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Chapter 13

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.

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Chapter 13

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  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. Geocentric vs. heliocentric model of earth • - 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. About falling objects • Aristotle (384-322 B.C.) Heavier objects fall faster than light objects (__________!) • Galileo (1564-1642) Neglecting air resistance, all objects fall at _____ acceleration

  3. G… Gravitational constant G = 6.673·10-11 N·m2/kg2 m1, m2…masses of particles 1 and 2 r… distance separating these particles … unit _________ in r direction Newton’s Law of Universal Gravitation 1687, (Newton 1642-1727) Every particle in the Universe attracts every other particle with a force of:

  4. Newton’s Law of Universal Gravitation - Particle 1 is attracted by particle 2 - Particle 2 is attracted by particle 1 - F12 and F21 form an ______________ pair - Force drops off as 1/r2 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. q Black board example 14.1 What is the attractive force you (m1 = 100 kg) experience from the two people (m2 = m3 = 70 kg) sitting in front of you. Assume a distance r = 0.5 m and an angle q = 30° for both?

  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 Gravitational force acts from a distance through a “field” Close to the surface Far away from the surface

  10. Black board example 14.2 Variation of g with altitude Everest North Face and Rongbuk monastery (5030m), Tibet May, 1997 Photo credit: Philippe Noth What is the value of the gravitational constant on top of mount Everest (h = 8848 m)? Assume ME = 5.960·1024 kg and RE = 6.370·106 m.

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