A MORE PERFECT UNIVERSE --------------------- John Pazmino NYSkies Astronomy Inc firstname.lastname@example.org www.nyskies.org 2012 May 10
Introduction -------- On 2012 May 7 the 'Science and the arts' series of public shows presented 'Copernicus: a more perfect universe' at City University Graduate Center on Manhattan. I and other NYSkiers regularly take in these shows, usually as individuals. On this instance, due to the glatt astronomy nature of the show, NYSkies made a social event of it, with several of us seeing the show and then doing supper afterwards. The Graduate Center is in the center of Manhattan's corporate district, on Fifth Avenue and 34th St, near many transit lines and a short walk from Grand Central Terminal, Port of Authority, Penn Station. Its talks are almost always completely filled with latecomers turned away for want of seats. The presentation was done by Dava Sobel, astronomy author of many excellent books. She now is trying her skill at writing astronomy plays. This Science and the Arts program was a act-out of parts of her play in simplified form and with her running commentary. It is based on her current book about the Copernicus meeting with Rheticus.
Presentation ---------- Science and the Arts engages the theatrical firm 'Break-A-Leg' that specializes in a minimalist style of acting. Actors work on bare stage with back-curtain dropped and in street clothes. Only a bit of styling is used in selecting the contemporary clothing. Props are limited to simple chairs and tables, likely already on premises for general use. There is no elaborate scenery or costume. In most cases the same dress is worn thruout the production. This format at first looks too schoolish. It is actually extraordinarily effective because it focuses the audience on the dialog with no distraction from the surrounds. The strength of the style is in the dialog among the actors,plus commentary offstage by the author. This minimalist style is an excellent method for astronomy centers not outfitted for conventional theatrical performances. It may be employed on a simple raised stage in an auditorium or at grade-level in the front of a classroom. The acting does have to be practiced and honed to a professional level.
The play ------ The segments of Sobel's play shown were the meeting of Rheticus with Copernicus. Rheticus came from Germany on foot thru dangerous territories into Poland. He faced many travel troubles but arrived at Copernicus's house in somewhat functional state. Poland was a completely Catholic country, with Copernicus holding a higher office, a canon, in the Church. He was aware of his bishop's hate of the uprisings against the Church that brewed in other countries in Europe. While personally tolerant of other faiths, Copernicus did have to heel to his boss's orders. Rheticus converted to the new Lutheran faith, then spreading rapidly thru Germany. Poland, fearful of the competitor faith, banned Lutherans from its land and was on the lookout for Lutheran intruders. If found, they were punished by typical nediaeval methods. Rheticus wanted to learn more about the Copernicus ideas of the planetary motions. The 'De revolutionibus' was not published but some articles were circulated among astronomers and mathematicians. Due to the antagonism among the faiths, Rheticus could not seek a direct invite from Copernicus. He came on his own with no advance notice. Copernicus found him sleeping on the stoop. The play centered on the dialog between the two men during which Copernicus explains the new order of the planets. Copernicus is always wary of entertaining Rheticus in his house being that as a Church functionary he was supposed to turn the visitor over to the authorities. At first he tries to dissuade Rheticus from staying, but ends up hiding him in the cellar as a guest.
Rheticus ------ Georg Rheticus was chair of mathematics at the University of Wittenberg in present-day Germany. He also was an ardent student of astronomy. Copernicus was already well-known, before the promotion of the heliocentric theory, as a leading astronomer, mathematician, civic administrator, physician. Rheticus just had to meet Copernicus and arrived at Copernicus's home in Frauenburg, Poland, in 1539. Rheticus did many works on maths, built mathematical models and measuring devices, compiled navigation tables, and calculated planet positions. He also worked up horoscopes in astrology, as did pretty much all astronomers of the time. Rheticus knew Martin Luther as a colleague at Wittenberg and took up his new belief system. He was, like all Lutherans and other protestants, persona non grata in Catholic Poland. His trip was always threatened by capture and dispatch. He was brought up under the Ptolemaeus system of planets and wanted to learn Copernicus's heliocentric model. The Earth-centered viewpoint was part of almost all faiths, even Lutherism and others protesting against the Church. Under Copernicus's mentoring Rheticus came to accept the Sun-centered model. By the later years of Copernicus, Rheticus was compiling and editing the 'De revolutionibus' and arranged for its publication in Germany. The first copy didn't reach Copernicus until he was dying in his bed from a stroke. After seeing the book Copernicus closed his eyes and died.
