The Contribution of Copernicus

 

INTRODUCTION

 

Copernicus (1473-1543) was a member of the Catholic clergy namely a deacon required to take the Holy Orders vow of chastity [1].  From this sinecure he administered secular Church affairs in return for a sustainable life on cathedral grounds. Because all Catholic Bishops were required to provide medical services to the local populace since the early fourth century A.D., Copernicus was trained also as a physician.
 

Copernicus

 

But it was his mathematical expertise that came to the attention of Catholic Church officials during his education in Italy (1496-1503) especially with his lectures on mathematical models of the heavens in Rome in 1500.  And so he was one of the experts who were asked to respond to Pope Leo X’s call to reform the calendar [2] at the Fifth Lateran Council (1512-1517).   His apparent contribution (1512-1514) was a handwritten treatise “Commentariolus” arguing for a heliocentric model with the sun at the center of the solar system but without the comprehensive geometrical details that would follow later

 

Over his lifetime, Copernicus continued to refine and circulate his ideas to an ever widening and admiring audience of fellow astronomers and Catholic Church officials [3][4].  Near the end of his life, he finally published his complete model in 1543 as “De Revolutionibus Orbium Coelestium”.

 

EARLY GREEK MODELS

 

With the invention of writing, agricultural considerations inspired Babylonian and Egyptian civilizations to create systematic astronomical tables from roughly 2000 B.C. and perhaps much earlier.  These records enabled the prediction of safe planting times and Nile floods but never advanced beyond the discovery of arithmetical correlations between solar and lunar cycles.  Starting about 1000 B.C. the Greeks built on this tradition to invent formal logic and mathematics and by about 500 B.C. had created the first geometrical models of the universe.   These come down to us notably in the writings of Plato (428-347 B.C.), Eudoxus (390/5-342/37 B.C.), and Aristotle (384-322 B.C.).

 

Aristotle noted the endless regularity of the cosmos and proposed the heavens thus consisted of an “ethereal” matter distinct from the dross of the earth which was ever changing and subject to decay.   To keep them from falling to earth, the stars and planets were supposedly attached to great crystalline spheres.  These obviously revolved around the center of the cosmos located at the center of a stationary earth.  Epicycles were added to account for the retrograde motion of the planets.

 

But with more extensive and accurate observation, slight discrepancies between the actual heavens and model predictions threatened to disrupt this comfortable world order.  And so the polymath Ptolemy (100-170 A.D.) from the center of Greek learning in Alexandria developed a model of the heavens that surpassed all others for 1400 years.  This model was purely mathematical but brilliant in both its simplicity and accuracy.

Copernicus was a firm believer in the Aristotle world model which Ptolemy had rent asunder.  There was no way interlocking crystalline spheres could move in this uneven manner without bumping into each other.


Copernicus' objections to the Geocentric model of Ptolemy (q.v. with the Earth at the center) were not in the accuracy of the Greek's predictions because his own model was both more complicated (more epicycles, i.e. he increased Ptolemy's 14 to his own 34 and finally to 48) and less accurate on average. The difficulty was that while
Ptolemy’s model was mathematically accurate it was not mechanically feasible.  And so Copernicus’ great contribution was to note that the sun-centered system was physically possible because it eliminated the "equant" which mathematical artifact could not be reconciled to rotating crystalline spheres.

 

It was only when Tycho Brahe measured the parallax to the Great Comet of 1577 and demonstrated it actually was not an atmospheric phenomena but rather moved beyond the orbit of the moon and penetrated several of these imagined spheres, that the idea of planets and stars travelling freely in space became plausible.

 

ADVANTAGES

 

His early heliocentric model asserted that the earth moved in three distinct ways [3] namely a daily rotation, a yearly revolution about the sun, and in a gradual precession of the earth’s axis which is an imaginary line through the North and South poles.

This model had the advantage of easily accommodating subtle variations in the length of the year.  In particular it explained the precession of the heavens as a nearly imperceptible rotation of the earth’s axis akin to that of spinning top.  This was simpler than requiring the entire vault of fixed stars to move as a unit and suggested the calculation of the sidereal year which otherwise had no significance [3].  When Copernicus did the arithmetic, he found this value to be a constant which further supported his model assumptions.  And his initial result was within one minute of the modern value.

