Kepler’s Laws
1. Definitions: Law, Theory, etc.
2. Johannes Kepler
3. Patterns of Orbits
4. Bonus: Tycho Brahe
Fact
• Data, measurements.
– “This winter Boston got 108.6 inches of
snow.”
• Sometimes, obvious conclusions from
data.
– “Boston’s winter of 2014-2015 was the
snowiest winter on record.”
Law
• A simple relationship or formula that is
found through observations or
experiment, and describes what
happens, and may or may not address
why it happens.
• Laws can later be explained (and turn into
a theory), or can remain unexplained and
thus just be coincidences (sometimes
called an empirical law).
Bode’s Law
Well, it’s also
possible we just don’t
understand planet
formation well
enough yet…
Theory
• A hypothesis (reason why) that has
been tested many times and is
accepted by the scientific community.
Example Theories
•
•
•
•
•
•
•
Gravity
Big Bang
Nuclear fusion and fission
Germs cause disease
Dinosaurs were killed by an asteroid
Evolution
Global warming / climate change
Kepler’s Laws don’t say WHY
things happen, they only
describe WHAT happens.
Johannes
Kepler
Germany
1571-1630
http://en.wikipedia.org/wiki/Image:Johannes_Kepler_1610.jpg
Kepler = Heliocentric
Tycho Brahe’s student, used
his data to support heliocentric
Kepler’s Laws
1. Ellipses
2. Equal Areas
3. P2=a3
1. Planets orbit the Sun in
ellipses, with the Sun at
one focus
http://www.astro.virginia.edu/class/oconnell/astr121/im/ellipse-geom-NS.gif
http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/kep5.gif
Kepler’s Laws
1. Ellipses
2. Equal Areas
3. P2=a3
2. Planets’ orbits sweep out
equal areas in equal times.
http://physics.uwyo.edu/~stark/outreach/Kepler/oldareaellipse.gif
http://upload.wikimedia.org/wikipedia/commons/7/75/Kepler2.gif
2. Planets’ orbits sweep out
equal areas in equal times.
When one planet is closer to the
Sun, it moves faster than when
the same planet is farther from
the Sun.
Kepler’s Laws
1. Ellipses
2. Equal Areas
3. P2=a3
3. P2=a3
• Period - in Earth years
• Semi-major axis (average distance from
the Sun) - in AU
• One planet close to the Sun orbits in a
shorter time than a different planet
farther from the Sun.
Kepler’s Law of Periods
Multiple Versions
1. P2=a3 – around the Sun, years and AUs
2. P2=ka3 – any units, but k is different for
each unit set and for each central object
3. (Below) – true for all units, all central
objects
2
 PA   a A 
   
 PB   aB 
3
Newton’s Laws (including
gravity) explain all of Kepler’s
Laws.
Newton’s Theories explain
Kepler’s Laws
1. Ellipses
•
Gravity (F=GMm/r2) makes objects move
in this sort of shape.
2. Equal Areas
•
Conservation of Angular Momentum,
which follows from Newton’s Laws.
3. P2=a3
•
Gravity (F=GMm/r2) causes this too.
Kepler’s Laws
1. Ellipses
2. Equal Areas
3. P2=a3
Tycho Brahe
Germany
1546-1601
http://en.wikipedia.org/wiki/Image:Tycho_Brahe.JPG
Tycho Brahe = Geocentric
Best measurements of planets
Post-Test