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

Tycho Brahe’s grave; PragueMust have been an important fellow.

Celestial GlobeNote the mechanism

Instrument and Map

Tycho Brahe

The nobel DaneThis guy does

science in style!

When does he go public?

Who gave the venture capital?

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.

See http://csep10.phys.utk.edu/astr161/lect/history/brahe.html

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.

``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

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 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

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

Royal Summer Palace of Queen Anne, in Prague, built 1538-1563, where Tycho and Kepler worked together

Statue of Tycho Brahe and Kepler in Prague.They came together in 1600.

Pictures from: http://otokar.troja.mff.cuni.cz/RELATGRP/Rudolf.htm

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.

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.

No Parallax of stars?Then I’ll pick A!

Otherwise the starswould be too far away.I can’t think that big!

A

B

Tycho’ssystem

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/johannes.html

Johannes Kepler

The firstnaturallaws!

Prague

Linz

Regensburg

Graz

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---------1715From: 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’ve been telling people for years (about 2000)

that everything was made of numbers and these shapes.Remember me? Pythagoras!

I - Kepler - though upthe sphere-solid stuffwhile giving a math lecture in Graz.

Pythagoras and Plato would have been proud; but it didn’t work!6 planets - 5 geometric spacers - GREAT

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).

It’s 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.

Excuse me! He doesn’t need these data any more.

Tycho’sData

Tycho died suddenly from a bladder infection.

"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

Kepler got Tycho’s complete set of 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."

"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 asall motions of the clock are caused by a simple weight. And I also show how these physical causes are to begiven numerical and geometrical expression."

Then he made the assumption that this “force” was the same as acted on regular objects on the earth. These ideas are really revolutionary.

The laws controlling my juggling and the pendulum clocks are the same as for the planets!

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.

From http://www.phys.virginia.edu/classes/109N/1995/lectures/morekepl.html

I showed thatEquants

don’t work!Tycho was

too accurate!

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!

Tycho’s data was the best by an order of magnitude of any earlier data

Kepler needed an accurate idea of earth’s orbit around the sun, because all his observations were from the earth

SunEarth

Mars

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.

This was “an ideaof true genius!

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.

I know the timing of Mars!

I can “fix”its relativeposition

Earth-sun closest approach= 91.4 million miles,speed = 18.8 miles/second

Earth-sun farthest approach= 94.5 million miles, speed = 18.2 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 = 1/1.03The ratio of the corresponding speeds = 18.8/18.2 = 1.03.!!

Because the speed is the inverse of the distancesI thought the force decreased as the inverse distance. But at least I thought of a force!

I (Kepler) thought it would go as 1/r2, just as the intensity of light

decreases with distance

Wrong!

Right!

He was soclose - whew!Left something

for me!

Kepler

NewtonSo, Kepler knew1) the speed of the earth is not constant!!

2) the distance from the sun is not constant!!

Because of the inverse “speed - distance” relationship, Kepler came up with the:“equal-area-in-equal-time” law!

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.

Radius

Distance/tim

eAREA

Area/time = (Radius) x (distance/time)

= CONSTANT!!!

CSM

A

0.00429

Now that Kepler knew the orbit of the earth, he could calculate the orbit of Mars.

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”

Orbit of Mars (M)inside of a circularorbit (red). C=center,S=position of sun

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