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Kepler’s Laws and Motion
Astronomy 311Professor Lee
CarknerLecture 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 A12A34
Major Axis
Minor axis
FocusFocus
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=Gm1m2/r2
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 Planets 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 in3 Kepler: P2=k a3
Newton: P2=[42/G(m1+m2)] a3
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
Next Time
Read 7.5-7.6
Summary
Kepler Planetary orbits are ellipses Planets sweep out equal areas in
equal times P2 = a3
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=Gm1m2/r2