The Beginnings of Modern AstronomyThe Beginnings of Modern Astronomy

Copernicus to Kepler

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Trouble in Vatican City

• The calendar was still a mess

• Three ways to describe a year:– Julian calendar year = 365.25 days

• Civil time

– Sidereal year = 365.256366 days – Tropical year = 365.242199 days

• Seasonal time

The Problem

• Because the Earth precesses the Tropical year is 11 min 14 sec shorter than civil (Julian) calendar year

• Every 130 years the calendar is off one day

• Eventually the calendar was 10 days out of sync with the seasons

• Lunar calendar off by 4 days

Why it Mattered

• Easter and other religious holidays are based on celestial motions– First Sunday after the first full moon after the Vernal Equinox

• But the Vernal Equinox was drifting• Without calendrical reform Easter would eventually be in

December!

• Other days were important for holidays, indulgences – Holidays were an enticement for lay parishioners as a

reaction to the Reformation – A partial indulgence is granted to Christian faithful who, on

day of the liturgical feast of any saint, recites in that Saint's honor a prayer

• Some historians suggest that this calendrical need inadvertently kick-started the scientific revolution, as well as fueled the cultural rebirth known as the Renaissance

• The Church certainly did not see where this reform would lead– Correcting the positions of planets was seen

as independent of Catholic cosmology• Gregorian Calendar fix

– Oct 5 – 14, 1582 never existed!– New leap year rules established

The Big Four

• Nicholas Copernicus

• Tycho Brahe

• Johannes Kepler

• Galileo Galilei– Featured in another slideshow

• Nicholas Copernicus

• “Swedish DNA expert Marie Allen speaks at a news conference to announce the identification of remains believed to belong to Nicolaus Copernicus, in Warsaw, Poland, on Thursday, Nov. 20, 2008. Researchers believe they have identified the remains of Nicolaus Copernicus by comparing DNA from a skeleton they have found with that of hair retrieved from one of the 16th-century astronomer's books.*”

*San Francisco Gate, 11/20/2008

• B. 1473, Torun, Prussia (present-day Poland) • Well educated:

– 1491 University of Kracow, studied church law– 1496 University of Bologna, studied Greek, philosophy,

astronomy, medicine– 1501 University of Padua; studied law and medicine

• 1503 returned from Italy to Torun; served as physician, cleric, scholar

• 1514 circulated Commentariolus (Little Commentary) among his friends– 40-page non-mathematical treatise extolling heliocentrism– Possible fix for the calendar

The Little Commentary (excerpt)The planetary theories of Ptolemy and most other astronomers,

although consistent with the numerical data, seemed likewise to present no small difficulty.  For these theories were not adequate unless certain equants were also conceived ... a system of this sort seemed neither sufficiently absolute, nor sufficiently pleasing to the mind. I considered whether there could be found a more reasonable arrangement of circles....

Let no one suppose that I have gratuitously asserted, with the Pythagoreans, the motion of the earth; strong proof will be found in my exposition of the circles.

For the principal arguments by which the natural philosophers attempt to establish the immobility of the earth rest for the most part on the appearances; it is particularly such arguments that collapse here, since I treat the earth's immobility as due to an appearance.

His Assumptions:

• Heliocentrism– Not the first: Aristarchus, for one– Used existing tables,

• Did no observations himself

– Tables were no better that those Ptolemy used

• Rorbit small compared to distance to stars: parallax, relative motion

• Apparent motion of heavens due to Earth motion• Retrograde motion a consequence of the other

assumptions

95 Theses

• 1517• Schlosskirche in

Wittenberg, the church where the theses were nailed

• No fan of heliocentrism, but poorer and less vindictive than Church in Rome– Luther actually protested

heliocentrism in 1539!

Georg Joachim Rheticus (1514-1575)

• A Copernicus protégé• 1541: encouraged him to prepare his treatise

The Revolutions of the Heavenly Bodies for publication– Copernicus had essentially finished it in 1532 but

resisted publishing: “[it would] expose himself [to scorn] on account of the novelty and incomprehensibility of [the] theses”

Cardinal Nikolaus von Schönberg, Archbishop of Capua, to Copernicus in

1536• “Some years ago word reached me concerning your

proficiency, of which everybody constantly spoke. At that time I began to have a very high regard for you... For I had learned that you had not merely mastered the discoveries of the ancient astronomers uncommonly well but had also formulated a new cosmology. In it you maintain that the earth moves; that the sun occupies the lowest, and thus the central, place in the universe... Therefore with the utmost earnestness I entreat you, most learned sir, unless I inconvenience you, to communicate this discovery of yours to scholars, and at the earliest possible moment to send me your writings on the sphere of the universe together with the tables and whatever else you have that is relevant to this subject …

