Today we began our study of Copernicus. The focus of today's activity was the three (really four) motions that Copernicus assigns to Earth. We also discover, right away, the obvious way to refute Copernicus' idea that Earth orbits the Sun (and also Copernicus' seemingly ad hoc solution to this problem).
The first two motions of Earth are pretty straightforward, and are easily demonstrated with my Daily Rotation simulation (not yet available on OSP). The Ancient Greeks thought the daily motion of the sky could be accounted for by a Celestial Sphere that rotates with a period of 23 hours, 56 minutes. Copernicus achieved the same effects by holding the Celestial Sphere still and letting Earth spin about the same axis, but in the opposite sense, with the same period.
The second motion accounts for the annual motion of the Sun around the Celestial Sphere and is demonstrated by my Earth Orbit simulation. The Greeks just had the Sun orbit the Earth in the Ecliptic plane over the course of a (sidereal) year. Copernicus instead has Earth orbit the Sun, also in the Ecliptic plane and in the same sense (counterclockwise as viewed from the North Ecliptic Pole). The rotational axis of Earth (see the first motion above) is not perpendicular to the Ecliptic plane (the plane of Earth's orbit). Rather, it is inclined away from perpendicular by 23.5 degrees. This gives rise to all of the seasonal variations in sunlight (both in the altitude of the Sun and in hours of daylight) that the Ancient Greeks accomplished by simply tilting the Ecliptic circle relative to the Celestial Equator.
So far, so good. Copernicus matches up with Ptolemy perfectly, although one might argue that he has done nothing new yet so what's the point? There is a point, but you don't really get to see it until you look at the planets. As far as Earth is concerned, its all downhill from here.
The first problem Copernicus runs into can be easily demonstrated. Grab a stick and hold it in your hand. Extend your arm. Don't point the stick straight up, but tilt it at an angle (say, 23.5 degrees from straight up?). Now spin your body, keeping your arm extended. Your hand orbits around you body just like Earth orbits the Sun in the Copernican system. The stick plays the role of Earth's rotational axis. You will find that the stick does not point in a fixed direction. Instead its direction changes as you spin around. This was a problem because the sky appears to spin about the same points (around a point near Polaris in the Northern Hemisphere) all year long.
These days we wouldn't even see this as a problem. We think of Earth as a freely spinning body that will automatically maintain the orientation of its rotational axis unless something messes with it. But for Copernicus the Earth was a heavenly body that had to be carried around by heavenly spheres. So in his mind it was much more like a hand holding a stick than like a freely spinning ball. But he solved the problem in a an ingenious way. While Earth orbits the Sun, its axis or rotation rotates around the Ecliptic poles in the opposite sense and at ALMOST the same rate. If he made the rate exactly the same (one rotation per sidereal year), then the rotational axis would maintain the same orientation forever. By making the rates SlIGHTLY different, Copernicus found an explanation for the precession of the equinoxes (see my Equinox Precession simulation). Brilliant! He turned what could have been a major weakness of his theory into a strength.
But a problem still remains. Even if the axis maintains a fixed orientation, that doesn't mean it will intersect the Celestial Sphere always in the same point. As Earth orbits the Sun, the rotational axis gets dragged around with it. So technically the point where the axis hits the Celestial Sphere (what we call the Celestial Pole) moves in a circle over the course of a year. This is NOT the same as the circle the poles make due to precession. For one thing, the poles complete this circle once per year, not once every 26,000 years as with precession. For another thing, the precession circle is centered on the Ecliptic pole, while this new effect has no relation to the Ecliptic poles.
Again, we simply do not see this effect. The North Celestial Pole stays right next to Polaris all year long. It doesn't move about the sky in any noticeable way. So it would seem that Copernicus' theory of Earth's orbit around the Sun has been refuted. It makes a prediction, that predictions fails the observational test. Throw out the theory, right? Of course, that's not what we do. Because Copernicus has an answer: the Celestial Sphere is just REALLY BIG compared to the size of Earth's orbit. If you push the Celestial Sphere far enough out, then the little circle traced out by the Celestial Pole becomes a tiny dot - so small that it looks like a point, even though it is really a very tiny circle.
For Copernicus himself, this was a satisfying explanation of the failure to observe the effect that his theory predicted. For most of his contemporaries it seemed like an ad hoc defense of the theory, exactly the kind of thing that Karl Popper would later say should never be done. Of course, in this case Copernicus' ad hoc defense would turn out to be completely correct. The Ancient Greeks thought the Celestial Sphere could hold more than a trillion Earths, but as it turns out they had vastly underestimated the distances to the stars.
Before I close, I should mention Copernicus' fourth motion for Earth. He introduced this little wobble to account for an effect known as "trepidation". This was an variation in the rate of precession that had been originally proposed, I think, by Medieval astronomers in the Middle East. However, this effect is not real and so this fourth motion is not needed. We barely even mention it in class, although I am quite interested to know the history of how astronomers eventually discovered that trepidation was not a real effect. Once you have measured something it is hard to make it go away, even if it is not really there. This issue comes up in my other astronomy class with regard to the rotation of spiral galaxies as measured by Adrian van Maanen - but that's another story.
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