 

For reference, the sidereal year is the time required for the earth to make exactly one revolution around the sun.   But the seasons are independent of the earth’s position along its orbit and are rather only a function of the tilt of the earth’s axis.  Summer begins in the Northern Hemisphere when the North Pole has the greatest tilt towards the sun.  The result is that in summer, the sun is higher in the sky and shines more directly on the earth.  In winter, the sun is lower and imparts less light and heat per unit area.

 

But because the earth’s axis precesses, the time between Summer Solstices, which is the calendar or tropical year, is shorter than the sidereal by about 20 minutes per year.  As a consequence the point along the earth’s orbit where summer begins, is on exactly the other side of the sun every 26,000/2=13,000 years. And over the centuries this correction to the calendar adds up to many days.

 

DIFFICULTIES

 

Unfortunately Copernicus’ data on planetary motion was inaccurate.  One result was his attempt to fit an imagined "non-linear" precession of Earth's axis which was the result of inaccuracies in historical records.  And he was a poor experimentalist with less than 100 recorded observations with inferior equipment and a limited interest in observation [5].  Tycho Brahe a century later actually purchased Copernicus's instruments and was famously critical as his own measurements of planetary positions were 10-100 times more accurate.  In fact Brahe’s tables were the best ever made in all of human history with naked-eye observation. And it was only this precision that allowed Kepler to distinguish between competing theories.

 

Another difficulty was that all the scientific evidence was against him especially the lack of an observed parallax. Since the stars and planets were about the same brightness, they were thought to be roughly the same distance away. Copernicus had to argue that the stars were very much brighter than planets and thus millions of times further away. This violated the "law of parsimony" or Occam's razor which states that if two theories give equal results, the simpler one has fewer ways to be wrong and should be preferred. Of course this is not a scientific or logical necessity but rather only a practical suggestion. And in hindsight it is not always correct.

 

In fact, the parallax to the nearest star, Alpha Centauri, is less than one arc-second or 1/360th of a single degree.   But in the time of Copernicus, no parallax was observed down to the limits of naked eye observation which was just slightly better than one arc-minute or 1/60th of a degree.

 

In this vein another consideration is that a heliocentric system with the Earth and Mars revolving around the sun has exactly the same interplanetary distance and direction as a geocentric one with Mars on a single epicycle with the size of the previous earth's orbit. They are geometrically identical so the heliocentric system again violates Occam's razor.

 

And in both models, both the heliocentric and the geocentric, the distance and direction from the Earth to Mars is identical and shows a retrograde behavior.  And this is also true in a similar fashion for all the planets.  This equivalence was discovered by Copernicus and a motivation for his innovations.  The distance is given below

 

 

 

PUBLICATION AT INSISTANCE OF CATHOLIC CHURCH

 

Because his earlier models were so inaccurate, Copernicus hesitated to publish despite the repeated urging of Catholic Church officials to do so (by Pope Leo X in 1514, by Albert Widmanstadt the secretary of Pope Clement VII in 1533, and especially by Catholic Cardinal Schonberog, then Archbishop of Capula, on 1 November 1536, who offered to have the heliocentric model published at his own expense, and by other Catholic Bishops and friends as well).
 
 

Finally a young math prodigy, Rheticus, fleeing his teaching position after a scandal, sought him out for room and board and assisted in the final calculations with advanced texts on geometry recently translated into Latin. These ideas were assembled in his great work of "De Revolutionibus Orbium Coelestium". The Catholic Church reviewed and authorized the publication of his heliocentric model with an official "Imprimatur" (1543) and the work was widely distributed throughout Europe.
 
Unfortunately Copernicus trusted Rheticus to get his work published and Rheticus gave the job to an outspoken critic. This militant Protestant minister, Osiander, added an unauthorized preface stating the heliocentric model was simply a mathematical convenience and didn't reflect physical reality.  Copernicus had firmly rejected this view in earlier correspondence with him. Rheticus was so distressed he destroyed the preface in every copy he could find. The local Catholic Bishop Tiedemann Giese wrote to the city fathers in Nurnberg demanding that the preface be destroyed in all extant copies and a new edition be issued which stated that the heliocentric theory was being presented as a physical fact.