• 1542: manuscript taken to Nuremburg– Rheticus is too busy with his teaching responsibilities – Publication task taken over by Andreas Osiander

• 1542: Copernicus suffers a stroke• The Revolutions of the Heavenly Bodies finally

published in 1543– Copernicus dies shortly afterward

• Some historians suggest that, since his theories were heretical, publication was put late in his life lest the Inquisition investigated

• Other historians deny this, saying the Church was always behind his work– Copernicus did include a letter to POPE PAUL III in his

Revolutions.

Preface

• Osiander, a cleric, was very offended by the book, so he wrote a huge disclaimer as a preface that Copernicus didn't approve

• The shock of reading it may have been the last straw for Copernicus!

“There have already been widespread reports about the novel hypotheses of this work, which declares that the earth moves whereas the sun is at rest in the center of the universe. Hence certain scholars, I have no doubt, are deeply offended and believe that the liberal arts, which were established long ago on a sound basis, should not be thrown into confusion… For it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study. Then he must conceive and devise the causes of these motions or hypotheses about them. Since he cannot in any way attain to the true causes, he will adopt whatever suppositions enable the motions to be computed correctly from the principles of geometry for the future as well as for the past...”

my italics

Results:

• The Revolutions of the Heavenly Bodies didn’t actually fix the calendar– Some aspects made it worse

• He insisted on circular orbits, constant speed

• Didn’t actually completely do away with epicycles but eliminated the equant

• Did explain retrograde motion– And why Mercury and Venus are always near the Sun in the

sky but Mars, Jupiter, and Saturn are not– Ptolemy’s system did not explain this

• Gave very good planetary distances

Ptolemy Copernicus

Mercury 100 430 (.4 AU)

Venus 600 820 (.75 AU)

Earth 1,200 1,100 (1 AU)

Mars 5,000 1,700 (1.5 AU)

Jupiter 11,500 6,000 (5.5 AU)

Saturn 17,000 10,500 (9.5 AU)

Stars 20,000 too far to measure

Distances of Planets from Sun in Earth Radii, (and

Astronomical Units)

Disadvantages

• Still no sensation of motion • Fixed stars show no signs of parallax shift

– Copernicus therefore could not calculate their distance

• Not really simpler • Violates principle of economy; why is there

so much empty space between Saturn and the fixed stars?

• No explanation for natural motions of terrestrial elements; why do things fall?

Still, a Turning Point

• Just as Columbus’ “discovery” of the New World was a turning point:– People knew of North America before

Columbus; Astronomers had seen the heliocentric model before

• But Copernicus’ book was the tipping point for the Sun-centered theory

Occam’s Razor• 14th-century English logician and Franciscan friar William

of Ockham

• The Razor: the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the predictions of the theory

• In Latin: lex parsimoniae ("law of parsimony" or "law of succinctness"): "entia non sunt multiplicanda praeter necessitatem", or "entities should not be multiplied beyond necessity“

• Heliocentrism is geometrically simpler than geocentrism

• Some acceptance, some rejection of the Copernican theory…

Aristotle Never Dies• Most people then still subscribed to Aristotle’s

Physics– Especially the Church, since it placed Earth in the

center of the cosmos with Heaven above and Hell below

• Universities continued to teach geocentrism• Even today, most people have an Aristotelian

sense of motion– Does the Sun really rise?– Why don’t we feel the motion of us turning, or

whizzing around the Sun?

No one in his sense, or imbued with the slightest knowledge of physics, will ever think that the earth, heavy and unwieldy from its own weight and mass, staggers up and down around its own center and that of the sun; for at the slightest jar of the earth, we would see cities and fortresses, towns and mountains thrown down....

For if the earth were to be moved, neither an arrow shot straight up, nor a stone dropped from the top of a tower would fall perpendicularly, but either ahead or behind....

Lastly, all things on finding places suitable to their natures, remain there, as Aristotle writes. Since therefore the earth has been allotted a place fitting its nature, it cannot be whirled around by other motion than its own.

