#### Transcript 5Kepler2s

```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

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

Focus
Minor Focus
axis
Major Axis
3
4
1
Sun
A12
A34
Comet
2
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.

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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 in
3 Kepler: P2=k a3
Newton: P2=[42/G(m1+m2)] a3
Science and Philosophy
Until the 1700’s science and philosophy

He did not speculate whether physical
laws were good or evil or how they fit
in with a higher meaning

Next Time
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
```