Lec16-KeplerAndMultivariable

Lec16-KeplerAndMultivariable - Math 32 A Wednesday,...

Info iconThis preview shows pages 1–19. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 32 A Wednesday, November 4, 2009
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Office Hours Today: 12 – 1 PM EXAM 2: Next week, Friday Nov. 13 REVIEW SESSION Monday Nov. 9, Kinsey Pavilion 1200B Google: UCLA map
Background image of page 2
The Law of Ellipses
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Newton’s demonstration of the law of ellipses is a watershed that separates the ancient world from the modern world .
Background image of page 4
It is one of the crowning achievements of the human mind, From: Feynman’s Lost Lecture David Goodstein, Judith Goodstein (Physicist, Vice Provost, CalTech)
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Comparable to Beethoven’s symphonies, or Shakespeare’s plays or Michelangelo’s Sistine Chapel
Background image of page 6
It is a conclusive demonstration of the astonishing fact: Nature obeys mathematics .
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Published 1687 Newton’s Geometric Proof of the Second Law
Background image of page 8
Second Law when G = 0 (gravitational force is zero
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Elementary Geometry: Triangle have SAME AREA
Background image of page 10
Newton observes: under a central force, The planet is displaced parallel to the radial vector. THE AREA SWEPT DOES NOT CHANGE by elementary geometry!
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Conservation of angular momentum The vector J = r x r' is constant
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Conservation of Angular Momentum
Background image of page 14
Energy r = distance from sun, v = speed Kinetic Energy: (1/2) mv 2 Potential Energy: -GMm /r TOTAL ENERGY = (1/2)mv 2 - GMm / r
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Conservation of Energy E = (1/2)v 2 - GM / r dE / dt = 0 E is a constant of motion.
Background image of page 16
Two Conservation Laws (1/2)v 2 - GM / r = E r v sin( Ψ ) = J
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ELIMINATE v GET EQUATION LINKING r and Ψ. (1/2) v
Background image of page 18
Image of page 19
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 61

Lec16-KeplerAndMultivariable - Math 32 A Wednesday,...

This preview shows document pages 1 - 19. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online