Theater of Universal Nature (1597) Jean Bodin (1520-1596) my italics

The Week, or Creation of the World (1578)

by Guillaume du Bartas (1544-1590)

…Arm'd with these Reasons, 'twere superfluous

T'assail the Reasons of Copernicus;

Who to salve better of the Stars th'appearance

Unto the Earth a three-fold motion warrants:

Making the Sun the Center of this All,

Moon, Earth, and Water, in one only Ball…

Thomas Digges (c.1546-1595)

Tycho Brahe

• Born in Denmark 1546 of wealthy parents, but leaned academic

• Studied at University of Copenhagen– Rhetoric and Philosophy– But always interested in Astronomy

and Astrology– Read horoscopes

• Lost his nose in a duel over who was the better mathematician

• 1572 supernova a watershed event for Brahe

• Family close to King Frederick II of Denmark

– Granted him the fiefdom of Hven (VEEN), 1576

– Brahe builds Uraniborg, the “Heavenly Castle” observatory with a great quadrant, metal, accurate to 1' of arc

• This construction distinguishes Brahe from earlier astronomers in that he actually took his data and didn’t rely on earlier tables

Uraniborg

The Observatory• Great Hall at

Uraniborg– Statues of all the

great Astronomers, including himself

• And his son, who never studied Astronomy

• Also had a backup observatory, Stjerneborg, Castle of the Stars

As an Astronomer• Tycho kept very accurate

records of 777 stars and planet locations, better than anyone before due to his metal quadrant

• Comet of 1577– calls for distant

observations to triangulate for distance

– discovers the comet was far, far away, little parallax

– not an atmospheric event as per Aristotle

• Came up with the geo-heliocentric or Tychonian model, partly to account for the “waste of space” between Saturn and the stars

• 1597 leaves Denmark to go to Prague and (crazy) Rudolf II

– 1588: Tycho’s patron king dies; King Christian IV finds him annoying and arrogant

– Rudolf II great patron of science, arts; wanted great mathematical tables named after him like 13th C. King Alphonso X

– Tycho actually tired of observing• 1599 Kepler joins him

– Tycho is envious of the young mathematician– Leary about giving him data– Gives Kepler only Mars position data

• 1601 dies of ureamia– Unusual circumstances– Kepler gets the rest of the data

Giordano Bruno

• Not one of the big four• B. 1548 in Nola, It.• Studied at the Monastery

of Saint Domenico where Thomas Aquinas had lived and taught

• Enthusiastic and frank student

• 1581: went to Paris and gave lectures on Philosophy

• Published the Shadow of Ideas– Ideas are only shadows of truth– Christianity is entirely irrational, contrary to

philosophy and it disagrees with other religions

– This did not make him popular!

• Moves to England, actively spreads the Copernican theories

• Meets with Queen Elizabeth who finds him wild, radical, and dangerous

• Fails to secure a position so he moves to Germany, did odd academic jobs

• Writes On Cause, Principle, and Unity

"This entire globe, this star, not being subject to death, and dissolution and annihilation being impossible anywhere in Nature, from time to time renews itself by changing and altering all its parts. There is no absolute up or down, as Aristotle taught; no absolute position in space; but the position of a body is relative to that of other bodies. Everywhere there is incessant relative change in position throughout the universe, and the observer is always at the center of things."

• He also writes that the stars are just other Suns with orbiting planets inhabited by intelligent beings

• This are the previous selection are extremely forward-thinking

• But also antithetical to the Catholic Church

• After 14 years wandering northern Europe he is lured to Venice with the promise of a home, then turned in to the Inquisition

• He remained in a papal prison for 7 years, refusing to recant his philosophy and writings

• Finally brought before the Grand Inquisitor Cardinal Bellarmine in Rome

• Pope Clement VIII declared Bruno to be a heretic; sentence: death

• “Perhaps you, my judges, pronounce this sentence (of death by fire) against me with greater fear than I receive it."

• Bruno was executed in 1600– But his ideas carried

on…

17th Century Cosmic PluralistsHenry More: “Essay Upon the Infinity of Worlds" (1647)

the frigid spheres that 'bout them fare;Which of themselves quite dead and barren are,But by the wakening warmth of kindly dayes,And the sweet dewie nights, in due course raiseLong hidden shapes and life, to their great Maker's praise.

John Milton: “Paradise Lost” (1667)

Her spots thou seestAs clouds, and clouds may rain, and rain produceFruits in her softened soil, for some to eatAllotted there; and other Suns, perhaps,With their attendant Moons, thou wilt descry,Communicating male and female light,Which two great sexes animate the World,Stored in each Orb perhaps with some that live

Johannes Kepler• B. 1571 at Weil-der-

Stadt, Germany• Earned a Master’s

degree from University of Tubingen, 1591

• Worked as a math instructor at Gratz

God as the Great Geometer• While teaching a

lesson on planetary conjunctions, Kepler draws a diagram to illustrate a series of conjunctions of Jupiter and Saturn. 

