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Kepler’s Laws and Motion Astronomy 311 Professor Lee Carkner Lecture 5

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Tycho and Kepler Tycho Brahe Johannes Kepler was Tycho’s assistant and he used Tycho’s data to formulate three laws of planetary motion

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Kepler’s First Law Planetary orbits are ellipses with the Sun at one focus

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Kepler’s Second Law The radius vector sweeps out equal area in equal times

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Kepler’s Third Law P = a= the semimajor axis in Astronomical Units (1 AU is mean Earth-Sun distance) P 2 =a 3

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Why Do Kepler’s Laws Work? Kepler didn’t know why the planets moved In the 17th-18th century Galileo and Newton would lay the foundations of physics

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Aristotle’s Laws of Motion Aristotle (384-322 BC) was for 2000 years the leading authority on everything Earth and Water (tended to move down towards the center of the Earth) Objects move with constant velocity and heavier objects fall faster Aristotle’s ideas were accepted without testing them

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Galileo’s Laws of Motion Galileo (1564-1642) conducted experiments with balls of different materials and an inclined plane to learn about motion Objects do not fall at a constant rate, they fall faster as time goes on All objects accelerate at the same rate He could not quite prove it with his equipment

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Comet Sun 1 2 3 4 A 12 A 34 Major Axis Minor axis Focus

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Newton’s Laws of Motion Isaac Newton Newton’s Laws are universal, they apply everywhere (on the Earth, in space, on the Moon …) It is sometimes difficult to see Newton’s Laws in action because of friction, gravity, air resistance etc.

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Newton’s First Law Inertia -- Friction sometimes makes this hard to see, think of objects in space or on a sheet of ice

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Newton’s Second Law Force -- equal to the product of mass and acceleration (change in velocity): F=ma This is true even without gravity

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Newton’s Third Law Action/Reaction -- Forces occur in pairs directed in opposite directions sit in a chair and gravity pulls down and the chair pushes up

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Newton’s Law of Universal Gravitation Gravity -- F=Gm 1 m 2 /r 2 Every object in the universe attracts every other object

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Another Look at Kepler’s Laws We can now understand Kepler’s Laws in terms of Newton’s Laws Why don’t the planets fly off into space? Why don’t the planets fall into the Sun?

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Orbits

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Newton’s Versions of Kepler’s Law’s 1 2Planets move faster when closest to the Sun because of conservation of angular momentum 3Kepler: P 2 =k a 3 Newton: P 2 =[4 2 /G(m 1 +m 2 )] a 3

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Science and Philosophy Newton’s methods and attitudes defined science as something separate from philosophy He used the language of mathematics rather than rhetoric

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Next Time Read 7.5-7.6

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Summary Kepler Planetary orbits are ellipses Planets sweep out equal areas in equal times P 2 = a 3 Galileo all objects fall with uniform acceleration regardless of mass

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Newton Inertia -- an object in motion remains in motion Force -- F=ma Action/Reaction -- Every action has an equal and opposite reaction Gravity -- F=Gm 1 m 2 /r 2

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