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 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 (384-322 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 (1564-1642) 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 1 2 3 4 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?