Phys205A_Lecture33

Physics for Scientists & Engineers with Modern Physics (4th Edition)

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Chapter 13 Universal Gravitation
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Johannes Kepler (1571–1630) and Tycho Brahe (1546-1601) The synergy of the theory and experiment Several decades of observations (different times of the year) and 29 years of data analysis (triangulation was done using Earth’s orbit as a baseline)
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Ellipse The orbital paths of the planets are elliptical ( not necessarily circular), with the Sun at one focus. An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time. The three shaded areas A, B, and C are equal. Any object traveling along the elliptical path would take the same amount of time to cover the distance indicated by the three red arrows. Therefore, planets move faster when closer to the Sun. Second law Kepler’s laws (1609 ) First law
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Kepler’s third law states that: The square of a planet’s orbital period is proportional to the cube of its semi-major axis. where P is the planet’s sidereal orbital period and a is its semi-major axis
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Notes About Ellipses z F 1 and F 2
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Phys205A_Lecture33 - Chapter 13 Universal Gravitation...

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