lecture8 - LECTURE8 ApplicationsofKepler'sandNewton'sLaws

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Applications of Kepler's and Newton's Laws •Precession of the Earth •Orbits of the Comets •Orbits of Binary Stars •Discovery of More Planets •Mass of the Milky way •Masses of Galaxies •New physics? LECTURE 8
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PUBLIC VIEWING NIGHT TOMORROW NIGHT!
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                               Precession of the Earth 1.   Precession  is the conical shifting of the axis of a  rotating object, also known as wobbling. 2. The Earth is not a perfect sphere; its equatorial  diameter is about 26 miles greater than its polar  diameter. Earth’s spinning on its axis causes it to  flatten slightly at the poles. 3.  Oblateness  is a measure of the “flatness” of a  planet, calculated by dividing the difference  between the largest and smallest diameter by the  largest diameter.
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The Earth is not a perfect sphere. At the equator,  centrifugal force  reduces  gravity a little, and therefore the Earth is bigger at the Equator than at the  Pole. (This  decreases  your weight some more at the Equator. ..). Centrifugal force No centrifugal force at  Pole. Radius at equator greater than Earth's radius at Pole by 26 miles.
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The  effect of Earth not being spherical, and the Moon not being on the  Equator. A twisting force, or  TORQUE , is applied, causing a wobble.
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Precession of the Earth's rotation axis over about 26,000 years.
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Although the angle between the spin and  orbital axes stays more or less constant, its  direction  changes as it  precesses . Spin axis Orbital axis N. ecliptic pole
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Path of North  Celestial Pole  over 26,000 yrs. North Ecliptic Pole  is where the Earth's  ORBITAL axis  goes to infinity (i.e.  Is on the Celestial  Sphere)
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    Precession of the Earth (cont.) 3.  Oblateness  is a measure of the “flatness” of a  planet, calculated by dividing the difference  between the largest and smallest diameter by the  largest diameter. 4. The Earth precesses very slowly, requiring a  period of about 26,000 years. 5. As the Earth precesses, stars different from  Polaris (or no visible stars) occupy the position  near the Earth’s north celestial pole. A  corresponding effect is that the position of the  vernal equinox changes over the centuries. 
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Path of North  Celestial Pole  over a full  Precession Period  of 26,000 years.  (Rotated a bit from  previous diagram). Radius of circle  = 23.5 degrees
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Earth's precession and a future Pole Star. 26,000 years for full circle 1 day 1 year
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Cometary Orbits — Isaac Newton and  Edmund Halley 1. Newton proposed that comets orbit the Sun according to  his laws of motion and universal gravity. He concluded that 
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This note was uploaded on 04/22/2009 for the course AST 210 taught by Professor Prof.stefanmochnacki during the Fall '08 term at University of Toronto- Toronto.

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lecture8 - LECTURE8 ApplicationsofKepler'sandNewton'sLaws

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