Department of History
University of California, Irvine
 Instructor:    Dr. Barbara J. Becker

Lecture 4.  The Copernicans.

Calendar Problems

Julian calendar year = 365.25 days; keeps civil time. 

The Julian calendar, first used in 45 BCE, is named for Julius Caesar who, after consultation with the Alexandrian astronomer Sosigenes, ordered a major reform of the unwieldy and often corrupt calendrical system then in use.  The Julian calendar was based on the cycle of the Sun's apparent motion through the fixed stars.  Designed to be self-adjusting, it needed little or no human meddling to remain tuned in to the regular cycle of the seasons.  Its rules were simple enough that everyone throughout the Empire could follow without confusion:  most years were set to be 365 days long; every year divisible by four was 366 days long.

Sidereal year = 365.256366 days (period of Earth's revolution about the Sun with respect to the stars).  Keeps star time.

The sidereal year is a little longer than the civil year (about 9 min 10 sec).  In time (over 157 years), that difference would add up to a full day.  An extra day would have to be added every 157 years to keep the civil and sidereal calendars in synchrony.

But, it turns out that things are a bit more complicated.  The Earth not only rotates on its axis -- like every spinning top -- but while it rotates, its axis of rotation exhibits a slow wobbling motion called precession.  Thus the Earth's north and south poles are not permanently fixed in their orientations with respect to the stars.  The angle of the Earth's tilt stays nearly the same (23.5°), but the direction in which they point is constantly changing.  The illustration below shows the large circular path that the north polar axis traces out on the sky as it wobbles.

About four thousand years ago, the north polar axis pointed near the star Thuban in the constellation Draco.  In recent years it has been pointing closer and closer to Polaris in Ursa Minor.  In 2017 the Earth's north polar axis will be aligned most closely to Polaris.  After that, as Earth continues its slow wobble, the north polar axis will begin pointing a little farther away from the star that has served as the Pole Star for modern navigators.  Twelve thousand years from now the north polar axis will point near the bright star Vega.  In about 26,000 years, it will point toward Polaris again.

Because of Earth's precession, a civil calendar -- even one that is well-tuned to keep pace with the sidereal year -- will drift seasonally.

Today the constellation Orion is visible during the northern hemisphere's winter months.  People living 6500 years from now will associate Orion's appearance in the night sky with the beginning of spring.  As the illustration above shows, Orion will be a familiar summer constellation in 13,000 years.  If we used a civil calendar linked to the sidereal year, all of these events would take place in the month we call December.  Regardless of the season, December would always be Orion time.

Astronomers may find the sidereal year to be a convenient unit of time to use, but it has generally proved more practical for most people to wed the civil calendar to a measure of the seasonal year -- the time from winter solstice to winter solstice, or vernal equinox to vernal equinox. 

Tropical year (period of Earth's revolution about the Sun with respect to the vernal equinox) = 365.242199 daysKeeps seasonal time.

Notice that the tropical year is shorter than the sidereal year (by 20 min 24 sec).  And it is 11 min 14 sec shorter than the civil calendar, a difference which adds up to roughly one day every 130 years.  No adjustments were made to the civil calendar Julius Caesar instituted to account for the fact that it is just a little bit too long. Over time, the difference between the civil year and the tropical year became increasingly significant:
40 BCE 360 CE 760 CE 1160 CE 1560 CE....
Mar 25
Julian Calendar
| | | | |
vernal equinox
| | | | |
day of
Mar 25 Mar 22 Mar 19 Mar 16 Mar 13....

By the 1500s, the discrepancy between the seasonal calendar and the civil calendar had become problematic, particularly for Christian church leaders: 

  • Christmas day had become locked into the civil calendar -- it is celebrated on December 25 every year.
  • Easter, on the other hand, is a "moveable feast" -- it is always celebrated on the first Sunday after the first full moon after the vernal equinox, thus its date changes from year to year.
  • Christian leaders recognized that if the calendar problem remained unresolved, the first day of spring would eventually shift into the civil calendar month of December; Christmas would become a spring festival and (on occasion) occur on the same day as Easter!
  • This serious calendar problem prompted Copernicus to conclude that something was fundamentally wrong with Ptolemy's system

Postscript on calendar reform:  The Gregorian Calendar

In 1582, Pope Gregory XIII decreed that in the Catholic Christian world, October  4, 1582 would be followed by October 15.  He took this drastic action to bring the civil and seasonal calendars back into sync by realigning the vernal equinox with a part of the civil calendar that had been traditionally associated with the beginning of spring -- around the 20th of March. 

