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