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  Planetary orbits are ellipses with the Sun at one focus

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

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

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 ( 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

Galileo’s Laws of Motion  Galileo ( ) 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

Comet Sun A 12 A 34 Major Axis Minor axis Focus

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.

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

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 --  Forces occur in pairs directed in opposite directions   sit in a chair and gravity pulls down and the chair pushes up

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 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

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

Next Time  Read

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

 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