To prevent such disparities from building up in the future, he modified the rule for determining leap years.  In the Julian calendar, every year that is divisible by four is a leap year.  But that practice clearly inserts too many days.  How many?  Over a 400-year period, it will add three extra days.  So every 400 years, three days must be eliminated to keep the civil calendar in seasonal alignment.  How to choose those three days?  Gregory decreed that century years would no longer be designated as leap years -- unless they were divisible by 400!

Nicholas Copernicus (1473-1543)
Revolutionary, or Reactionary?
Notable Events in Copernicus's Life
1473 born in Torun, Prussia (present-day Poland)
1491 enrolled at University of Cracow studied church law
1496 enrolled at University of Bologna studied Greek, philosophy, astronomy, medicine
1500 summoned to Rome for symposium on calendar reform
1501 enrolled at University of Padua; studied law and medicine
1503 returned to Torun; served as physician, cleric, scholar
1514 circulated treatise called Commentariolus (Little Commentary) among his friends

excerpts from
Commentariolus (1514)
by Nicholas Copernicus
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.

Copernicus's assumptions in Commentariolus:
  • Earth is not center of universe
  • Earth's distance from Sun is small compared to distance to stars
  • apparent motions of heavens arise from motion of Earth
  • retrograde motion is natural consequence of structure of system

Notable Events in Copernicus's Life (cont'd)
1538 Georg Joachim Rheticus (1514-1575) arrived in Torun to study with Copernicus
1540 Rheticus published Narratio Prima (First Account)
1541 Rheticus encouraged Copernicus to prepare his treatise for publication
1542 (May) manuscript taken to printer in Nuremberg

Rheticus unable to oversee publication

task taken over by Andreas Osiander

1542 (Dec) Copernicus suffered cerebral hemorrhage
1543 (May) publication of De Revolutionibus completed

Copernicus died shortly afterwards

Advantages to Copernicus's System

  • Explains variations in planetary brightness
  • Makes it possible to determine, with certainty, the proper ordering of celestial bodies in the heavens
Disadvantages to Copernicus's System
  • No sensation of motion
  • Fixed stars show no signs of parallax shift
  • Still uses circles on circles; 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?

Why change?

Determining Relative Planetary Distances from the Sun
in Copernicus's Heliocentric System

In Copernicus's system, the orbits of Mercury and Venus are closer to the Sun than Earth's.  An earthbound observer who begins to watch Venus on a daily basis when the planet first appears in the evening sky after sunset will notice the planet appear to move farther and farther away from the Sun over a period of months until the two bodies reach a maximum separation -- Venus's "angle of greatest elongation" (46°).  Then, over time, Venus will appear to move closer to the Sun once again.

The same is true for Mercury, but its angle of greatest elongation is far smaller (27°) than that of Venus.  Copernicus believed this demonstrated that Mercury was always closer to the Sun than Venus.


Here is how Venus's path around the Sun appears from far above the orbital plane: 

Distance of Venus from the Sun (Sun-Earth distance = 1 AU)

Notice that, from the point of view of an earthbound observer, Venus's greatest elongation occurs when the planet is located on the line of sight that lies tangent to its orbital path.

Copernicus argued that an astronomer who knew Venus's and Mercury's angles of greatest elongation could apply simple geometric principles to determine the relative distances of these planets from the Sun compared to that of Earth. 

NOTE:  It is important to mention here that the true distance from the Sun to the Earth was not known with any certainty until the nineteenth century.  Even so, the principles of geometry made it easy for Copernicus to use the Earth-Sun distance as a standard "yardstick" of comparison (= 1 astronomical unit) in order to calculate relative distances from the Sun to the other planets.


Mars, Jupiter and Saturn are not tied to the Sun like Mercury and Venus.  To determine relative distances from the Sun to these planets, Copernicus took advantage of his claim that the Earth itself is in motion.  Earthbound observers view the other planets from an ever-changing vantage point. 

