Copernican Revolution Continued
Kepler, a German astronomer and mathematician was a mystic, believing that
he could by thought alone divine the structure of the universe. Unlike many
mystics, Kepler believed in the need for accurate observation, though he also
practiced astrology. Above all, he had complete faith in Tycho's observations,
and eventually he found the answer: the planets move around the sun, not in
circular orbits, but in ellipses. He was thus able to draw up the three famous
Laws of Planetary Motion which bear his name, the last of which was published
in 1618. By then the telescope had been invented.
To learn a more detailed account of this incredibly intuitive
astronomer, click on his image to connect to the CSEP site. For now, here is
a brief summary of his work. Kepler joined Tycho Brahe's observatory in 1600
and quickly demonstrated to Tycho that he had extraordinary academic skills.
As you read on the previous page, Kepler was denied access to Tycho's notes
and maps until his Tycho's unusual death in 1601. Upon gaining access to these
notes, it was clear to Kepler that Tycho's model was incorrect. It was also
clear that Ptolemy was quite wrong too. Why, even Copernicus was not completely
right, although he was in principle. To Kepler, Tycho's notes showed that the
Sun did occupy the central spot in the Universe, but the planets do not orbit
in perfectly circular paths. This could be considered heretical in the eyes
of religious zealots, but to Kepler, an elliptical path is no more than a circle
with two focal points. In the case of each planet, the orbital path is an ellipse
with the sun occupying one focus, while the second focus remains empty. This
simple leap removed all need for epicycle motion, explaining changing orbital
velocities and varying season lengths. Copernicus was right with the heliocentric
concept, but the need for perfect circles was unnecessary. From 1601-1618, Tycho
made his own observations and referred to Tycho's notes to develop his 3 Laws
of Planetary Motion. A copy of one of his papers is shown below.
Of great interest to the historical storyteller is Kepler's relationship with
the family of Tycho. While Tycho had an ego which was as big as anyone, Kepler
came from a more poor family background. His father was a mercenary who one
day never returned from fighting. His mother was accused of practicing witchcraft,
and Kepler battled the courts for three years to gain her freedom. He had an
extremely sharp mind but also a humble spirit. When Tycho died, all of the astronomical
instruments and papers, including the precious star maps and notes of planet
motion. Apparently when Tycho's surviving family members discovered that Kepler
was advocating the Copernican view, they sued to get the instruments and notes
back. Kepler was forced to give up the instruments, but he did keep the notes,
and from them derived his laws.
He published his first book, Astronomia Nova (New Astronomy)
in 1609 and another, Harmonice Mundi (The Harmony of the World) in 1619.
In these two books are the three laws which govern the motion of the planets
and which confirm the basic model of Copernicus. The cover page for the latter
book appears to your left. He also wrote about a nova which appeared in 1604
and was known as Kepler's star.
Kepler's Laws are listed below is short form:
1) A planet moves around the sun in an ellipse, the sun occupying
one focus of the ellipse while the other is empty. One can define an ellipse
as a curve, where the sum of the distances of the point C from the two foci,
A and B, is constant. Thus a circle is a special kind of ellipse where the two
foci come together. The father apart one spaces the foci, the greater the eccentricity
of the ellipse
2) The radius vector -- the line joining the center of the sun
to the center of the planet -- sweeps out equal areas in equal times. The planets
sweep out equal areas in equal intervals of time. This accounts for the earth
moving faster in winter when nearest the sun (perihelion) and slower in summer
when farthest from the sun (aphelion). I personally call this the Law of Equal
Pies. No matter how much differently the pie shape becomes, if the length of
time is constant, the amount of pie cut out of the ellipse remains equal. Maybe
this terminology indicates my preference for a good piece of French Silk or
homemade Apple Pie.
3) For any planet, the square of the revolution period (P) is
directly proportional to the cube of the planet's mean distance from the sun.
The square of the periodic time (measured in terms of years) is equal to the
cube of the mean distance, expressed in units of the earth's mean distance from
the sun, the so-called astronomical unit. p^2 = a^3.
It is pretty cool to think of such great discoveries and the
idea of having a physical law of nature named after one's self would be a great
honor. I thought my doctoral work on snails was pretty exciting, but few in
the science world shared my joy in researching snails or concern to their struggle
against the cold extremes of Minnesota winters. Alas, I finished my work, few
took notice, and no laws bear my name. Not even a measly asteroid. At least
they named one after my uncle Bill Albrecht.
Where are we so far in the history of the Copernican Revolution?
Martin Luther encouraged people to think differently. Instead
of blindly accepting what a priest told them the truth to be, read for yourselves
and make your own conclusions.
Copernicus dared to rethink the Ptolemaic geocentric model, proposing
a heliocentric view. Like Luther, he dared to think differently.
Tycho took detailed notes of the motion of planets against the
starry background. While the maps were excellent, he misinterpreted his notes
and drew incorrect conclusions. His failure to listen to the opinions of others
is an example of personal ego clouding good judgment.
Kepler reevaluated the work of Tycho and offered the correct
interpretation of the data. Copernicus was almost completely right. Kepler gave
some mathematical proof for the Copernican model.
You can now move forward to see how Galileo
provided visual proof of the Copernican model.
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