

At that time there was no observational evidence to discredit Tycho's system. Galileo's main reason for rejecting it was simply that it seemed mechanically unbalanced to have all the planets going around the sun, which in turn whirled around the earth. The Copernican picture of the Universe was certainly neater. (And wouldn't God choose the more elegant design?)

 

But as we will see in the next lesson, the theologians had their own ideas about how God put the Universe together--and they were quite different from Galileo's.

YOU SHOULD NOW DO THE READING ASSIGNMENT.

 

Study Suggestions

 

 

1.Add significant events and their dates to your chronological
list.

2.Learn to spell any new words and the names of the principal characters in our story.

3.Review the explanation of stellar parallax in Chapter IV.

4.Make sure you can draw diagrams showing both diurnal and proper motions for each of the three models of the Universe. Include epicycles where required to account for retrograde motions.