Terrestrial surveyors use this technique to determine the distance to an inaccessible object.

Determining the distance to the tree on the other side of the canyon would be impossible if the
surveyor was restricted to viewing it from only one vantage point.  It is an easy task for a mobile
surveyor who can mark out a long baseline and then view the tree from each end of the baseline.

The surveyor uses simple geometric principles to triangulate the distance to the tree.

Copernicus reasoned that an earthbound observer could determine the relative distance from the Sun to Mars by viewing the planet from two ends of a long baseline.  The baseline is established by first making one observation of Mars's precise position with respect to the fixed stars.  One martian year later, when Mars has returned to its original position, the Earth, which moves around the Sun faster than Mars, will be located in a different point in its own orbit.  The observer will now be able to view Mars from a new and different vantage point and triangulate the relative distance from the Sun to Mars.

Distance of Mars from the Sun (Sun-Earth distance = 1 AU)

Distances of Planets from Sun in Earth Radii (and Astronomical Units)
430 (.4 AU)
9,600 (.4 AU)
820 (.75 AU)
17,000 (.72 AU)
1,100 (1 AU)
23,500 (1 AU)
1,700 (1.5 AU)
35,700 (1.5 AU)
6,000 (5.5 AU)
122,000 (5.2 AU)
10,500 (9.5 AU)
224,000 (9.5 AU)
too far to measure
6,300,000,000 to nearest star

Copernicus's system of the world from de Revolutionibus Orbium Coelestium (1543)

Which is simpler?

The world system of Copernicus....

...or that of Ptolemy?

Response to the Copernican System
from The Week, or Creation of the World (1578)
 by Guillaume du Bartas (1544-1590)

... some brain-sicks live there now-a-days,
That lose themselves still in contrary ways;
Prepostrous wits that cannot row at ease,
On the Smooth Channel of our common Seas.

And such are those (in my conceit at least)
Those Clerks that think (think how absurd a jest)
That neither Heav'ns nor Stars do turn at all,
Nor dance about this great round Earthy Ball;
But th'Earth itself, this Massy Globe of ours,
Turns roundabout once every twice-twelve hours:
And we resemble Land-bred Novices
New brought aboard to venture on the Seas;
Who, at first launching from the shore, suppose
The ship stands still, and that the ground it goes.

So twinkling Tapers, that Heav'n's Arches fill,
Equally distant should continue still.
So never should an arrow, shot upright,
In the same place upon the shooter light;
But would do (rather) as (at Sea) a stone
Aboard a Ship upward uprightly thrown;
Which not within-board falls, but in the Flood
A-stern the Ship, if so the Wind be good.

So should the Fowls that take their nimble flight
From Western Marches towards Morning's light;
And Zephyrus, that in summer time
Delights to visit Eurus in his clime;
And bullets thundered from the cannon's throat
(Whose roaring drowns the Heav'nly thunder's note)
Should seem recoil:  sithens the quick career,
That our round Earth should daily gallop here, 
Must needs exceed a hundred fold (for swift)
Birds, Bullets, Winds; their wings, their force, their drift.

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.
But sithence here, nor time, nor place doth suit,
His Paradox at length to prosecute;
I will proceed, grounding my next discourse
On the Heav'ns motions, and their constant course.

from The Apology for Raimond de Sebonde (1580)
by Michel de Montaigne (1533-1592)

[Natural] philosophy is nothing but sophisticated poetry.... 

Just as women use false teeth when their real ones drop out, and in place of a natural complexion lay on a manufactured one, and round out their figures with cotton stuffing, so ... science pays us with hypotheses which it confesses are pure invention. 

These epicycles with which astronomy moves the stars are merely the best devices it can contrive.... 

It was the stars and the heavens that were in motion for three thousand years.  Or so everyone believed.... 

Now, in our time, Copernicus has so firmly established [that the earth moves, not the stars] that it serves everything we can observe astronomically. 

What shall we conclude from this, except that it is hardly worth while to heat ourselves up over one or the other?  Who knows but what in a thousand years from now a third opinion will not supplant them both?

