Motions of the Sun

So in my last class we started learning about the motion of the Sun.  I have them measure the transit time for a star (23 hours, 56 minutes) and then the transit time for the Sun (the expected 24 hours).  We think a bit about relative motion and realize that both the stars and Sun are moving Westward across our sky, but the stars are moving faster (since they go all the way around in a shorter time).  Therefore the Sun is moving Eastward relative to the stars.  The concept of relative motion is challenging if you haven't thought about it before, but I usually talk about driving down the highway heading West and passing another car.  To you, that car appears to be moving backward (Eastward).  So the motion of that car relative to you is Eastward.  They usually get that.

But the Sun now throws a wrench into our wonderful Celestial Sphere theory.  ALL of the stars move as though they are attached to our Celestial Sphere - but the Sun does not.  Therefore we must posit a new motion for the Sun.  Does this represent an ad hoc modification of our Celestial Sphere theory?  According to some philosophers of science, like Karl Popper, we shouldn't make ad hoc adjustments to our theory when we encounter an anomaly like the Sun.  Should we, instead, just give up on our Celestial Sphere?

There are a few reasons why we shouldn't.  The first involves the idea of classification.  The stars all look very similar: tiny points of light that are only visible in the night sky.  But the Sun appears to be a fundamentally different critter (forget what you've been told for the time being).  It is much brighter, is noticeably disk-shaped rather than point-like, and it lights up the day so much that we can't even see the stars when the Sun is in the sky.  Why should we expect the Sun to follow the same rules as the stars when it is obviously a very different thing.

This classification helps us to limit the scope of the Celestial Sphere theory (to the stars, but not the Sun) without having to toss out the whole thing.  This is really what classification is all about.  We classify things because certain groups of objects follow certain rules that others don't follow.  To extend our Game of Science analogy, think about chess.  All the pawns move the same way, but the thing that looks like a horse moves in a very different way.  It looks different from the pawns, so maybe we shouldn't expect the knight to move the way the pawns do.  Some deal with the stars and Sun.

The second reason we wouldn't want to throw out our Celestial Sphere theory is that it actually helps to explain the Sun's motion, even though it doesn't fully explain that motion.  The Sun's actual motion across the sky is not quite circular like that of the stars.  Instead, the Sun spirals (albeit very slowly).  This spiraling motion, viewed in full, would appear quite complicated.  But if we start off with the spinning Celestial Sphere, we find that we can describe the Sun's spiraling motion by simply having the Sun move slowly along the Celestial Sphere on a circular path.  It is the combination of the circular motion of the Celestial Sphere (which takes 23 hours, 56 minutes to complete) and the circular motion of the Sun along the Celestial Sphere (which takes a year to complete) that produces the observed spiral motion of the Sun.  If we don't start with the Celestial Sphere, the Sun's motion would be much harder to model.

My class will continue exploring this model (Celestial Sphere plus moving Sun) next week.  This simple model explains much that is of great importance to humans, which is why the study of the "The Sphere" was the focus of the medieval and early modern astronomy curriculum in the universities.  The classic work was the De Sphaera of Johannes de Sacrobosco (John of Holywood), but many students learned "spherics" from later commentaries which elaborated on Sacrobosco's book.  We will be finished with spherics in another week or so!