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

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)

P2=a3

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

34 A12A34

Major Axis

Minor axis

FocusFocus

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=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

2 Planets move faster when closest to the Sun because of conservation of angular momentum

3 Kepler: P2=k a3

Newton: P2=[42/G(m1+m2)] a3

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 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