From Galileo to Newton Daily Schedule Term 3

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See also: Daily Schedule Term 2

Week 8 — Apollonius Propositions 1-3 — Begin Newton Proposition 11

Week 9 — Properties of Ellipses — Continue Gleick through Chapter 8

Week 10 — Continue Newton Proposition 11

Context: With the possible exception of Proposition 1 and Proposition 6, Corollary 1, upon which Proposition 11 directly depends, Proposition 11 is probably the single most important Proposition we have encountered. It was also composed of a lot of steps, many of which used special properties of ellipses.

Why is this Proposition so important? Because Kepler has demonstrated, using Brahe’s observations, that the planets go around the Sun in ellipses with the Sun at one focus, and they trace out equal areas in equal times.

We know that for an orbit of any shape, equal areas in equal times implies a centripetal force. In Proposition 11, Newton shows that for ellipses with the centripetal force originating from one focus the force obeys an inverse square law. He is going to show many more things, but with this, he could already close up shop. He has rigorously demonstrated in Proposition 11 what others have only conjectured: that the motion of the planets are caused by a centripetal force in the direction of the Sun, and that the strength of this force follows an inverse square law. Because of this Proposition’s importance and difficulty, we must spend more time on it.

Week 11 — Newton Propositions 13 to 16 — Book III: The 4 Rules of Philosophizing

More Context: Proposition 11 is for ellipses, Proposition 12 is for hyperbolas, and Proposition 13 is for parabolas. All three come to the conclusion that an inverse square law force is causing the observed motion. Parabolas are important because the very long-period comets seem to follow parabolas. Hyperbolas describe extremely rare objects that pass once through our solar system, never to return. The first ever observed was ʻOumuamua.

Week 12 — The Modern Treatment of Elliptical Orbits — Finish Book I — Book III: Begin The Phenomena

Week 13 — Book III: The Phenomena (Continued)

Compressed schedule this week due to Friday all-hands preg check

Week 14 — The Remainder of Book III (pp. 422-484) — The Shell Theorem and Its Consequences

And when is Newton going to explain to us the origin of Ocean Tides!?! Is there only the brief comment in III.5 Corollary 3 (Densmore p. 385): hence, “the sun and moon perturb our sea,” as will be explained? If there is no more on the tides in our reading, I will make a problem for you.

Week 15

Thursday’s class moved to Monday because Monday was regarded by most people as best for an exam