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October 10, 2011 – 10am Class

October 10, 2011 – 10am Class. Symphony #14 in D major by William Herschel. Johannes Kepler (1564-1630). Worked as Tycho’s assistant Took Tycho’s observations when Tycho died and spent the next 29 years analyzing them. First, he wrote “ Mysterium Cosmographicum ”

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October 10, 2011 – 10am Class

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  1. October 10, 2011 – 10am Class Symphony #14 in D major by William Herschel

  2. Johannes Kepler(1564-1630) Worked as Tycho’s assistant Took Tycho’s observations when Tycho died and spent the next 29 years analyzing them First, he wrote “MysteriumCosmographicum” The orbits of the 6 known planets were described By 5 “Pythagorian” polyhedra in spheres:

  3. Eventually abandoned this model and came up with Kepler’s Three Laws of Planetary Motion Planets move in elliptical orbits (not circles), with the Sun at one focus.

  4. 2. An imaginary line connecting the Sun to any planet sweeps out equal areas in equal time.. Planets move faster when near Sun Area 1 Area 2

  5. 3. The square of a planet’s orbital period is proportional to the cube of its semi-major axis. P2(years) = A3(astronomical units) 1 Astronomical Unit = The Earth-Sun Distance The farther out a planet is in the solar system, the longer it takes for it to go around the Sun.

  6. Kepler’s Laws are empirical descriptions of the data. The don’t explain WHYthe planets move as they do.

  7. Isaac Newton (1642-1727) Bubonic Plague 1665: While home for 2 years with nothing to do he figured out Laws of motion Gravity

  8. “PhilosophiaeNaturalis Principia Mathematica” The laws explained not only why planets move as they do, but why objects in general move as they do. Newton's First Law of Motion: Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. An object at rest stays at rest; an object in motion at a constant velocity stays moving at that velocity unless a force is exerted on it. Objects with mass have INERTIA.

  9. How do we describe motion? Precise definitions to describe motion: • Speed: Rate at which object moves • Example: 10 m/s • Velocity: Speed and direction • Example: 10 m/s, due east • Acceleration: Any change in velocity units of speed/time (m/s2) speed: how many miles per hour velocity: speed and direction of motion acceleration: change in velocity, i.e. change in speed and/or change in direction of motion

  10. Momentum and Force • Momentum = mass velocity • A net force changes momentum, which generally means an acceleration (change in velocity). • Rotational momentum of a spinning or orbiting object is known as angular momentum. • Angular momentum = mass x velocity x radius

  11. Newton’s second law of motion: Force = mass  acceleration F = m a a = acceleration, ie change of velocity with time m = mass F = force

  12. Newton’s third law of motion: For every force, there is always an equal and opposite reaction force.

  13. Law of Gravitation: Fg = Force of Gravity

  14. From kepler.nasa.gov

  15. Forces of Nature: Gravity: very weak, but very long range. always attractive. always acts between any two masses Electro-Magnetism: Electric & Magnetic fields; light Result of charged particles, or magnets Long range Weak responsible for radioactive decay, e.g. beta decay -- n --> p + e + anti-neutrino the interaction of neutrinos Strong extremely strong on very short distance scales: only really important on scales of 10-13 cm holds neutrons and protons in the nuclei of atoms together

  16. James Maxwell (1831-1879) “Unified” Electricity and Magnetism  Electro-magnetic field, light Maxwell’s equations:

  17. Glashow, Weinberg and Salaam got the Nobel Prize in Physics in 1979 • for "unifying” Weak & EM forces and coming up with one theory • which describes the "Electroweak Force" Grand Unified Theories: attempt to unify Electroweak and Strong forces Theory of Everything: one theory to describe all 4 forces Plus quantum mechanics

  18. STRING THEORY everything is ultimately made of strings (sub-sub-sub atomic particles) • How big are strings? • Smaller than a Planck length, • which is about 10-33 centimeters • or about a millionth of a billionth of a billionth • of a billionth of a centimeter.

  19. Strings vibrate Closed string Open string

  20. In many string theories the Universe is 10 dimensional, with the "extra" dimensions COMPACTIFIED. All HS math geeks read a book called FLATLAND: A Romance of Many Dimensions, by Edwin A. Abbott (1884) FLATLAND: a "first person" account of life of a 2-dimensional society a radical named Arthur Square figures out that space is really 3 dimensional.

  21. So what the string theorists say is that in ordinary life we think we live in 3 dimensions, and we have to think of ways to detect the other 7. The extra-dimensions in string theory are Calabi-Yau figures:

  22. Knitted Calabi-Yau Figures

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