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[1] Early Greek Model: (500 B.C., Pythagoreans) The
seven objects (sun, 5 planets, and the moon) are attached
to seven concentric transparent spheres (at a uniform
rate).
The early Greek Model predicted a uniform motion of the
planets. What observation contradicted this prediction?

                           Retrograde Motion
A new theory was required to account for retrograde motion:


[2] Aristachus’ Theory: (~ 300 B.C.) Planets follow circular
orbits around the sun. This theory was shot down because
(a) Aristarchus did not have scientific “status” and (b)
people had a hard time believing that the earth could move
at all since it is so large.
It was noticed that during the retrograde motion of a planet,
the planet seemed BRIGHTER. What would cause that?


The planet would be brighter if it were CLOSER TO EARTH
during its retrograde motion!


A new theory was required ….
[3] Simple Epicycle Theory: (~ 100 B.C.)
The simple epicycle theory [3] could not account for the finer
details of planetary motion. It had to be modified, and this was
done by Ptolemy…
[4] Ptolemy’s Epicycle Theory: (~ 100 A.D.) In order to describe
these finer details, more than 80 epicycles were required. Also,
Earth had to be slightly off center..



     This theory
     lasted 1500
     years!!!
In the year A.D. 1543, on his deathbed, Copernicus Signed his book,
           On the Revolutions of Heavenly Spheres
The year A.D. 1543 is often taken as the “birth of modern science”.



Copernicus agreed with the Pythagoreans: a theory of the physical
world should be elegant—not complicated like Ptolemy’s epicycle
theory.


The Copernicus’ theory was not new (first was Aristarchus), but
he was able to describe retrograde motion …
[5] Copernican Heliocentric theory: sun centered, everything
tracked on circular orbits.
The heliocentric theory correctly described
retrograde motion!
We now have TWO theories that were capable of describing all of
the currently observable phenomena:

Ptolemy’s Epicycle Theory      Copernicus’ Heliocentric Theory
[4]                            [5]




                 Which one is correct???
 A better question might be: Which theory is WRONG?

We need an experiment (in the form of an observation) that
would show contrast between the theories.


         The test was the observation of the
         phases of the planet Venus.


 To give you an understanding of the meaning of
 phase, let’s look at the phases of the moon...
If Venus followed the epicycle path as formulated by Ptolemy, we
would never see the “full Venus” but we would see a “new
Venus” twice:
Remember the location of the various planets vis-à-vis Earth in
Ptolemy’s and Pre-Ptolemy’s theories




                                                Venus




                                              Sun
But if Venus went around the Sun instead of the Earth, we would
see a “full Venus” during its epicycle:
Remember the location of the various planets vis-à-vis the Sun
in Copernicus’ theory




                                     Venus




                                             Earth
Why didn’t they just check this immediately to check
which theory was correct??


Ans: They couldn’t see the phases of Venus with the
bare eye -- they needed experimentalists: they needed a
TELESCOPE!


Galileo Observed a “Full Venus” in the 1600’s, thereby
eliminating the geocentric epicycle theory.
Copernicus himself admitted that his theory did not agree with all
of the known data/measurements.

    DEFINITIONS:
    Qualitative: general behavior not directly compared to
    actual measurements (numbers).
    Quantitative: quantitative measurements compare
    numbers calculated from a theory to numbers measured
    through experiment.

So the Copernican theory could describe qualitative features
such as retrograde motion and the phases of Venus, but did NOT
compare well with quantitative measurements of orbits.
Quantitative measurements: Tycho Brahe


He developed very accurate instruments to measure the angular
positions of the stars and planets. Not with a telescope but
sighting along sticks (see figures 1.18 – 1.20 on p. 21).



He cataloged the positions of the planets for over 20 years!
Johannes Kepler joined Brahe in 1600, about a year before
Brahe’s death.


Kepler could not be an observational astronomer due to bad
eyesight, but he was a good mathematician. He analyzed Brahe’s
data in detail.

At the time (still before the observations of Venus by Galileo),
Kepler was stuck on the Epicycle and Copernican theories. He
favored the Copernican theory, but could not make the theory
match the observations!
After much work, Kepler came up with a new theory:


Circle: the set of all points equidistant from a center point.
Ellipse:
Kepler’s Theory [7]: Kepler’s Laws


Kepler’s 1st Law: Each planet move in an elliptical orbit
around the sun with the sun occupying one foci of the ellipse
(the other one is empty).

Kepler’s 2nd Law: The imaginary line connecting the planet
to the sun sweeps out equal areas in equal times

Keplers 3rd Law: The square of any planet’s period of
revolution is proportional to the cube of its mean distance
from the sun.
Kepler’s 1st Law: Each planet move in an elliptical orbit
around the sun with the sun occupying one foci of the ellipse
(the other one is empty).
Kepler’s 2nd Law: The imaginary line connecting the planet
to the sun sweeps out equal areas in equal times
Keplers 3rd Law: The square of any planet’s period of
revolution is proportional to the cube of its mean distance
from the sun.


        P2(in Earth years) = a3(in astronomical units)

       An astronomical unit the average distance
       between Earth and the Sun: 149,600,00 km.

								
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