1. Chapter 13 Reading assignment: Chapter 13.4-13.7 Homework :(due Friday, Nov. 28, 2005): Problems:3, 6, 8, 13, 25, 26, 35, 40, 43, 51 Historically very interesting, Geocentric vs. heliocentric universe The main cast: Copernicus, Brahe, Galileo, Kepler, Newton

2. - Ptolemy (100 –170 A.D.) geocentric model: Sun revolves around earth (Wrong!) From astronomical observations: - Copernicus (1473-1543) heliocentric model: Earth & planets revolve around ____ - Galilei (1564 - 1642) (1610) supports (loudly) the _______________ model - Brahe (1546 - 1601) Accurate observation of ____________________ motion - Kepler (1571-1630), 1609: Laws I, II of planetary motion, took Brahe’s data - Kepler _______: Law III of planetary motion, 18 years after murdering(?) Brahe. - Aristotle (384-322 B.C.) Heavier objects fall faster than light objects (__________!) - Galileo (1564-1642) Neglecting air resistance, all objects fall at _____ acceleration Geocentric vs. heliocentric model of earth About falling objects

3. Newton’s Law of Universal Gravitation 1687, (Newton 1642-1727) Every particle in the Universe attracts every other particle with a force of: G… Gravitational constant G = 6.673·10 -11 N·m 2 /kg 2 m 1, m 2 …masses of particles 1 and 2 r… distance separating these particles … unit _________ in r direction

4. Newton’s Law of Universal Gravitation - Particle 1 is attracted by particle 2 - Particle 2 is attracted by particle 1 - F 12 and F 21 form an ______________ pair - Force drops off as 1/r 2 as distance r between particles increases - Can treat spherical, symmetric mass distributions as if the mass were concentrated in __________________.

5. Newton’s Law of Universal Gravitation The force exerted by the earth on a particle near the Earth’s surface is What is the force exerted by the particle on the earth?

6. What is the attractive force you (m 1 = 100 kg) experience from the two people (m 2 = m 3 = 70 kg) sitting in front of you. Assume a distance r = 0.5 m and an angle  = 30° for both? Black board example 14.1 

7. Measuring the gravitational constant – Cavendish apparatus (1789)

8. Free-Fall Acceleration and the Gravitational Force Gravitational force: Thus : g is not ________ as we move up from the surface of the earth!!

9. Earth’s gravitational field Close to the surface Far away from the surface Gravitational force acts from a distance through a “field”

10. What is the value of the gravitational constant on top of mount Everest (h = 8848 m)? Assume M E = 5.960·10 24 kg and R E = 6.370·10 6 m. Black board example 14.2 Variation of g with altitude Everest North Face and Rongbuk monastery (5030m), Tibet May, 1997 Photo credit: Philippe Noth