PTOLEMY’S MODEL – WHAT GOOD WAS IT?
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The Ptolemy model of the solar system seems stupid to us today, but this is probably not fair to Ptolemy. He was working hard to make sense of the data and information that he had available. These days we struggle to understand some very complex phenomena, and we are not always doing a good job either. For a while, physicists thought of an atom as a nucleus surrounded by electrons that move smoothly in orbits around the nucleus just like the planets move around the sun. Probably many people still think of it this way, and there are many pictures of atoms drawn according to this model. But there are several reasons why such a picture could not possibly be true. There is a nucleus OK, and there are electrons outside the nucleus. But the motion of these electrons is so complicated that it can hardly be thought of as motion at all. It takes the complete quantum theory to explain it. However, it was not wrong for physicists to create the “solar system” model of the atom. It was a valuable stepping-stone to a better model. It was also not wrong for Ptolemy to try to explain what he knew with his model. Eventually observations showed that it could not be correct, but the model did manage to predict the positions of the planets in our sky fairly well for a long time.
The stories from Galileo’s time, about 1400 years later, make it clear that people had held onto the Ptolemy model for too long. But it did accomplish some things in its time.
Of course the Ptolemy model was not really Ptolemy’s. Hipparchus had developed the main ideas of the model, but Ptolemy did refine it into something that worked better and then published his work in a famous book. So for better or worse, we name it after Ptolemy.
It could explain the general ideas about the motion of Mercury and Venus, and it could also explain the retrograde motion of Mars, Jupiter, and Saturn. Here are links to a couple of slide shows that should give an idea how this worked as well as an idea of what the Ptolemy model looked like in general. Have a look at them, and then come back here for a little more discussion of what this model could and could not do.
Click here for a slide show explaining how the Ptolemy model explained the motions of the inner planets, Mercury and Venus.
Click here for a slide show explaining how the Ptolemy model explained the retrograde motion of Mars and the other outer planets.
Although Ptolemy had an explanation for this retrograde motion, there was something about it that he could not explain. Retrograde motion of Mars, Jupiter and Saturn takes place only when these planets are on the opposite side of the earth from the sun. In other words, it occurs when these objects line up in the order [Sun, Earth, Other Planet] so that the other planet is high in the sky in the middle of the night. That happens roughly every two years for Mars and at different intervals for Jupiter and Saturn. Ptolemy did not know about Uranus, Neptune, and Pluto, but the same thing happens with these planets.
This lineup of planets is called “opposition”, so Ptolemy
could not explain why retrograde motion takes place at opposition. Since he placed the sun in a separate orbit
around the earth, he just had to deliberately place the sun on the opposite
side of the spot where the retrograde loop was. [By the way, if you have not looked at the slide show about
retrograde motion, this discussion will not make any sense whatever to you. Look at the show. If it still does not make any sense, come to class on the day it
is explained there. If you still do not
understand it, ask.]
Placing the sun this way amounts to explaining this point about retrograde motion and opposition by just putting it in the model as a separate assumption. The best theories explain the greatest number of observations with the fewest assumptions, so this sort of thing weakened the Ptolemy model.
Ptolemy could also make the moon look the right way at the right time. Of course the moon goes through phases so that it is sometimes a full moon, sometimes a new moon, sometimes a first quarter moon, and so on. These phases are very regular, and the moon goes through a complete cycle of phases in about four weeks. Ptolemy could make his model predict when each phase was going to happen and where the moon would be in the sky for each phase. Of course, the moon really does revolve around the earth, so he had the right general idea about the moon.
However, there is more to predicting the appearance of the moon. Ptolemy had the moon moving sometimes closer to the earth and sometimes farther away. When it is farther away, it will appear smaller to humans on the earth. When it is closer it will seem to be larger. So Ptolemy had some predictions about this as well as about the phases. There will be a lab in this course to investigate how well Ptolemy did in this prediction, so we will leave the discussion of this point to the day of the lab.
There was also a problem with the apparent brightness of each planet. A planet shines by reflected sunlight. If a planet is closer to the sun, it will receive more sunlight and can be brighter. On the other hand, if the planet is farther away from the earth, then it will seem dimmer from the earth no matter how much sunlight it receives. So the apparent brightness of a planet depends in a complicated way on how far it is from both the sun and the earth. Ptolemy’s model had the motions of the planets all mixed up from the real motions. Since he had each planet as well as the sun revolving around the earth, then he also had the distances from the sun to each planet mixed up. That was also true of the distances from the earth to the planets. So he frequently had a planet brighter when it should have been dimmer and vice versa. Anyone noticing this should have known that the Ptolemy model could not have been the final word on the subject. In the ancient world someone may have known this, but it did not seem to penetrate too many heads in the days of Galileo.
There was, however, something the Ptolemy model could do. It could predict where in our sky each planet was going to be at some time in the future. It was not perfect at this, but it did fairly well for a long time. Such predictions were considered important for determining calendars, telling time, navigating, probably just for the sake of curiosity, and for that matter for reasons involving astrology.
If you have a model that works sometimes and does not work for others, then go ahead and use it where you know it works. Be sure to avoid using it for situations where it does not work, and understand that it is not the final word. It is just a step toward more complete knowledge. A globe of the earth is such a model. It can tell you what is where on the surface of the earth, but do not try to use it to predict what is at the center of the earth. And realize that it is not really the earth. None of this causes trouble for the average human.
Ptolemy’s model could be used to predict where planets would be and when, and long tables were prepared from it for this purpose. As time went by, however, the predictions would become worse and worse. So new tables would be necessary – sort of like resetting a watch that was running too slowly. By the time of Copernicus, the tables in use at that time were up to three months off. They would predict something would happen on a certain night and it would not really happen for three months. Furthermore the model was extremely complicated, and there was always the chance that it could be simplified. Copernicus seems to have decided to make a new metaphorical watch with a simpler mechanism.