Lutherism ------- Martin Luther, a monk in the Catholic Church, issued in 1517 a protest against what he saw as abusive practices. He made a series of claims, including the sale of 'indulgences' and apparent discrepancies of theology compared to the scriptures. His ideas were taken up by many others who felt abused by the local Church authorities and as a unit they broke away into their own form of Christianity. In time the faith was named Lutherism or Lutheranism. Lutherism is the first major break-away faith system, now being the main faith system in Germany, Norway, Sweden, Finland, Denmark. There is substantial Lutheran presence in all parts of the world but the center is Germany and Scandinavia. Mind that there was no 'Germany' in the 1500s as a consolidated nation as yet. There were separate smaller countries which are more or less the provinces in modern Germany. Outside Germany other groups split off from the Catholic Church in protest, often under the leadership of a specific person. Collectively, even among rival factions, these belief systems are called protestant faiths and their members are genericly Protestants. Note well that the word is 'proh-TESS-tant', the active participle. Over the centuries the accent slided to form 'PRO-tess- tant' or, a bit sloppily, 'PRO-teh-zant'. The Church was fearful of such insurrections. Poland banished Lutherans from its land. Any found were, uh, dealt with sternly. As barbaric as this policy seems today, many faiths protesting against the Church engaged in nasty practices. Recall that in the American colonies, there were ugly suppressions of alternate beliefs. These were carried out by the very people who fleed from faith-based persecution in Europe, Even to this 21st century, there are remanents of this intolerant mindset in various pockets of the United States. Most notable is the faith-based aggression against assorted alternative lifestyles.
Planetarium --------- Rheticus notices a large machine like a cabinet or hut and inquiries about it. Copernicus dismisses the query but Rheticus persists. Copernicus allows Rheticus to climb inside while he, from a crank outside, sets the machine to rotate. There is no actual machine on stage, but a phantom one that's acted out in mime. Copernicus makes like he's cranking while Rheticus Injun-squats on the floor. He squeals in delight at the scene inside the machine. He shouts that he's sitting still but the entire machine spins around him. He points out a few constellations as they pass around him. The cranking gets tiring for Copernicus. He tells Rheticus that time's up. This act in Sobel's play is entirely imaginary, like certain other segments later. There never was such a planetarium or other device in Copernicus's life. On the other hand one could have been built using materials and mechanisms known at the time, after DaVinci. Rheticus asks, after getting out how the whole room could turn so smoothly while he was sitting still in the middle. Copernicus explains that the hut was stationary on the floor. The seat span around. At first, given the crude state of machinery in the 1500s, this seems to be an unlikely achievement. It could be done by mounting the seat on a a polished bamboo bearing lubricated by lard. The crank could be attached to a spindle under the seat by a leather belt. Since the rider has to squat inside, imbalance as the seat started or stopped would be masked by the general wobbliness of the posture. The idea of this segment is to demonstrate that motion is relative. The sky turns around the Earth because the Earth rotates and orbits around the Sun. The sky does not move over a stationary Earth.
Speed of Earth ------------ During the debate about the motion of the Earth,Rheticus asks how fast must the ground move to complete one turn per day. Copernicus does an in-head calculation, figuring 25,000 'miles' for the Earth's circumference and 24 hours in the day. Earth's ground (at the equator) must speed around at about 1,000 miles per hour (1,600 KMH). In the 1500s this was a stupendous speed, one that prompts Rheticus to argue about the blast of wind this must create, like some extra fast ride on a wagon. In the 21st century this is still a humongous speed, faster than most airliners travel. Only for a brief period in the 1970s-1990s was it surpassed by the Concorde. The use of 'miles' is Sobel's fictitious feature in her play. She later explained that she wanted to use some ancient measuring system, not current metrics. There really is only one such scheme, the oldstyle British units, still familiar in the United States. Poland and Germany never employed this scheme. They lived with other peculiar units. These would be too obtuse for Americans. Rheticus then asks about the speed of Earth's orbital motion around the Sun. Here Copernicus draws a blank because he did not know the actual distance of Earth from Sun. If he did, the answer would be simply the circumference of that orbit divided by 8,766 hours, the number of hours in one year (including the 1/4 fractional day). Today we know that speed as 30 KMS (not KMH). In the De Revolutionibus Copernicus does offer a radius for the Earth's orbit of 1,000 Earth radii (rounded), this being some 6,400,000 kilometers. I forget where he got this figure but it is close to the Aristarchus value of 1,200 times Earth's radius. Using this grossly too-small value we have the orbital speed of Earth as 1.29 KPS or 4,620 KMH. These would be insanely humongous speeds for the 1500s mind to comprehend. They were not achieved by humna flight until the Space Age.
