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Universal Gravitation

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  1. Universal Gravitation

  2. Objectives for today • Introduce Newton’s Universal Law of Gravitation • Applications • Historical context Scientific Process • Opportunity for Creativity • For all but a few, problem solving will wait until Monday!

  3. Applications • Apollo • Space probes • Satellites, TV, GPS, XM, Sirius

  4. Names in History • Ptolemy (Claudius Ptolemaus) • Greek, 2d Century A.D. • Geocentric still use in navigational astronomy • “Sunrise”, “Moonrise” epicycle Mars earth Sun Moon Mercury Venus

  5. Names in History • Copernicus (Nicolas, 1473 -1543, Poland) • Heliocentric • More elegantly explains Retrograde motion of Mars • But, still used epicycles Mars Moon earth Sun Mercury Venus (Columbus)

  6. Names in History • Tycho Brahe(1546 -1601) • Controversy between Ptolemaic and Copernican views • Made observations without a telescope (Galileo 1609) • Had an assistant named…

  7. Names in History • Johannes Kepler (1571 -1630) • Analyzed data over 20 years • Identified regularities in the motions of the planets • Three Laws (empirical)…

  8. Kepler’s Three Laws • All planets move in elliptical orbits having the sun as one focus. • A line joining any planet to the sun sweeps out equal areas in equal times. • The square of the period on any planet about the sun is proportional to the cube of the planet’s mean distance from the sun. P 208

  9. Names in History • Issac Newton (1642-1727) • Cambridge “Plague days” 1665 • Began to think about gravity extending to the moon • Tea under an apple tree • His work built on those before him. He was able to derive Kepler’s Laws, p 208.

  10. F=GmM r2 P 201 • Cavendish exp. – solve for G, p 203 • Knowing period, and radius of the moon’s rotation, calculate the mass of the earth. • Knowing G and mass of the earth find the altitude a satellite will orbit over a constant longitude. • Given the general form of gravitational potential energy, find the “escape velocity” from the earth.

  11. Assignment • Groups of no more than three • Use you imagination • Write a brief creative historical fiction or loosely based short story • Draw a “poster” • Perform a skit… • I’ll require a few overachievers to work some integrals and other exciting stuff to walk the class through later. • Come back when the 9am bell rings and we’ll review them with the rest of the class. • Turn in one paper per group with names of your partners on it…and bring your fork!

  12. Ready, set, … • GO!