Tycho demonstrating a celestial globe to the Emperor Rudolph II in Prague

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Tycho Brahe
Celestial Globe Note the mechanism
Tycho demonstrating a celestial globe to the
Emperor Rudolph II in Prague
The nobel Dane
This guy does science in style!
When does he go public?
Tycho Brahes grave Prague Must have been an
important fellow.
Instrument and Map
Who gave the venture capital?
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Brahe was an extremely colorful character. He
supposedly challenged a fellow student to a duel
with swords in an argument over who was the
better mathematician. Brahe's nose was partially
cut off. Boys will be boys! He wore a gold and
silver replacement nose upon which he would
continually rub oil.
In 1572 he made observations of a supernova (an
exploding star, not a new star, as he thought).
This clearly was a major change in the sky, and
he showed it was a real star (no parallax). This
was a "star" that appeared suddenly where none
had been seen before, and was visible for about
18 months before fading from view. This showed
that the heavens were not unchanging, as in the
Aristotelian view. It made him dedicate the rest
of his life to astronomy.
See http//csep10.phys.utk.edu/astr161/lect/histor
y/brahe.html
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Consecrated to the all-good, great God and
Posterity. Tycho Brahe, Son of Otto, who realized
that Astronomy, the oldest and most distinguished
of all sciences, had indeed been studied for a
long time and to a great extent, but still had
not obtained sufficient firmness or had been
purified of errors, in order to reform it and
raise it to perfection, invented and with
incredible labour, industry, and expenditure
constructed various exact instruments suitable
for all kinds of observations of the celestial
bodies, and placed them partly in the
neighbouring castle of Uraniborg, which was built
for the same purpose, partly in these
subterranean rooms for a more constant and useful
application, and recommending, hallowing, and
consecrating this very rare and costly treasure
to you, you glorious Posterity, who will live for
ever and ever, he, who has both begun and
finished everything on this island, after
erecting this monument, beseeches and adjures you
that in honour of the eternal God, creator of the
wonderful clockwork of the heavens, and for the
propagation of the divine science and for the
celebrity of the fatherland, you will constantly
preserve it and not let it decay with old age or
any other injury or be removed to any other place
or in any way be molested, if for no other
reason, at any rate out of reverence to the
creator's eye, which watches over the universe.
Greetings to you who read this and act
accordingly. Farewell!''
At the entrance to the observatory Stjärneborg
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Tycho Brahes life -1572. He found a new star,
Stella Nova, in the formation
Cassiopeia. -1576. Tycho Brahe received the
island Hven from king Fredrik II. -1576. The
foundation of the castle Uranienborg.
Tycho Brahe studies the stars at
Uranienborg and Stjärneborg. -1597. Tycho
Brahe looses the royal support and leave the
island. Tycho goes to Wandsbech (near
Hamburg) and then to Prag. Emperor
Rudolf II gives him the castle Benatky 30 km
from Prag, but he later moves to a house in Prag
suited for observations. -1600. Johannes Kepler
is employed. -1601. Tycho Brahe dies. Kepler
writes down his last words "Ne frustra vixisse
videar" (May I not seemed to have lived in
vain)
Tycho Brahe built a small beautiful castle on the
island Hven, located in between Denmark and
Sweden. This castle, named Uraniborg, after
Urania, the Goddess of the sky
The observatory Stjärneborg located underground
Text and pictures from http//www.nada.kth.se/f
red/tycho.html
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After leaving Denmark, Brahe performed his
astronomical observations in the castle of
Benatky on the Jizera River, about 40 km north of
Prague.
Pictures from http//otokar.troja.mff.cuni.cz/REL
ATGRP/Rudolf.htm
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Statue of Tycho Brahe and Kepler in Prague. They
came together in 1600.
Royal Summer Palace of Queen Anne, in Prague,
built 1538-1563, where Tycho and Kepler worked
together
Erasmus Habermel provided for Tycho a sextant
which permitted angle readings with a precision
of 2 minutes of arc. This set hitherto
unattainable accuracy. In the Prague National
Technical Museum. This was before the invention
of the telescope.