 

Nor was this preface any real protection from fundamentalist Protestant interpretations of the Bible.  For as Copernicus immediately made clear from the very first chapter, his prime motivation was to create a physically realizable cosmos entirely unlike that envisioned by Ptolemy.   Indeed, every single argument throughout the body of the work amplified that thought.

 

PROTESTANT OBJECTIONS
 

All the contemporary Protestant reformers, to include Martin Luther and John Calvin, railed against Copernican heliocentrism with unbridled fury rejecting it as pure heresy. The manifestly radical suggestion of a moving earth was used to buttress their theological attack (to include rewriting the Bible as with Luther's addition of "sola fide") against the Catholic Church.

 

Martin Luther (1483-1546) explicitly condemned Copernicus as reported (on 4 June 1539 [6]) as follows:

 

“There was mention of a certain new astrologer [i.e. Copernicus whose “Little Commentary” or “Commentariolus” c. 1514 and annual almanacs were being circulated in academic circles] who wanted to prove that the earth moves and not the sky, the sun, and the moon.  [Luther then remarked] ‘This would be as if somebody were riding on a cart or in a ship and imagined that he was standing still while the earth and the trees were moving. So it goes now. Whoever wants to be clever must agree with nothing that others esteem. He must do something of his own. This is what that fellow does who wishes to turn the whole of astronomy upside down. Even in these things that are thrown into disorder.  I believe the Holy Scriptures, for Joshua commanded the sun to stand still, and not the earth.’ [q.v. Joshua 10:12]”

 

Luther also attacked the heliocentric model as heresy in his later writings as in his “Lectures on Genesis” [7].

 

John Calvin (1509-1564) went further in a sermon on 1 Corinthians in which he condemned heliocentrism as the crazy idea “that the sun does not move and that it is the earth that moves” [8] and described its Jesuit proponents in the Catholic church as “stark raving mad” and also as “possessed” by the devil. [9].

 

On the other hand Copernicus and his theories were widely praised in Catholic circles (especially by Jesuit geometricians [10] despite a few dissenters in vigorous debates within the Church) and were employed by Pope Gregory XIII to create the modern “Gregorian” calendar in 1582.  Protestants refused to accept this improvement for several centuries.  In Great Britain and its colonies it was not adopted until 1752.

 

On notable Protestant who advocated heliocentrism was the Lutheran, Kepler, although his Lutheran mentor Tycho Brahe was definitely not.   But the bottom line is that even in modern times and in keeping with their new reformed theology and rewriting of Catholic-Christian dogma, many fundamentalist Protestant sects continue to deny and agitate against most aspects of modern cosmology.

 

MATHEMATICAL TABLES

 

The first accurate model of the heavens was a geocentric one created by Ptolemy in the Greek city of Alexandra (150 A.D.). This gave by far the best predictions until the collaboration of Tycho Brahe and Johannes Kepler (1609-1619). Despite many attempts at refinement, no other work before Kepler was either as simple or as accurate. Indeed all modern planetariums still use Ptolemy’s model to display the heavens from the perspective of the earth’s surface for just these reasons.
 
With the rediscovery of ancient Greek science through Arabic translations, updated mathematical tables (Alfonsine) using the Ptolemaic model were prepared in Spain (1252) under the patronage of King Alfonso X. These gained a wider acceptance when they were translated into Latin in Paris (1320) and even more with their printed version (1483). So Copernicus' contribution was definitely not in the invention of mathematical tables nor in the concept of a mathematical model from which they were derived.


While Copernicus’ heliocentric model excited great interest, it never found much practical use outside of German speaking Europe which used it sparingly and mostly out of nationalistic pride. Nevertheless, some seven years after Copernicus’s death, the Protestant Duke Albert I of Prussia sponsored Erasmus Reinhold to publish the Prutenic Tables in 1551 based on the heliocentric model. But in an appendix, additional tables were added so more familiar and accurate results could be obtained using the geocentric calculations of Ptolemy which model was a universal and non-negotiable element of Protestant theology.
 
Considering that the Ptolemaic model was more accurate, the Alphonsine tables remained the reference of choice for greater part of Europe. It was only with the publication of the Rudolphine tables (1625-1627) based on the work of Johannes Kepler, that the phenomenal accuracy of modern times was achieved.

