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

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

3. Kepler’s First Law 

4. Kepler’s Second Law 

5. 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)

6. 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

7. 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

8. 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 

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

10. 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.

11. 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.  

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

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

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

15. 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? 

16. Orbits

17. 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

18. 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 

19. Next Time  Read 7.5-7.6

20. 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

21.  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