Pictures from http//otokar.troja.mff.cuni.cz/REL
ATGRP/Rudolf.htm
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Brahes measurements were extremely accurate, and
actually gave Kepler, and others, the data they
needed to say that the earth was not at the
center of the universe. But this was not true of
Brahe himself. -He made the best measurements
that had yet been made in the search for stellar
parallax. -He found no parallax for the
stars. -He concluded 1) either the earth was
motionless at the center of the Universe 2) the
stars were so far away that their parallax was
too small to measure. Brahe could not believe
that the stars could be so far away therefore,
he concluded that the Earth was the center of
the Universe and that Copernicus was wrong.
No Parallax of stars? Then Ill pick A! Otherwise
the stars would be too far away. I cant think
that big!
Tychos system
A
B
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Johannes Kepler
A List of Kepler's Firsts -First to correctly
explain planetary motion, thereby, becoming
founder of celestial mechanics -The first
"natural laws" in the modern sense being
universal, verifiable, precise. In Astronomia
Pars Optica founder of modern optics -First to
investigate the formation of pictures with a pin
hole camera -First to explain the process of
vision by refraction within the eye -First to
formulate eyeglass designing for nearsightedness
and farsightedness -First to explain the use of
both eyes for depth perception. In his
book Dioptrice he was -First to describe real,
virtual, upright and inverted images and
magnification -First to explain the principles
of how a telescope works -First to discover and
describe the properties of total internal
reflection. From http//www.kepler.arc.nasa.gov/j
ohannes.html
Graz
The first natural laws!
Prague
Linz
Regensburg
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People and Events Contemporary to Kepler
(1571-1630) Nicolas Copernicus
1473--------1543 De Revolutionibus by
Copernicus 1543 Tycho Brahe
....................1546------1601 Galileo
Galilei .................1564---------1642
William Shakespeare .............1564------1616
Johannes Kepler ................1571------1630
Defeat of Spanish Armada .............1588
Discovery of Australia by William
Janszoon.1606 Jamestown established
.....................1607 Telescope invented
by Johann Lippershey ...1608 King James
Version of The Holy Bible ......1611 Thirty
Years War ...........................1618--1648
Pilgrims landed at Plymouth ................162
0 Dutch bought Manhattan for 24.00
...........1626 Taj Mahal built..............
..................1632-45 Harvard College
founded .......................1636 Isaac
Newton ....................................1642---
-------1727 Reign of Louis XIV
..............................1643---------1715 Fr
om http//www.kepler.arc.nasa.gov/johannes.html
The Holy Roman Empire at the time of Kepler
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In 1597 Kepler published his first important
work, The Cosmographic Mystery, where he argued
that the distances of the planets from the Sun in
the Copernican system were determined by the five
regular solids.
I - Kepler - though up the sphere-solid
stuff while giving a math lecture in Graz.
Ive been telling people for years (about 2000)
that everything was made of numbers and these
shapes. Remember me? Pythagoras!
Pythagoras and Plato would have been proud but
it didnt work!
6 planets - 5 geometric spacers - GREAT
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A closer look In the Copernican system, the
planetary orbits are six concentric circles. A
natural question to ask is why did the Creator
make the orbits the particular sizes they are?
Kepler argued that the orbits might be arranged
so that regular polygons (triangles, squares,
etc.) would just fit between adjacent orbits. But
this didn't work out---the ratios were wrong.
Then he came up with the idea that if the
universe were really three-dimensional, then the
orbits would run along spheres (rather than
circles), with the planetary orbits being along
the equators. In three dimensions, the five
spaces between concentric spheres two spheres
could just be the five regular solids! The outer
sphere passes through the vertices of the regular
solid, and the inner sphere touches all its
sides. This worked out great because there were
six planets, just right! This was really an
elegant geometric model but the distances did
not come out exactly right, but Kepler was so
sure of the rightness of his scheme, that he
blamed the discrepancies on errors in Copernicus'
tables. He titled his work Mysterium
Cosmographicum--the mystery of the universe
(explained).
Its so beautiful, its gotta be right!
Where did these things come from?
This was the last gasp of such completely
non-mechanical ideas, as we will see.
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Tycho died suddenly from a bladder infection.
Kepler got Tychos complete set of data.
"I confess that when Tycho died, I quickly took
advantage of the absence, or lack of
circumspection, of the heirs, by taking the
observations under my care, or perhaps usurping
them... Kepler
Excuse me! He doesnt need these data any more.
Tychos Data
Tychos castle-like home was destroyed 1 year
after he died.