MISCONCEPTIONS

 

Unfortunately Galileo (1564-1642), nearly a century after Copernicus, began to write that, in accordance with longstanding Catholic principles after St. Augustine Bishop of Hippo (354-430) that reason and scientific observation cannot be in conflict with Christian faith, that perhaps glib associations of Biblical allegory with actual cosmology were wrong. Galileo went on to demand that the Catholic Church support his theories by making an official pronouncement of new dogma. This incidentally would have been the Church's very first official preference for a physical model of the heavens. Since many of Galileo's theories are now known to be wrong, especially on the tides, the Church fortuitously declined.
 
Nor did it help Galileo's credibility that he caricatured Pope Urban VIII (1568-1644), who had earlier sponsored him and his theories, as an idiot in print and in the local vernacular. Whatever the personal animosity this created, it was also seen as a subtle theological attack on the Church itself.
 
But at the height of the Protestant Reformation with the mass murder of tens to hundreds of thousands (because of relatively minor theological differences, e.g. starting with Luther's instigation of the Peasant's War (1524-1525) and escalating thereafter) coupled with ambitious land grabs by various aristocrats (especially in the many warring German states before unification centuries later) this was too much of an incitement to further violence.  And so Copernicus' work and Galileo's musings were put on the "Index" in 1616 which required special permission to read (but interestingly never in Spain) and remained there until 1835.  The heliocentric model was however continuously taught and discussed in Catholic universities without interruption.


But even in 1616 these models were by then obsolete and known to be scientifically inaccurate at best.  They were superseded by modern models as the result of the collaboration between Tycho Brahe and Kepler.

 

Despite a lot of inventive suppositions imagining a religious requirement for perfect circles demonstrating the beauty of God's creations, this only reflects an ignorance of the mathematical necessities. Indeed one ideal circle describes the majority of the daily circular motion of the heavens and is the simplest single shape to do so. And as we know from modern numerical analysis, the easiest way to make corrections is to add more circles in a "Fourier Transform" which can be rigorously demonstrated to achieve any desired degree of accuracy.

But in fact the heavens do behave in an elegantly simple and esthetically pleasing manner. Kepler was able to demonstrate this in his three laws of planetary motion. His first law states that planetary motion is the sum of two perfect circles revolving at a uniform rate about their proper centers.  Only the total sum is in any way non-uniform.  This construct is a single epicycle which is the mathematical equivalent of an ellipse with the addition of the sun at one foci. This geometrical fact was known to Copernicus but his imprecise observational data were not a match.


And so we still do believe that epicycles describe planetary motion despite uninformed comments on ellipses as being qualitatively different to the contrary.   In any event, despite theoretical musings this was not widely appreciated nor demonstrated conclusively with any observation or physical measurements until the early 1800s.  The breakthroughs were the discovery of a parallax by Friedrich Bessel in 1838 in 61 Cygni and by Foucault’a pendulum in 1851.

 

REFERENCES

1.      Edward Rosen claims that although Copernicus was ordained as deacon (i.e. a “canon” or the lowest of the three levels of Holy Orders and a necessary precursor to priesthood), he was never actually ordained as a priest, q.v. "Biography of Copernicus and “Three Copernican Treatises (New York: Octagon, 1971), page 3.  On the other hand Ernst Zinner quotes a document identifying Copernicus as being "Domherr und Priester" (canon and priest) in “Entstehung und Ausbreitung der Copperni- canischen Lehre” (Vaduz: Topos, 1978), p. 158.  Apparently this post expressly required ordination without which he could not have been appointed.

2.      Pope Leo X presided over the Fifth Lateran Council which began to reform the calendar but was interrupted by an invasion of French forces.  Copernicus did not actually attend despite later claims by Galileo but did offer written comments.

3.      Copernicus, sometime before 1514, had written an early manuscript describing the heliocentric model in his manuscript “Nicolai Copernici de Hypothesibus Motuum Coelestium a Se Constitutis Commentariolus” know more simply as the “Commentariolus” which was known throughout Krakow and Rome and part of which was referenced in the later writings of Tycho Brahe.

4.      In 1535 a certain Bernard Wapowski wrote a publisher asking that Copernicus’ almanac (for which no copies remain) as well as his heliocentric model be printed.

