# Constructing Physics

## Elementary Physics Course Notes

Department of Physics
Weber State University

When we last saw our hero, the hypothetical early astronomer of Ancient Greece, she was trying to figure out exactly what was going on up there in the sky.  If it's the middle of the day and you want to simulate this, you can use this tool, as we did in class.

Of course, we all know that the Earth is fixed and the heavens revolve around us as dictated by the celestial sphere, but it was unclear why/how the planets would wander in the way that they did to include both retrograde (backwards) kinds of motions and changing brightness.

The notewriter would like to interject something here: Let's be fair to Aristotle and others of his day.  He was trying to find some kind of "truth," and he saw this quest as being a lot like a prisoner in Plato's cave.  Aristotle figured that there were certain things that we just simply cannot see directly (e.g., planets), and that we need to thinkabout how they should be rather than observe them directly.  Thus, his description of the celestial spheres and the planets was dictated by simplicity and philosophy.  In the science of today, we strive to describe the real, physical world as closely as possible, and we assume that there is data that we can collect to describe such.  Philosophers would call this "realism" because we assume that there are real physical objects, mechanisms, etc. that can be interacted with and observed.  (And yes, there is such a thing as "antirealism".)

End of interjection.

Anyway, Ptolemy (150 AD) comes along and gets really bent out of shape about the whole idea that Aristotle's system doesn't really explain all the intricacies of planetary motion.  So, he adds some things to Aristotle's basic model.  These include:

• setting each planetary sphere off center, so that there motion is "eccentric" -- in other words, the Earth is not at the exact center of any given planet's motion
• varying the speed at which planets move about
• giving each planet an "epicycle" to move about, in addition to the primary path

The idea of an epicycle is probably the most fundamental here, and it has some neat consequences:

• your instructor does a funny dance to demonstrate this motion
• it accounts for retrograde motion
• it accounts for changing brightness of any planet (and accounts for a planet being its brightest while doing the retrograde part of its path)

(To convince yourself of these consequences, you should draw yourself a picture and/or act out the epicycle dance on your own.)

This is all fantastic!  We can have the Earth stand still and save the phenomena/appearances displayed by the planets.  But, there are a few problems.  First, the whole system is very complicated.  All of these adjustments are customized for each observable planet, and there are lots of pieces to tune.  Partially as a result, the system has to be re-adjusted every now and then so that it still makes accurate predictions.  Still, it would last until the 1600's.

In the 1500's, Copernicus was kicking around an idea that was really nothing new, just recycled.  He suggested that the Sun is a perfectly fine, life giving object that could be at the center of it all, and if this were the case then we could make the planets all go around in circles and account for retrograde motion and changing brightness in a more simple manner than Ptolemy's model.  (This was drawn out and demonstrated in class.)
Why is this such a good idea?  Copernicus himself suggested that it would be much simpler and would be a good model to use to make predictions.  In fact, this model was actually used by the Roman Catholic Church to build a good calendar system (still in use today) before the Church actually advocated any belief in the model.  However, there were good reasons NOT to buy Copernicus' heliocentric madness:

• the model was originally even worse than Ptolemy's at making predictions, and only after Copernicus added extra complications (including some of his own epicycles!) did it get better . . . but once you do this you make the model less simple again!
• it contradicted the philosophy of old and the religion of new (Catholic Church as well as Protestant leaders who were breaking away from Catholicism)
• we don't feel like we're moving, and if we were, wouldn't we fall off?  wouldn't the stars seem to move as we "flew" past them?  Frankly, the whole notion of the Earth moving is completely crazy if you really think about it.  How does it do such a thing and why don't we run into something or fall off or . . . ?

For these reasons, the idea of a heliocentric system didn't stick right away.  But, we still refer to the "Copernican Revolution".  It's just that Copernicus didn't convince too many people.  It would require some more convincing data and a more convincing explanation of it all.

Copernicus leaves us with an incomplete revolution: Although he reintroduced the idea that the Earth moves around the solar system, he was not able to make a completely convincing argument.  Copernicus' system was any more accurate than a geocentric system, and it was hard to believe.

Science not only looks for data, evidence, stuff, etc., but explanation.  In fact, explanation is the end goal of everything that we do.  So, you can't blame anyone for not buying the idea that the Earth and other planets could travel around the Sun, for there wasn't any reason or explanation for how this would work.  It would require better data and a better idea of how physics works before anyone could allow the Earth to move.

To gather more data, we look to Tycho Brahe, a Danish astronomer whose prime was in the late 1500's.  Tycho basically is stubborn and perseverant and astute enough to collect so much more precise data than ever before that others to follow would be able to see that much more clearly the details of planetary wanderings.  He did all of this without telescopes, but created some very sophisticated instruments used to measure angles.  Some of his work impressed the king, and he was granted use of an island, observatory, castle, and lots of support and funding.  Unfortunately, Tycho had the nasty habit of throwing residents of the island into the dungeon, actions that did not amuse the king.  Tycho was basically kicked out of the country.

We know exactly how Tycho died, because at the time of his death he had taken on a very observant and dedicated assistant, Johannes Kepler.  Kepler documents how Tycho drank lots and lots at a party, but as the etiquette at the time went, Tycho knew it would not be polite to go to the bathroom before the host of the party.  The host never went potty, so Tycho never got a chance to go potty.  So, his bladder ruptured, and the infection which ensued killed him over the period of a painful two weeks.

Kepler wrote everything down and was incredibly meticulous about details.  This is the perfect person to look over the data of Tycho, and in so doing, Kepler sees patterns that no one had been able to see before.  These are summarized in Kepler's 3 laws:

1. planets go around the Sun in elliptical orbits
2. planets change their speed as they orbit, speeding up when closest to the Sun
3. different planets have different average speeds, based on their respective closeness to the Sun
(These aren't the exact statements of the 3 laws, but a rough description.  Remember, these are the "notes" for the course!)

These three laws took an immense amount of data and evidence to comb through, and represent a huge achievement that goes far beyond what anyone before had been able to produce.  Still, Kepler would go to his grave never understanding how the planets got such specific motions.  He found this incredibly frustrating.

Another major player in this revolution was Galileo.  Even though Galileo and Kepler weren't working together, they were a part of the same team, each working on different facets of the same problem.  Galileo (who we'll return to later to see his many other contributions) was staring up at the skies looking through a new invention we now call a telescope.  (This is the early 1600's in Italy.)  He saw fascinating things such as:

• huge numbers of stars never seen before
• spots on the Sun
• craters and mountains on the Moon
• moons orbiting Jupiter
• phases of Venus that weren't possible if Ptolemy's system were correct
• possibly rings of Saturn

These observations were impressive and were read about by many because Galileo wrote about this stuff in an entertaining manner, and because her wrote in Italian instead of in the traditional Latin.  This made a lot of people think, and also got Galileo into a bit of trouble with the Roman Catholic authorities.

So, Kepler finds the pattern that the planets seem to fit into.  Galileo shows that these things up in the sky are really very physical and share characteristics with Earth (and thus, have some similar physics).  But, we're really not done.  It would require a new idea, called physics, to first be developed by Galileo and later by Newton before any of this really started to make sense.