Transcript Greek geocentric model

Chapter 2
Patterns in the Sky
(LOOKING UP/OUT)
2.1
2.2
2.3
2.4
2.5
Earth Spins on its Axis
Revolution About the Sun Leads …
Motions and Phases of the Moon
Eclipses: Passing through a Shadow
Motions of the Planets in the Sky
Let’s back up a bit and start from the beginning
We trace modern science to the Greeks.
Why?
1. Tried to understand nature without resorting to
supernatural explanations.
(debate and challenges of ideas)
2. Used mathematics to give precision to their ideas.
3. Applied reasoning to observations.
4. Applied the concept of MODELS.
Greek astronomy: their observation was:
They saw the celestial bodies move around them (Earth):
GEOCENTRIC model
Eratosthenes measures the Earth (c. 240 BC)
Plato, Aristotle ---> Earth is the center and the heavens
must be “perfect” defined as perfect spheres and
perfect circles.
Ptolemy
Ptolemaic model was the
most sophisticated version
of the geocentric model
(A.D. 100-170)
It was sufficiently accurate
to remain in use for 1,500
years!
The geocentric universe
Greek geocentric model (c. 400 B.C.)
But this model was not perfect … because of an observation
Dr. Ted Snow’s web page at The University of Colorado, Boulder
Retrograde Motion
1. Planets usually move slightly eastward
from night to night relative to the stars.
2. But sometimes they go westward relative to the stars
for a few weeks: apparent retrograde motion
This needs to be explained with the geocentric model
Dr. Ted Snow’s web page at The University of Colorado, Boulder
Epicyles
Review this brief history of ancient astronomy:
The Earth OBVIOUSLY stands still (Ptolemaic model)
therefore:
1. The Sun rises and sets, orbiting the Earth
(geocentric model)
2. The moon rises and sets (it does orbit Earth!) 
3. The stars all rise and set together, rotating about
point, centered on the Earth (geocentric model)
4.
If the Earth revolved around the Sun, the positions
of the stars would appear to change (parallax), but,
stars did not appear to exhibit parallax .
Greeks
Library of Alexandria
Islamic Science Preservation
House of Wisdom (Baghdad) 800 A.D.
European Science Renaissance
Europe (1453)
• Copernicus realized
the Solar System was
heliocentric—centered
on the Sun.
• Planets exhibit
apparent retrograde
motion due to their
distances from
Earth.
– Appear to turn
around.
Nicolas Copernicus
(1473-1543, Poland)
•
•
•
•
•
•
The center of the Solar System is near the Sun.
(published 1543)
Parallax: Earth-Sun distance <<< distance to the stars.
The rotation of the Earth accounts for the apparent daily
rotation (diurnal motion) of the stars.
The apparent annual cycle of movements of the Sun is caused
by the Earth revolving round the Sun.
The apparent retrograde (backward) motion of the planets is
caused by the motion of the Earth around the Sun
The planets follow
circular orbits around the Sun.
Recall the Ptolemeic/geocentric model
http://cygnus.colorado.edu/Animations/mars2.mov
So, in a mere 1500 years, we went from:
Ptolemic/geocentric model
Copernican/heliocentric model

http://amazing-space.stsci.edu/resources/explorations/groundup/lesson/basics/g37/graphics/g37_copernicus.gif
http://amazing-space.stsci.edu/resources/explorations/groundup/lesson/basics/g37/graphics/g37_ptolemy.gif
Tycho Brahe
(1546-1601, Denmark)
Geocentrist
• Compiled the most precise measurements of
the planets’ positions for his time, with no
telescope
• Observed a supernova (1572), and showed it
was at the distance of the stars, not close to
Earth http://www.space.com/24712-tycho-supernova-mach-1000-shock-wave.html
• He could not detect a stellar parallax, and
proposed that stars were too far away or Earth
is the center of Universe.

Earth being the center.
• Hired Kepler
Quadrant
Johannes Kepler
(1571-1630, Germany)
• Brahe assigned him the tough
problem of Mars’ retrograde motion.
(Cannot explain retrograde if
Earth is at the center)
• Found that planetary orbits were
heliocentric and elliptical (not circular)
Heliocentric = centered around the SUN
If I had believed that we could ignore these eight minutes
[of arc], I would have patched up my hypothesis accordingly.
But, since it was not permissible to ignore, those eight
minutes pointed the road to a complete reformation in
astronomy.”
1400
1500
1600
1700
Copernicus + Tycho + Kepler = Kepler’s Laws
• Kepler’s 1st Law: Planet orbits are ellipses.
• Each ellipse has two foci.
• The Sun is at one focus of a planet’s elliptical orbit.
An ellipse is characterized by:
semi-major axis (the distance between the two foci)
eccentricity
• Each orbit has a shape and a size.
• The eccentricity describes how elongated the ellipse is
and how far the foci are separated.
EARLY PERSEID METEORS: Earth is entering a broad stream of debris
from Comet Swift-Tuttle, source of the annual Perseid meteor shower.
Meteoroids in the outskirts of the stream are now hitting Earth's atmosphere,
producing as many as 10-15 meteors per hour according to worldwide
counts from the International Meteor Organization. NASA's network of all-sky
meteor cameras captured 17 Perseid fireballs on the nights of July 28th
through 30th. Here are their orbits:
• Kepler’s 2nd Law: the Law of Equal Areas.
As a planet moves around its orbit,
it sweeps out equal areas in equal times.
tB
areas:
A=B=C
slow
tA
tC
fast
tA = tB = tC
• Consequences:
 A planet will go fastest when closest to the Sun.
 It will go slowest when farthest from the Sun.
slow
tA
tC
fast
• Kepler’s 3rd Law:
A planet’s orbital
period depends
on its distance from the Sun
orbital period (P)
is the time to orbit the Sun once.
distance (a), actually the average distance
2
P
=
3
a
P is in units of years
a is in units of A.U.
Kepler’s 3rd Law
• Consequences:
– Distant planets take longer to orbit the Sun.
– Distant planets travel at slower speeds.
Summary
• How did Copernicus, Tycho, and Kepler
challenge the Earth-centered idea?
 Copernicus created a sun-centered model
 Tycho provided the data needed to improve this model
 Kepler found a model that fit Tycho’s data
• What are Kepler’s three laws of planetary
motion?
1. The orbit of each planet is an ellipse with the Sun at one focus
2. As a planet moves around its orbit it sweeps our equal areas
in equal times
3. The time for planets to orbit the Sun is related to its distance
from the Sun:
P2 = a3
Summary
Kepler’s three laws of planetary motion
1. The orbit of each planet is an ellipse with the
Sun at one focus
2. As a planet moves around its orbit it sweeps
our equal areas in equal times
3. The time for planets to orbit the Sun is related
to its distance from the Sun:
P2=a3
AstroTour
Kepler’s laws
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End of Chapter 2
Now you know !