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Kepler asked himself why the outer planets move
more slowly? Saturn's orbit is about twice the
size of Jupiter's, but Saturn takes substantially
more than twice as long to go once around. His
answer was "...we must choose between two
assumptions either the souls which move the
planets are the less active the farther the
planet is removed from the sun, or there is only
one moving soul in the center of all the orbits,
that is the sun, which drives the planet the more
vigorously the closer the planet is, but whose
force is quasi-exhausted when acting on the outer
planets because of the long distance and the
weakening of the force which it entails."
(Kepler, see Arthur Koestler, The Sleepwalkers,
Arkana Books, London, 1989 ).
Then he started to crystallize the idea of a
force between two objects "If we substitute for
the word "soul" the word "force" then we get just
the principle which underlies my physics of the
skies...For once I firmly believed that the
motive force of a planet was a soul...Yet as I
reflected that this cause of motion diminishes in
proportion to distance, just as the light of the
sun diminishes in proportion to distance from the
sun, I came to the conclusion that this force
must be something substantial-"substantial" not
in the literal sense but...in the same manner as
we say that light is something substantial,
meaning by this an unsubstantial entity emanating
from a substantial body."
The laws controlling my juggling and the
pendulum clocks are the same as for the planets!
Then he made the assumption that this force was
the same as acted on regular objects on the
earth. These ideas are really revolutionary.
"My aim is to show that the heavenly machine is
not a kind of divine, live being, but a kind of
clockwork, insofar as nearly all the manifold
motions are caused by a most simple, magnetic,
and material force, just as all motions of the
clock are caused by a simple weight. And I also
show how these physical causes are to be given
numerical and geometrical expression."
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First Kepler tried to use a circle with an
equant, and adjust the parameters. But Tychos
data was so good (within 1 minute of a degree)
that he could see this did not fit.
Tychos data was the best by an order of
magnitude of any earlier data
I showed that Equants dont work! Tycho was too
accurate!
From http//www.phys.virginia.edu/classes /109N/19
95/lectures/morekepl.html
Kepler did not like epicycles either, because
they were just descriptive. He wanted to
incorporate dynamics, as we saw above.
What force could be pushing things around an
epicycle with nothing in the center? I want
dynamics!
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Kepler needed an accurate idea of earths orbit
around the sun, because all his observations were
from the earth
Earth-sun farthest approach 94.5 million
miles, speed 18.2 miles/second
I know the timing of Mars! I can fix its
relative position
Mars
Kepler found The earths orbit is essentially a
perfect circle! But the center of the circle is
1.5 million miles away from the sun.
Sun
Earth
This was an idea of true genius!
To position something relative to the other, you
have to have two landmarks. Tychos data was so
accurate, that he knew the exact timing of Mars
orbit (687.1 days). He used the large data set of
Tychos data gathered over years to construct
earths orbit.
Earth-sun closest approach 91.4 million
miles, speed 18.8 miles/second
Actually he did not know the distances exactly
but their ratios, and this was enough.
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The ratio of the min/max earth-sun distances
91.4/94.5 1/1.03 The ratio of the
corresponding speeds 18.8/18.2 1.03.!!
He was so close - whew! Left something for me!
Because the speed is the inverse of the
distances I thought the force decreased as the
inverse distance. But at least I thought of a
force!
Kepler
I (Kepler) thought it would go as 1/r2, just as
the intensity of light decreases with distance
Wrong!
Right!
So, Kepler knew 1) the speed of the earth is not
constant!! 2) the distance from the sun is not
constant!!
Newton
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Because of the inverse speed - distance
relationship, Kepler came up with
the equal-area-in-equal-time law!
Radius
Distance/time
AREA
Area/time (Radius) x (distance/time)
CONSTANT!!!
This was the constant dynamic relationship that
Kepler was searching for! Actually he first
thought of it in relation to the nearly circular
orbit (relative to the sun) of the earth.
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Now that Kepler knew the orbit of the earth, he
could calculate the orbit of Mars.
Orbit of Mars (M) inside of a circular orbit
(red). Ccenter, Sposition of sun
Tychos data told him that AC/MC1.00429. He
also noted (accidently) that SM/CM1.00429. He
said that noticing this equality I felt as if I
had been awakened from a sleep
By staring at his figures for a long time he
realized that the orbit of Mars was an ellipse.
Remember that Cartesian coordinates had not yet
been invented.
This was the result of six years of calculations
with thousands of pages, and endless mistakes