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Lecture 30

# Lecture 30 - Last Meeting Physics 231 General University...

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1 Physics 231 General University Physics Lecture 30 Lecture 9 1 Last Meeting ± Gravitation ² Newton’s Universal Law of Gravitation Lecture 9 2 Today ± Gravity and Planetary Motion ² Kepler’s Laws Lecture 9 3 Lecture 9 4 Lecture 9 5 Kepler’s Laws, Introduction ± Johannes Kepler was a German astronomer ± He was Tycho Brahe’s assistant ² Brahe was the last of the “naked eye” astronomers ± Kepler analyzed Brahe’s data and formulated three laws of planetary motion

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2 Lecture 9 6 Kepler’s Laws ± Kepler’s First Law ² All planets move in elliptical orbits with the Sun at one focus a b Lecture 9 7 Kepler’s Laws (cont.) ± Kepler’s Second Law ² The radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervals ² Consequence of conservation of angular momentum ± Consequence of central force Lecture 9 8 Kepler’s Laws (cont.) ³ Kepler’s Third Law ² The square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbit 3 2 a T Lecture 9 9 Notes About Ellipses ± F 1 and F 2 are each a focus of the ellipse ² They are located a distance c from the center ± The longest distance through the center is the major axis ² a is the semimajor axis Lecture 9 10 Notes About Ellipses (cont.) ± The shortest distance through the center is the minor axis ² b is the semiminor axis ± The
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Lecture 30 - Last Meeting Physics 231 General University...

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