Large and small Earth ------------------- Note that Copernicus accepts the 'large Earth' school, claiming the Earth to be 40,000km circumference. The 'small Earth' school argued for a 25,000km circumference. The disparity came from disputes in measuring the linear length of angular arcs, a situation not resolved until the mid 1600s. The two factions in the late 1400s competed for the feasibility of sailing from Europe to China via Atlantic Ocean. It was just possible to build and kit out a ship to last the journey (in ignorance of the Americas) for the smaller circumference. This was Columbus's thesis for soliciting support for his trip. It was beyond possibility for the larger circumference. The ship would fall apart from want of repairs and the crew would die from want to food and drink. In the open ocean there would be no ports for replenishing the ship and crew. Columbus was as lucky as hell that when his ship was almost exhausted of supplies and provisions, he hit land in the Caribbean Sea. This land by great fortune is where China would be for the smaller Earth. Columbus thought he was in the Indies, the islands dotting thee Pacific Ocean near China. To this day we the Caribbean islands are called the West Indies, preserving their initial identity with the Indies (now East Indies) near China. If there was no American continent but only a vast Atlantic Ocean on the larger world, the voyage -- the one and only one! -- of Columbus would be but a footnote in history. Europe would probably have never again considered a westward trip to China until the era of steamships in the 19th century.
Attachment of the air ------------------- Rheticus argues that if the Earth moved the air would slip away, causing massive winds. Copernicus replies that the air is attached to the Earth and moves along with her. He's at a loss to explain why or how the air, so tenuous a substance, can adhaere to the ground but he's sure in his heart it must. Rheticus had a convincing argument. If you on a wagon hold a candle and then move forward, the smoke and flame drift backward, In the real sky clouds move about over the ground under the push of winds with no regard to a gross movement of the Earth. The quiet behavior of the air, having only local motions, is evidence for a stable Earth. Copernicus has no solid basis to elaborate why the air stays with the Earth. He merely repeats the assertion again to Rheticus. As late as the mid 1000s the behavior of the air was not well appreciated. One of Verne's stories explained how a balloon allowed his heros to escape from a comet. They waited until the comet came close enough to Earth to join their atmospheres. The balloon then was steered thru the united air to land safely back on Earth.
Relative motion ------------- Rheticus asks how the Earth can be moving around the Sun if he feels nothing of its movement. On a horse he feels the bumps and jolts under him and feels the air blowing against him and sees the scenery slide backward. Copernicus tries to describe the feeling on a ship gliding on a smooth water. Inside the ship there is no feeling of motion. This is also an imaginary scene in the play. The concept of relative motion, with this example from Galileo's 'Dialogues', just wasn't in place for Copernicus. Nor was the concept of inertia, mass, force. The lack of firm understanding of these principles hindered Copernicus's theory of the solar system. The Galileo demonstration was elegant. He postulates a ship with no windows to refer to the outside scene. In it the rider has several experiments while the ship is gliding over still calm water. I don't recall rightly but the rider has such things as a jar of bugs, a candle, a ball, some kind of toy. The bugs are released and they fly around the room exactly as if they were on solid ground. The candle flame and smoke drift upward as they do on stable ground. A game of ball plays the same as on land. The toy works the same way on the ship as on land. Galileo concludes that the behavior of natural events is the same regardless of the relative motion of the observer's platform (the ship in this case) against another platform (the land). By this argument he allows that the Earth can move, like the ship, within the outer frame of the stars and Sun, as in the Copernicus model of the solar system. This was not proof of the heliocentric theory but merely evidence that it could be valid. It is a mistake some simple accounts of Galileo make that he proved the Earth orbited the Sun. He didn't and he couldn't. He gathered observations and experiments, crucial ones, to show that the heliocentric system is plausible. His own faith in it made him state it was an actuality. This, the Galileo Principle, 300 years later became the foundation of Einstein's theory of relativity. In more concise form, all the behaviors of nature operate the same for all observers, regardless of their motions relative to each other. One of the behaviors of nature is the speed of light. This is derived from physical properties and laws and not by a mechanical measurement. As a behavior of nature it is the same for all observers.
