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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

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Kepler’s Second Law

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Kepler’s Third Law P = the period in years (time to complete one orbit) a= the semimajor axis in Astronomical Units (1 AU is mean Earth-Sun distance)

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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 Divided the universe into 4 elements: 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 Discoveries acceleration of gravity He also believed that with no friction or gravity objects in motion would continue to move

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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 (1642-1727) used Galileo and Kepler’s Laws to discover the laws of motion and gravity 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 -- An object in motion remains in motion (an object at rest remains and rest) unless acted upon by a force.

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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 -- For every action there is an equal and opposite reaction Forces occur in pairs directed in opposite directions

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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 1Planets orbit the Sun in elliptical orbits because only one specific initial velocity would produce a circular orbit 2 Think of a skater pulling her arms in 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 Until the 1700’s science and philosophy were linked He did not speculate whether physical laws were good or evil or how they fit in with a higher meaning

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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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