Slide1: Historically very interesting, Geocentric vs. heliocentric universe The main cast: Copernicus, Brahe, Galileo, Kepler, Newton Chapter 13: The Law of Gravity Reading assignment: Chapter 13.1 to 13.5 Homework : (due Tuesday, Nov. 14): Problems: 3, 5, 9, 11, 17, 20 Midterm 3 coming up on Thursday Nov. 16, 5-6 pm and 6-7 pm Practice test will be posted on web page


Slide2: - Ptolemy (100 –170 A.D.) geocentric model: Sun revolves around earth (Wrong!) From astronomical observations: Copernicus (1473-1543) heliocentric model: Earth andamp; planets revolve around sun Galileo (1564 - 1642) (1610) supports (loudly) the heliocentric model Brahe (1546 - 1601) Accurate observation of planetary motion Kepler (1571-1630), 1609: Laws I, II of planetary motion, Kepler 1619: Law III of planetary motion Aristotle (384-322 B.C.) Heavier objects fall faster than light objects (Wrong!) Galileo (1564 - 1642) Neglecting air resistance, all objects fall at same acceleration Geocentric vs. heliocentric model of earth About falling objects


Slide3: Newton’s Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force of:


Slide4: 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 action-reaction 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 center of mass.


Slide5: 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?


Slide6: 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? Black board example 14.1


Slide7: Measuring the gravitational constant – Cavendish apparatus (1789)


Slide8: Free-Fall Acceleration and the Gravitational Force Gravitational force: Thus: g is not constant as we move up from the surface of the earth!! G is a universal constant (does not change at all).


Slide9: Earth’s gravitational field Close to the surface Far away from the surface Gravitational force acts from a distance through a 'field'


Slide10: 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. What is it in a space station that is at an altitude of 350 km Black board example 14.2 Variation of g with altitude Everest North Face and Rongbuk monastery (5030m), Tibet May, 1997 Photo credit: Philippe Noth


Slide11: Kepler’s first two laws (1609): Planets move in elliptical paths around the sun. The sun is in one of the focal points (foci) of the ellipse The radius vector drawn from the sun to a planet sweeps out equal areas in equal time intervals (Law of equal areas). Kepler’s laws about planetary motion These laws hold true for any object in orbit Area S-A-B equals area S-D-C


Slide12: Kepler’s third law (1619): III. The square of the orbital period, T, of any planet is proportional to the cube of the semimajor axis of the elliptical orbit, a. Kepler’s laws about planetary motion Thus, for any two planets:


Slide13: Kepler’s laws about planetary motion Most planets, except Mercury and Pluto, are on almost a circular orbit Earth: Ratio of minor to major axis b/a = 0.99986. For planets around sun:


Slide14: Black board example 14.3 The solar system If the Mars year is 1.88 earth years, what is Mars’ distance from the sun Calculate the mass of the sun using the fact that the period of the earth’s orbit is 3.157·107 s and it’s distance from the sun is 1.496·1011 m. Inner planets Further out: Saturn, Uranus, Neptun, Pluto


Slide15: All nine eightplanets of the solar system