Download Brahe, Kepler

Tycho Brahe
Celestial Globe
Note the mechanism
The nobel Dane
This guy does
science in style!
Tycho demonstrating a celestial globe to
the Emperor Rudolph II in Prague
When does he
go public?
Who gave the venture capital?
Instrument and Map
Tycho Brahe’s grave; Prague
Must have been an important fellow.
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/history/brahe.html
At the entrance to the observatory
Stjärneborg
``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!''
Tycho Brahe’s 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)
Text and pictures from:
http://www.nada.kth.se/~fred/tycho.html
Tycho Brahe built a
The observatory Stjärneborg
small beautiful castle located underground
on the island Hven,
located in between
Denmark and
Sweden. This castle,
named Uraniborg,
after Urania, the
“Goddess of the sky”
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/RELATGRP/Rudolf.htm
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/RELATGRP/Rudolf.htm
Brahe’s 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.
Tycho’s
system
No Parallax of stars?
Then I’ll pick A!
Otherwise the stars
would be too far away.
I can’t think that big!
A
B
Johannes Kepler
A List of Kepler's Firsts
Graz
-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
The first
natural
Prague
laws!
Linz
Regensburg
-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/johannes.html
The Holy Roman Empire
at the time of Kepler
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 ................1620
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
From: http://www.kepler.arc.nasa.gov/johannes.html
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.
I’ve been telling people
for years (about 2000)
that everything was made
of numbers and these shapes.
Remember me? Pythagoras!
6 planets - 5 geometric spacers - GREAT
Pythagoras and Plato
would have been proud;
but it didn’t work!
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).
Where did these things come from?
It’s so beautiful,
its gotta be right!
This was the last gasp of such completely
non-mechanical ideas, as we will see.
Tycho died suddenly from a bladder infection.
Kepler got Tycho’s 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 doesn’t
need these data any more.
Tycho’s
Data
Tycho’s castle-like “home”
was destroyed 1 year after
he died.
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."
Tycho’s data
was the best by
an order of
magnitude of
any earlier data
First Kepler tried to use a circle with an equant, and adjust the
parameters. But Tycho’s data was so good (within 1 minute of a
degree) that he could see this did not fit.
I showed that
Equants
don’t work!
Tycho was
too accurate!
From http://www.phys.virginia.edu/classes
/109N/1995/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!
Kepler needed an accurate idea of earth’s orbit around the sun,
because all his observations were from the earth
Mars
I know the
timing of Mars!
I can “fix”
its relative
position
Earth-sun farthest approach
= 94.5 million miles,
speed = 18.2 miles/second
Earth
This was “an idea
of true genius!
To position something relative to the
other, you have to have two
landmarks. Tycho’s data was so
accurate, that he knew the exact
timing of Mars orbit (687.1 days).
He used the large data set of Tycho’s
data gathered over years to construct
earth’s orbit.
Kepler found:
The earth’s orbit is
essentially a
perfect circle! But
the center of the
circle is 1.5 million
miles away from
the sun.
Sun
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.
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.!!
Kepler
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!
Wrong!
I (Kepler) thought it would go
as 1/r2, just as the
intensity of light
decreases with distance
Right!
So, Kepler knew
1) the speed of the earth is not constant!!
2) the distance from the sun is not constant!!
Newton
Radius
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.
Distance/time
Because of the inverse “speed - distance”
relationship, Kepler came up with the:
“equal-area-in-equal-time” law!
Now that Kepler knew the orbit of the earth,
he could calculate the orbit of Mars.
A
Orbit of Mars (M)
inside of a circular
orbit (red). C=center,
S=position of sun
M
C
S
0.00429
Tycho’s data told him that:
AC/MC=1.00429. He also
noted (accidently) that
SM/CM=1.00429. He said
that noticing this equality “I
felt as if I had been
awakened from a sleep”
This was the result of six years of calculations
with thousands of pages, and endless mistakes
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.