Kepler, Newton, and laws of motion University （开普勒、牛顿运动定律大学）.pdf

Kepler, Newton, and laws of motion The only history in this course: Geocentric vs. heliocentric model (sec. 2.2-2.4) The important historical progression is the following: Ptolemy (~140 AD) … Copernicus (~1500 AD), Galileo (~1600), Tycho Brahe, Kepler (sec. 2.5), Newton (sec. 2.6). It is important to recognize the change in world view brought about by this transition: Geocentric model (Ptolemy, epicycles, planets and Sun orbit the Earth) Heliocentric model (Copernicus, planets orbit the Sun) Empirical, based on observations; NOT a theory (in the sense of Newton’s laws). So they are “laws” in the sense of formulas that express some regularity or correlation, but they don’t explain the observed phenomena in terms of something more basic (e.g. laws of motion, gravity--that waited for Newton) Kepler’s 1st law: 1. Orbits of planets are ellipses (not circles), with Sun at one focus. Must get used to terms period (time for one orbit), semimajor axis (“size” of orbit), eccentricity (how “elongated” the orbit is), perihelion (position of smallest distance to Sun), aphelion (position of greatest distance to Sun) Examples: comets, planets: Why do you think these have such different eccentricities ? (Don’t expect to be able to answer this, just find whether you understand the question.) Escaping from the assumption of perfect circles for orbits was a major leap, that even Copernicus was unwilling to take. Kepler’s 2nd law : 2. Equal areas swept out in equal times more simple: planet moves faster when closer to the sun. Good example: comets (very eccentric orbits, explained in class). Once you know the slightest thing about the force of gravity, this law is obvious. Kepler’s 3rd law Square of the period “P” is proportiona