The Sun as center --------------- Copernicus had no way to put forth a physical reason to place the planets around the Sun. The nature of the SUn was thoroly unfathomable and there was no concept of attraction, force, gravity. He put out soft arguments about the Sun being the most glorious of the orbs. He was the body that shines light and heat on Earth, making the existence of life possible on Earth. He mixed in some belief features about the Sun shining his glory like God and how we circle around God. Stuff like that. Hardly the making of good science, but there was little enough good science in the Renaissance to all short of. Why should the Earth move at all rather than let the Sun and his retinue of planets, and the stars circle Earth? COpernicus notes that under his scheme the stars had to be immensely far away in order that they still remain 'fixed stars' to observation. The stars, the celestial sphere was simply 'too big and heavy' to do the moving. Apart from Sobel's show the De Revolutionibus explains this point. Copernicus states the size of the solar system where the Sun is 1,000 times (rounded) farther away than the Earth's radius, Saturn is 10,000 times Earth's radius from the Sun, and the stars must be perhaps 100,000 times the Earth's radius away. Such immense a world could not turn around the Earth. Rheticus pleads that the Copernicus world has so much wasted space between planets, orders and orders bigger than the whole Earth. The geocentric world nests the planets in closely fitting shells. Copernicus has no strong response but again appeals to the grandeur of God and the majesty of His creation. Copernicus was skating on thin ice. With the threat of protests in Poland the Church wasn't eager to take in new ideas outside the power structure of the day. The scriptures speak of the heavens going around the Earth, never minding that this could mean an apparent or relative motion. It's best that the scriptures be taken as are than open them to invasion by alternative beliefs. Copernicus had to cool it, being himself part of the Church. He had some supporters but far too many opponents to come out in public with his heliocentric system. As it happened, he was in his death bed when the first complete copy of De Revolutionibus was placed in his hands. He probably didn't notice that, altho printed in Germany, the book had a preface added by the local protesters that declaimed the actuality of a Sun-centered world. Even Protestants were leery of, erm, revolutionary thoughts.
Astrology ------- It can be a shock to modern newcomers into the astronomy profession to discover that many of their ancestral fellows did astrology. In the 1500s there was still a general acceptance of astrology as part of astronomy, or the other way round. The times were such that astrology was an odium to be tolerated by astronomers, partly as a means of subsistence. People pay to get a fortune reading but not for learning where Mars is in the sky. And the amount earned thru astronomy lectures and shows was too infrequent and inconsistent to build a livelihood on. One aim of astronomy at that time was to refine the calculation of planet positions by tweaking the Ptolemaeus model. The value for an excentricity was adjusted, so was the longitude of a perigee, and so on. Some of these fixes were caused by real mutation of the orbits over the centuries, a fact not realized by the Mediaeval and Renaissance astronomer. He thought the revision was the result of more and better observations or errors in previous determinations. Rheticus and Copernicus discuss astrology as a casual part of their careers. Copernicus notes that his heliocentric model yields more accurate planet positions for that purpose.
