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

When does the full moon rise? a)Noon b)Sunset c)Midnight d)Sunrise e)The time that the full moon rises is different every month

If you were standing on the moon during a penumbral lunar eclipse, what would the sun look like? a)It would look normal b)It would be partially blocked by the Earth c)It would be completely blocked by the Earth d)It would be completely blocked by the Earth but some sunlight would filter around through the Earth’s atmosphere e)It would depend on the phase of the moon

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