• A pattern emerged that he believed was a key to the "cosmic mystery"

Mysterium Cosmigraphicum, 1596 There were three things in particular about which I

persistently sought the reasons why they were such and not otherwise:  the number, the size, and the motion of the circles....  In the beginning I attacked the business by numbers, and considered whether one circle was twice another, or three times, or four times, or whatever, and how far any one was separated from another according to Copernicus.  I wasted a great deal of time on that toil, as if at a game, since no agreement appeared either in the proportions themselves or in the differences; and I derived nothing of value from that except that I engraved deeply on my memory the distances which were published by Copernicus....  If (thought I) God allotted motions to the spheres to correspond with their distances, similarly he made the distances themselves correspond with something....

His fourth lawBehold, reader, this is my

discovery and the subject matter of the whole of this little work.  For if anyone having a slight acquaintance with geometry were informed of this in so many words, there would immediately come to his mind the five regular solids with the proportion of their circumscribed spheres to those inscribed....

This accident was also the happy ending of my toil. 

Addicted to Euclid

• He adhered to the Copernican view– Especially the idea of

circular orbits

• Mystical, numerological

1599: Watershed

• Accepts a position with Tycho in Prague

• Anxious to get all the very accurate data Tycho has compiled

• But Tycho is jealous, gives Kepler only data for Mars

• Has to wait less than two years: Tycho dies, Kepler gets the notebook

Three Laws• From Tycho’s notebook, Kepler develops

three laws of planetary motion• We list them out of order from his order of

discovery1. Planets orbit the Sun in ellipses;2. Planets sweep out equal areas in equal times3. The square of the orbital period is proportional to

the cube of the mean radius• Takes him ten years to develop these laws• Aided by the invention of logarithms by

John Napier

Ellipses

• Like an oval, but mathematically precise– Around 1080 a Muslim astronomer in Toledo, Spain,

named Arzaquen suggested that planetary orbits are elliptical, but his conjecture was ignored.

• Remember his love of circles?• “Why should I mince my words?  The truth of

Nature, which I had rejected and chased away, returned by stealth through the backdoor, disguising itself to be accepted…Ah, what a foolish bird I have been!”

• Actually, a circle is a kind of ellipse!• His second discovery

Equal Areas in Equal Times, and Ellipses

The Mathy One

• The first two laws were completed by 1609, but Kepler was dissatisfied– Called elliptical orbits a “cartload of

schiesse”

• With the discovery of the third law by 1619, he was ecstatic and wrote in his book “On the Harmony of the World” (Harmonice Mundi):

“I saw the dawn 18 months ago; the bright day three months ago, and several days ago the brightest sun of a most wonderful vision. Now, nothing can restrain me. I let myself go in divine rage. I defy human beings with contempt in this; I have stolen the golden vessels of the Egyptians to create from them a sacred place from my God, far from the borders of Egypt. If you are angry with me, I shall bear it; the die is cast; I write for my contemporaries, or it does not matter for the future. Perhaps, my book will not have readers for 100 years but God himself has waited 6000 years for someone to gaze upon his creation with understanding.”

But Why?

• Kepler had no mathematics to explain why the planets orbited the way they did– That would have to wait for Newton

• His laws explain nothing about why things fall to the ground

• He had a belief that gravity was like magnetism

• He did postulate the idea of inertia

Later in Life

• 1627: published Rudolphine Tables, the first astronomical tables based on Kepler's new system of elliptical orbits– These are the tables that Tycho wanted named

after him– Frontispiece to follow

Hven

Tycho pointingTo the book

Hipparchus

PtolemyCopernicus

To Be A Copernican• Not only to accept that the Earth orbits the Sun• The new Physics for this system requires:

– New instruments– New techniques– New criteria for judging validity– In short, a new way of doing science

• A sea-change from Aristotle– Abandon natural and violent motion– Abandon the Earth as center– Incur the wraith of Rome, as Bruno did

• There will be a profound change in academia but it will take 200 years to complete

Letter From Johannes Kepler to Galileo Galilei, Delivered in April

of 1610:• “There will certainly be no lack of human pioneers

when we have mastered the art of flight. Who would have thought that navigation across the vast ocean is less dangerous and quieter than in the narrow, threatening gulfs of the Adriatic , or the Baltic, or the British straits? Let us create vessels and sails adjusted to the heavenly ether, and there will be plenty of people unafraid of the empty wastes. In the meantime, we shall prepare, for the brave sky travelers, maps of the celestial bodies - I shall do it for the moon, you, Galileo, for Jupiter.”