De Revolutionibus Orbium Celestium --------------------------------- Copernicus's book translates as 'Concerning the revolutions of the celestial orbs'. The parsing is preposition 'De', ablative plural of 'revolutio', genitive plural of 'orbis', genitive plural of 'celestis'. Some negligent authors call the book '...bus Orbitum Cel...', perhaps by thinking of orbits. The word 'revolution' refers to the circulation of the planets. Because the book caused a mass change of human thought and collateral social and political change, the word came be mean 'sudden forceful change'. Our use of the word brings up insurrection, civil uprising, overthrow of rulers, and similar, ahem. revolutions. De Revolutionibus was written originally in Latin, the language of the time for scholarly works. It's available today in Latin and many other languages. English translations are plentiful in both print for pay and download for free. It really is a valuable exercise to read the Latin work, taken from a large library in modern reprint, to properly take in the mind of Copernicus. I realize Latin is not any where so common a language in American schools, but astronomers commonly study it on their own. The book is large and heavy, causing many early students to wonder why it's any better than the Ptolemaeus method of working the planetary motions. The maths are about as convoluted for both geocentric and heliocentric models and the results seem about equally good when compared with the sky. Copernicus made two major breakthrus in maths, explained in an early part of the book. First, he employs the Hindu notation of numbers, what we call Arabic, rather than the Roman number scheme. This immediately eased the chore of doing even simple maths if you ever tried doing long division with Roman numbers. (Go ahead, try it.) He also switched to decimal notation, also from the Hindu world, setting aside the base-60 system. This, too, vastly simplified the maths. In fact, the change to Arabic and base-10 numbers arguably saved De Revolutionibus from regressing into neglect. It also is easier for us astronomers today to walk thru the book with modern calculettes. In the Sobel show, neither point of maths was made in the presented segments of the full play. Unlike the Ptolemaeus method, the Copernicus method explicitly includes the Sun in the computation of planet positions. The Sun's motion was buried in Ptolemaeus, not put out in front as a direct part of the work. In essence, you calculate the planet position relative to the Sun and then the Earth's position relative to Sun. The combination of the two yields the place of the planet relative to Earth. Because the Sun's location, for a run of several planet calcs need be done once for the whole run, already the maths are simplfied. Under Ptolemaeus each planet needed its own peculiar computation. The parts involving the Sun were there but hidden.
Some Copernicus premises ---------------------- In spite of Copernicus's sea change in perspective for the solar system he held to a few ancient principles. These got hi into massive troubles with the planet calculations, so much so that many opponents questioned the need for the heliocentric model. He insisted that all motion be uniform circular motion, constant angular speed around a center. The center of motion did not have to be the center of the circular path of the planet. Ptolemaeus made this premise, too, to build his scheme. Copernicus, to duplicate the actual path n the sky, mounted small circle on large circles and shifted centers of motion from geometric centers of circles, much as Ptolemaeus did. Copernicus also insisted that the orbits of the planets be all in the same plane, a flat plate of rings, around the Sun. Planets in coplanar orbits would travel in the ecliptic. They don't. They wander north and south in ecliptic latitude. Both Ptolemaeus and Copernicus employ subsidiary circles mounted on the main orbit to waggle and wobble to shift the planet's latitude. Copernicus banked his calculations off of the mean Sun. It was usual to smooth out the irregular movement of the Sun by posting a phantom Sun that travels at a uniform speed thru the zodiac. The real Sun moves a bit faster in northern winter and a bit slower in northern summer. Stating positions relative to the phantom Sun made it harder to relate the computations to the sky. A secondary worksheet was needed to correct the planet to ride on the real Sun. This is a superfluous exercise today but because the character of the Sun was unknown, it could have been a ball of aethereal light. It seemed natural to leave it alone and work with a better behaved mean Sun, a geometric point that didn't shine. Kepler first demonstrated that the planet orbits are rooted on the globe of the Sun. Once he did this, in his Law #0, or #1a, Kepler broke open the way for a vastly easier and quicker method of calculating planet motions and positions. One interesting point sometimes asserted is that Copernicus predicted the phases of Venus. He didn't in the De Revolutionibus. It is true that by letting Venus be a globe like Earth it would display the Galileo pattern of phases as it rounds the Sun. It would be dicey for Copernicus to banner this prediction. It was impossible to test without the telescope, not even with daVinci's foggy blurry lens. It would be lousy science for a Renaissance gentleman, must more so for a fellow of civic authority. Maybe he did so in a private letter or article, but curiously the story didn't come out until long after Galileo found the Venus phases by telescope. Copernicus seems to say nothing about the nature of the planets. The planets while philosophicly worlds like Earth with Earth being now the third of these worlds from the Sun, they could just as well remain insubstantial points of light.
