# Constructing Physics

## Elementary Physics Course Notes

Department of Physics
Weber State University

Today's discussion reviews some of the beginnings of science that we've inherited from Ancient Greece.  We mention Pythagoras as a major advocate of looking at the geometry of things, and Plato as an advocate of looking past the "shadows" and for the ultimate truth.  This is the intellectual background for Aristotle (384-322 BC), who is going to develop a system for how the heavens go 'round that is as geometrically simple as possible (using a bunch of circles) and tries to look beyond the way that things initially appear to be.

Aristotle knows that the Earth is round.  It could be easily observed that:

• Ships seem to "sink" into the horizon
• Views of the stars from different positions on Earth show different perspectives, suggesting a spherical things under our feet.
• Shadows of the Earth cast on the Moon (during a "lunar eclipse") are always circular.  The only shape that can always cast a circular shadow is a sphere.  (Try it yourself.)

Also, it is generally assumed that the Earth is both at the center of everything (because where else could we possibly be?) and that we're standing still (because we don't feel like we're moving!), so that any motion in the sky must be the sky moving around us.  The sky must be moving in perfect circles, because the sky and all of the stuff within it are within a perfect domain, untainted by our Earthly vices (such as beer and algebra), and so it must move in perfect ways.

So, you end up with a beautiful crystalline sphere, driven by something known as the Prime Mover, going round and round and round.  Pasted to this celestial sphere are little pinpricks of light that we call stars.  But, there are some other pinpricks of light that wander through the sky a little differently than the rest of the celestial sphere.  These "wanderers," or "planets," are simply deviant little stars, so they each must have their own respective sphere.  In this manner they can do the wandering that they seem to do.  Keep in mind that planets (as well as stars) were not seen as physical objects, but as nice little ornaments decorating the heavens.  You can't go there and you never will so don't worry so much about what their real essence is, argues Aristotle.

There's a problem, though.  First, every now and then the planets don't just drag behind the stars, they actually go backwards.  This is known as retrograde motion.  Aristotle could actually account for these motions with a more complicated working of circles within circles, kind of like a system of gears.  The details weren't worked out in as much detail as others would later go to the trouble to do, but for the level of detail that Aristotle wanted, perhaps this was okay.  A bigger problem may have been the fact that planets change their brightness.  If they change their brightness, this suggests that they must change their distance from/to us.  But, this is a problem, because the outside of a circle is (by definition) always the same distance from its center, which is supposed to be where the Earth is.

So how do we deal with this inconsistency?  There are a couple (at least) of different solutions, and the trick will be to find the best possible fit to the "truth" that Plato was such an advocate of.