COPERNICUS – CIRCLING THE SUN

Go to:

Home

Course Outline

Terms

Web Links Page

The sheer size and mass of the ground around us makes it difficult to believe that the earth can move, although if you have been in an earthquake you know better. But Copernicus suggested that the whole earth moves around the sun, which was pretty hard to swallow. With this suggestion, he made the crucial step for getting models of the solar system right, but he was still wrong on many details.

The idea was to predict the positions of the planets among the stars (as seen from the earth) for reasons involving navigation, determining human events such as holidays, and astrology. Tables for this purpose based on Ptolemy’s model were up to three months off. Copernicus never said much about just what motivated him to change the model, but it seems to have been mainly an attempt to simplify the calculations. Such calculations were very difficult based on the Ptolemaic system because of all of the deferents, epicycles, and other motions.

Position of planet as seen from earth

Copernicus could not make it work using circular orbits and constant velocities, which he thought he must use. He was still addicted to that idea, an idea as old as Pythagoras. So he adopted the idea of epicycles, as Ptolemy and Hipparchus had done, and furthermore he put the sun off to one side of the center of the orbit of a planet – also an idea borrowed from Ptolemy. According to Copernicus, the orbit of a planet around the sun looked something like this:

Notice that the actual path of the planet is sort of an elongated circle. Also the motion of the planet along the epicycle adds to the motion of the epicycle itself at the bottom of the figure (where the planet is closest to the sun) and opposes the motion of the epicycle at the top (farthest from the sun). So the planet is moving fastest when it is closest to the sun. In the section on Kepler, we are going to see that the real path of the planet is an ellipse, which is in fact sort of an elongated circle. Copernicus was trying to draw an ellipse, but he had no idea that was what he was trying to do. The shape drawn by Copernicus was not quite an ellipse, though. It can be shown that you cannot make an ellipse by adding two circles in this way.

Copernicus was also on the right track about the speed of the planet being the greatest when it was closest to the sun, but he did not quite have the correct speed. So no matter what Copernicus did, his model never did predict the positions of the planets any better than the Ptolemy model did.

Copernicus was able to explain the approximate motions of the planets in a simpler way that the Ptolemy model. For the explanation of the motions of Mercury and Venus, click here for a slide show on the subject.

Copernicus also had a simple explanation of the retrograde motion of Mars, Jupiter, and Saturn. Click here for a slide show on this subject.

The Copernicus model could predict several observations about planets better that Ptolemy could. For one thing, Copernicus had the distances between the sun and the planets as well as the distances between the planets and the earth. Since the planets shine by reflected sunlight, this made the changes in the apparent brightness of each planet come out about right.

Furthermore, Copernicus could explain why retrograde motion took place at opposition (the time when the planet was opposite the sun as seen from the earth). This was a natural result of the Copernicus model; the earth passed the planet at opposition just as the retrograde motion took place. In the Ptolemy theory, this aspect of retrograde motion had to be put in as a separate assumption. In general the theory that explains the most with the fewest assumptions is the better theory, a principle known as Occam’s Razor. So there are a few good points for Copernicus here.

In addition, the Copernicus model still explained why Mercury and Venus stayed so close to the sun, and it explained the phases of the moon by reflected sunlight.

Of course, any model of the planets must be able to predict the positions of the planets night after night if it is to be accepted. Ptolemy could do this but only up to a certain point; there were errors that became worse with time. It turned out that the Copernicus model was no worse than Ptolemy in this respect but also no better. So there was no good way to choose between them just from watching the positions of the planets and comparing these positions with the predictions of the models.

Besides there were some serious objections to this model of Copernicus. In our day, with plenty of hindsight, the main objection is that the circular motions and epicycles do not fit any kind of sensible theory of physics. In other words, no one has a clue about what could produce such a goofy set of motions. Certainly Newton’s Laws of motion cannot explain them. Copernicus lived well before Newton, and no one had yet heard of his laws. But no one had any explanation for motion of this type either.

There were several other objections that can actually be explained but which could not be explained then. The most serious was that no one could observe anything like parallax of stars. “Parallax” means that, if the earth moved then the stars should seem to move in the other direction to an observer on the moving earth just as houses and telephone poles seems to move backwards when you observe them from a moving car. In fact, this apparent motion of stars is there to be seen but only with equipment much more sophisticated than anything that existed during the time of Copernicus. See the terms file and click on “Parallax” for more explanation of this. This seemed to argue strongly against the idea that the earth moves at that time.

It seemed to many people that an earth that moved so fast would be torn apart or at least that objects would be thrown off of it. This was especially true because the earth had to have a double motion for the Copernicus model to work. It had to rotate on its axis to produce day and night, and it also had to revolve around the sun. Gravitational theory was not yet understood at the time; therefore it was difficult to explain how gravity could hold the earth together and could hold objects on the earth. At least, Copernicus could ask why, in the Ptolemy model, the other spheres such as the one holding the planets and stars, did not fly apart due to their rapid motion.

Copernicus could not explain how the planets started to move in the first place, although there is a fairly well developed theory of this now. Of course Copernicus would not necessarily have to explain that if observations had been with him. But, of course, the observations were ambiguous.

Finally, there was the objection that you could not throw an object in the air and have it some straight back to you if the earth were moving. The idea was that anything thrown into the air would become detached from the earth, and the earth would move under it. Then it would come down somewhere else. Since this was not observed, it was thought to disprove the idea that the earth moves. Of course the whole line of reasoning is nonsense. If you throw something in the air from a moving platform, it keeps the forward motion of the platform. Then it comes back down on the same platform. You can check this yourself. Walk forwards with a baseball. While you are still walking, carefully throw the ball straight up into the air. If you keep on walking, the baseball will come down right into your hands since it kept your forward motion all the time. It remained for Galileo to explain this after his careful, general study of motion.

The Copernicus model explained the motion of the planets as well as, but no better than, the Ptolemy model. Copernicus did it more simply with fewer assumptions. But there were several objections to a moving earth, which seemed valid at the time. A better theory and more study of motion in the abstract were both needed.