Spheres of the planets -------------------- In the prevailing model of the Earth-centered universe it was natural that the planets and stars circulate around the Earth. Thee was no need of a deeper explanation. One spinoff of this geocentric model ws the lack of external means to set the sequence of the planets upward from Earth. In which sphere or shell or ring did each planet run? This was a probelem for Prolemaeus, who confessed that there was no objective way to tell the height of each planet above Earth. They all looked like points or discs of invariant aspect no matter where on Earth they were viewed from. They displayed no parallax to form a surveying triangle on them. Ptolemaeus allowed a traditional, for Greek times, order largely based on the angular speed of each planet thru the zodiac. The Moon was obviously the fastest, rounding the zodiac in 27 days. She also was the only planet that altered shape, being mutable like the earthly world. She must be closest to Earth at the lowest elevation. In fact, she distance from Earth was actually triangulated to be about 60 Earth radii away, a figure that by the stroke of luck is the base of the maths system of the era, base-60. Where we say a radius is one, or 10 or 100, unit, the Greek said it was 60 units. The Sun passed thru the zodiac in, uh, one year, Mars in about two, Jupiter in 12, Saturn in 29. So far so good. Sun, Mars, Jupiter, Saturn stacked up over the Moon in that order. Saturn was up against the sphere of the fixed stars. Mercury and Venus were a problem. Over the long term they circulated thru the zodiac in one year pacing the Sun. Unknown to Prolemaeus and all time until Copernicus, these planets are tied to the Sun and are dragged around the zodiac with him. Mercury whacked around form morning to evening and back in 4 months while it took Venus about 19 months to do the same. Let's put Mercury next above the Moon, then Venus, Sun, and the other planets. Some astronomers figured differently and put the order as Moon, Venus, Mercury, Sun, &c. There were over the millennia pitched battles over the due and proper location of Mercury and Venus. As history fell out, the Moon-Mercury-Venus-Sun order is used to assign the names to our days of the week. With Venus the lower, the days would have a different sequence of names. Because the week of seven days in the current order was a fixture of human society for many millennia, there is no hope of ever altering it. We must keep the Ptolemaeus order of planets in the geocentric model for ever more.
Solar system ---------- The core of the Copernicus model was the creation of a true solar system, a unified mechanism that somehow held the planets in orbit around the Sun. He had no notion of what the force was to keep the orbits intact. The whole pwah of 'force' and all that was missing from human thought in the 1500s. Not even magnetism, coming into use for the marine compass, was associated with the Sun. By placing the planets around the Sun Copernicus found that the sizes of the orbits fell into fixed steps. Mercury had to be closest to the Sun about 4/10 the size of Earth's orbit. Saturn had to be farthest out, some 10 times the Earth's orbit radius from the Sun. No arbitrary scheme of orbits worked. The motions of the planets thru the zodiac plus the centering on the Sun forced not only the sequence of the orbits but the relative sizes. This brings up the illustration so often shown from De Revolutionibus. It's the solar system with neatly compacted nested orbits centered on the Sun. Each planet is equispaced outward from the Sun with lordly Latin captions. This is nothing but an illustration! It does not propose to show the correct spacing of the planets. Diagrams further in the book are drawn to correct scale, with explanation for their construction.
Conclusion -------- Only a few parts of the full play were presented at this show. They were enough to spawn many questions for Sobel, with many coming from the NYSkies delegation. She noted parts that were purely artistic freedom in order to enhance the tuitional value of the play. There was no such planetarium machine and there ws no such deliberate idea of relative motion and force. She explained about Kepler alluding to magnets in the Sun, banking of the current work of William Gilbert in 'De magnete'. That was many decades in the future. After the show let out, Sobel did a book signing for the Copernicus book. Many audience purchased a copy for her autograph. The NYSkies party went to Brendan's restaurant, a block away, for a lengthy supper and free-flowing chat about Copernicus, astronomy, science, and other sundry topics. This Dava Sobel event is the paenultimate one in the 2011-2012 running of Science and the Arts. The next season starts in October 2012. While most shows are not stricta mente related to astronomy, all are of instructive value for any City astronomer. The events are listed in NYC Events for each month during the series.