[As Lucretius has written (Book V, On the Nature of Things:]

Thus time as it goes round changes the seasons of things.  That which was in esteem, falls at length into utter disrepute; and then another thing mounts up and issues out of its degraded state and every day is more and more coveted and blossoms forth high in honor when discovered and is in marvellous repute with men.

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

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.

A Perfit description of the Cælestiall Orbes according to the most auncient doctrine of the Pythagoreans, latelye reuiued by Copernicus and by Geometricall Demonstrations approued (1576)

Thomas Digges (c.1546-1595)

To The Reader

Having of late (gentle reader) corrected and reformed sundry faults that by negligence in printing have crept into my father's General Prognostication, among other things I found a description or Model of the world, and situation of Spheres Celestial and Elementary, according to the doctrine of Ptolemy, whereunto all Universities (led thereto chiefly by the authority of Aristotle) have ever since then consented.  But in this our age, one rare wit (seeing the continual errors that from time to time more and more have been discovered...) has by long study, painful practice, and rare invention delivered a new Theory or model of the world, showing that the Earth rests not in the Center of the whole world, but only in the Center of this our mortal world or Globe of Elements, which environed and enclosed in the Moon's Orbit, and together with the whole Globe of mortality, is carried yearly round about the Sun, which like a king in the midst of all reigneth and gives laws of motion to the rest, spherically dispersing his glorious beams of light through all this sacred Celestial Temple.  And the earth itself to be one of the Planets ... turning every 24 hours round upon his own Center, whereby the Sun and great Globe of fixed stars seem to sway about and turn, albeit in deed they remain fixed. 

So many ways is the sense of mortal men abused, but reason and deep discourse of wit having opened these things to Copernicus ... I thought it convenient ... to publish this, to the end such noble English minds (as delight to reach above the baser sort of men) might not be altogether defrauded of so noble a part of Philosophy.  And to the end it might manifestly appear that Copernicus meant not as some have fondly accused him, to deliver these grounds of the Earth's mobility only as Mathematical principles, feigned and not as Philosophical truly averred.... 

Why shall we so much dote in the appearance of our senses, which many ways may be abused, and not suffer our selves to be directed by the rule of Reason, which the great GOD has given us as a Lamp to lighten the darkness of our understanding, and the perfect guide to lead us to the golden branch of Verity amid the Forest of errors.... 

And let us not in matters of reason be led away with authority and opinions of men....

The Globe of Elements enclosed on the Orbit of the Moon I call the Globe of Mortality because it is the peculiar Empire of death.  For above the Moon they fear not his force....

In the midst of this Globe of Mortality hangs this dark star or ball of earth and water, balanced and sustained in the midst of the thin air only with that propriety which the wonderful workman hath given at the Creation to the Center of this Globe, with his magnetical force vehemently to draw and [pull forcibly] unto itself all such other Elemental things as retain the like nature.  This ball, every 24 hours by natural, uniform and wonderful sly and smooth motion rolls round, making with his Period our natural day, whereby it seems to us that the huge infinite immoveable Globe [i.e., the sphere of the fixed stars] should sway and turn about. 

The Moon's Orbit, that houses and contains this dark star and the other mortal, changeable, corruptible Elements & Elementate things is also turned round every 29 days 31 minutes 50 seconds ... and this period may most aptly be called the Month.  The rest of the Planets' motions appear by the Picture, and shall more largely be hereafter spoken of.

Herein, good Reader,... I mean though not as a Judge to decide, yet at the mathematical bar in this case to plead, in such sort as it shall manifestly appear to the World whether it be possible upon the Earth's stability to deliver any true or probable Theory and then refer the pronouncing of sentence to the grave Senate of indifferent discreet Mathematical Readers. 

Farewell, and respect my travail as you shall see them tend to the advancement of truth and discovering the Monstrous loathsome shape of error.

Go to:
  • Astronomia Magna (1537), by Paracelsus (1493-1541)
  • The pryncyples of astronamye the whiche diligently perscrutyd is in maners pronosticacyon to the worldes end (1542?), by Andrew Boorde (1490?-1549)
  • The Discovery of a World in the Moone (1638), by John Wilkins (1614-1672)
  • The Man in the Moone:  or, A Discourse Of A Voyage Thither (1638), by Domingo Gonsales [Francis Godwin  (1562-1633)]
Weekly Readings
Lecture Notes