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

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

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

Kepler’s First Law 

Kepler’s Second Law 

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)

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

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

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 

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

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.

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.  

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

Newton’s Third Law  Action/Reaction -- For every action there is an equal and opposite reaction  Forces occur in pairs directed in opposite directions  

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

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? 

Orbits

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

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 