5.      Copernicus made three observations of Mercury, with errors of -3, -15 and -1 minutes of arc. He made one of Venus, with an error of -24 minutes. Four were made of Mars, with errors of 2, 20, 77, and 137 minutes. Four observations were made of Jupiter, with errors of 32, 51, -11 and 25 minutes. He made four of Saturn, with errors of 31, 20, 23 and -4 minutes.   All of Tycho Brahe’s measurements were accurate to better than one arc minute.   And the difference between Kepler’s original geocentric model for the orbit of Mars and the final heliocentric model was only 8 minutes of arc.

6.      ”Luther’s Works : Table Talk (Tischreden)”, Volume 54 page 358-9. Edited by Helmut T. Lehmann and published by Fortress Press (Philadelphia, PA), 1967.  The quote referenced is actually in response to the publication of the brief Commentariolus, which appeared several decades before De Revolutionibus.

7.      Martin Luther, “Luther’s Works, Volume 1, Lectures on Genesis”, ed. Jaroslav Pelikan, Concordia Publishing House, St. Louis (1958)

8.       “The Calvin Handbook” page 452.  Edited by Herman Selderhuis and published by Eerdmans (Grand Rapids, MI), 2009.

9.      “Calvin and the Natural World” page 47 by Young.

10.   One prominent Jesuit was Christoph Clavius (1537–1612) who was the leading astronomer of his day and who directed the creation of the Gregorian calendar in use today.

REFLECTIONS

1.      Aristarchus of Samos (310-230 B.C.) apparently proposed a heliocentric system but his original work did not survive and we have but a single line referencing him from Archimedes (287-212 B.C.) in “The Sand Reckoner”.  Nor is it certain as to whether this was a pagan cult worshiping the sun or something other than a hypothesis.  Nor is it true that his proposal of a sun centered model made him the subject of any religious criticism or persecution.  Aristarchus’ surviving work, “On the Sizes and Distances to the Sun and Moon”, was based on a geocentric model and  was used by both Copernicus and Tycho Brahe.

2.      Christian Europe relied on the original geocentric model of Ptolemy from 150 A.D. and made no use of any imagined Islamic improvements.  Rather the Arab contribution was to preserve the original Greek works.

3.      The contribution of Copernicus was not to make any observations which were more accurate.   His own observations were few in number and less accurate than those tabulated since well before the time of Ptolemy.  He was plagued with many inaccuracies to include those from Arab astronomers.   Rather his observations mostly served to acquaint him with the geometry of the heavens.   He did not invent mathematical models but rather struggled all his life to understand and improve models dating back many millennia.

4.      No astronomer, to include Copernicus, felt a religious obligation for perfect circles.  Rather they were a geometric necessity in order to create mechanical models.  And they were easy to use and were more than sufficient to achieve any desired degree of mathematical accuracy.  Rather the challenge was to find the correct circles and to do that, from the earliest times, deviations of all types from idealized perfection was ubiquitous.

5.      Copernicus’ heliocentric model was not a simpler model of the heavens.   Indeed it was demonstrably more complicated than Ptolemy’s by adding epicycle after epicycle and the final version was less accurate.

6.      The contribution of Copernicus was to find a model which was mechanically feasible by eliminating Ptolemy’s equant.  The heliocentric model was not a more accurate kinematic understanding but rather simplified the dynamics.  Copernicus demonstrated that planetary position and direction were precisely identical for simple versions of an earth centered and a sun centered system.

7.      The Catholic Church was at the forefront of attempts to better understand the heavens through observation and reason and invented the scientific method to do so.

8.      The Catholic Church attempted to reform the calendar and asked Copernicus to improve upon and to improve his heliocentric system.   The modern calendar was derived in part directly from the heliocentric model of Copernicus.

9.      Copernicus was a devout and respected member of the Catholic clergy for his entire life.

10.  Copernicus did not delay publication until he was on his death bed because he was afraid of censure by the Church but rather the Catholic Church repeatedly insisted he publish.  When he did publish, the Church officially approved the heliocentric model with an “Imprimatur”.

11.  When Kepler discovered the modern vision of planetary motion, he did not abandon perfect circles and epicycles but rather found that one perfect circle and one perfect epicycle (mathematically equivalent to an ellipse) were sufficient.

12.  Protestants did not accept heliocentrism but were militantly hostile and used Catholic tolerance and acceptance to attack the Christian theology maintained by the Catholic Church from the earliest times.