Astronomy 161:
An Introduction to Solar System Astronomy
Prof. Richard Pogge, MTWThF 9:30

Lecture 14: "The Revolutions" of Nicolaus Copernicus

"If the Lord Almighty had consulted me before embarking upon the Creation, I should have recommended something simpler."
Alfonso X El Sabio [The Wise], of Castile (1221-1284)
upon being instructed in the Ptolemaic system.

Key Ideas:

The Medieval Interruption

Copernicus' Heliocentric System:

Earth rotates on its axis once a day.
Earth & Planets revolve around the Sun.
Retained epicycles, but purged Ptolemy's equant, restoring uniform circular motion.

Scientific Objections:

"Impossibility" of a moving earth
Non-observation of stellar parallaxes

The Great Interruption

Most classical knowledge was lost, or only dimly remembered, in Europe after the fall of Rome c. 400AD.

However, the rise of a brilliant Islamic civilization in the Middle East c.750AD led to survival of classical learning in Arabic translation:

The Baghdad-Abbasid caliphs sponsored the work of systematically translating classical Greek and Syraic texts into Arabic in the 9th century (e.g., the famous "House of Wisdom" of the Baghdad Caliph Abu al-Abbas al-Ma'mun).
Islamic scholars not only preserved these older works, they also advanced knowledge themselves with original discoveries in mathematics & astronomy,
This included the invention of algebra & advancement of trigonometry, and fundamental work in optics, astronomy, geography, and medicine.

In this way, the ancient classical learning was to be nurtured and extended by Islamic society while most of contemporary Europe fell into a kind of intellectual slumber.

European Rediscovery

Spain became the center for translation of Arabic texts into Latin in the 11^th century.

Primarily the work of Jewish scholars working between the Christian and Islamic worlds.
The principal centers of this work were the magnificent libraries of Toledo and Córdoba.

As these works made their way out of Spain, Europeans slowly rediscovered their intellectual heritage:

Aristotle & Ptolemy rediscovered in the 12^th century.
Christian scholars (e.g., Aquinas) reconciled these with works with the body of Christian dogmas (13^th century)

In particular, the astronomy of Ptolemy, in the form of his Almagest (the Arabic name of the Syntaxis), was to be elevated to the almost to the level of religious dogma.

From Rediscovery to Rebirth

The period between the Middle Ages and the Renaissance were times of great social and intellectual change:

The rise of the great Universities.
The invention and spread of printing.
Challenges to the spiritual and political authority of the Roman Church by reformers.
Extended ocean voyages of discovery and trade by Portugal and Spain.

Nicolaus Copernicus (1473-1543)

Born in Torun, Poland. Educated at Krakow, Bologna, and Padua in mathematics, medicine, law, astronomy, & philosophy. Spent most of his life as a Canon at Frauenberg Cathedral in Poland.

Copernicus was a very traditional thinker:

Aristotelian in outlook.
Conservative compared to his contemporaries (e.g., the humanist philosopher Erasmus)

Copernicus' Discontents

Copernicus sought to purge Ptolemy's system of the messy expedient of the Equant:

It violated the Aristotelian notion of uniform circular motion.
He felt that a good system must please the mind as well as "preserve appearances" (i.e., make accurate predictions).

1514: Circulated a brief pamphlet, the "Commentariolus", describing a new system of the heavens.

Note:
Copernicus was not alone in his discontent with the Equant. Arabic astronomers in the 13th and 14th centuries undertook reforms to the Ptolemaic model (specifically the astronomer/mathematicians al-Tusi, al-`Urdi, and ash-Shatir), while preserving its overall geocentric character.

The Heliocentric System Revived

Copernicus revived the Heliocentric system of Aristarchus, which he did not know in detail, but rather through Archimedes' mention of it in The Sand Reckoner.

The Sun, not the Earth, is at the center.
The Earth rotates around its axis, producing the daily motions of celestial bodies.
The Earth revolves (orbits) around the Sun, producing the annual motions.

These were radical ideas for their time, but Copernicus was no radical.

De Revolutionibus Orbi Coelstium

On the Revolution of the Heavenly Orbs (1543)

The work was dedicated to Pope Paul III
It was printed with the formal approval (Imprimatur) of Church authorities.

It was not, however, a bestseller:

It was a long, difficult Latin treatise
It was not widely circulated

Despite this, his ideas got serious attention, both for and against. Far from being "the book nobody read" as it is often incorrectly portrayed, De Revolutionibus was widely read and commented upon by the scholars of the day, both for and against his ideas.

When is a revolution not a revolution?

Copernicus still clung to strict Aristotelian ideas in his heliocentric system:

It retained epicycles, if now they were centered on the Sun instead of the Earth.
It required uniform circular motion.

This made his system complex:

48 epicycles, compared to 40 in the Ptolemaic geocentric system.
but, it did not use the complicated equant.

Still only described the motions of the planets without explaining them physically.

One point, however, needs to be emphasized. The geocentric models of Ptolemy and others described in Lecture 14 introduced epicycles in order to produce the observed retrograde motion of the planets. In the Copernican system, retrograde motion comes naturally, without resort to epicycles. While Copernicus' system does not need epicycles to produce retrograde motion, because of his insistance on uniform circular motion he still had to use them in order to get his model to make accurate predictions (i.e., to "preserve appearances") .

Simple in principle

While it was more complex in detail, the Heliocentric system does lead to a considerable measure of conceptual simplification.

Herein lies its virtue. It explained naturally what was more difficult to explain in the Ptolemaic system without things being "just so" or highly contrived. Specifically...

Inferior and Superior Planets:

Mercury & Venus orbit closer to the Sun
Mars, Jupiter, & Saturn are in larger orbits.

Diagram of the Ptolemaic System (10Kb GIF)
Diagram of the Copernican Solar System (13Kb GIF)
In each, much of the detail of both systems has been stripped away to show the basic arrangement of planets and orbits. The Copernican diagram entirely omits the epicycles that Copernicus employed, opting instead for a view of the true Solar System.

Retrograde Motion:

Natural consequence of observing moving planets from a moving Earth.
By contrast, Ptolemy's system required epicycles to get retrograde motion.
Copernicus still needed epicycles to reproduce the non-uniform apparent speeds of the planets.

(Click on the image to view at full scale [Size: 11Kb])

Geometric Distances to Planets

The Heliocentric system's geometry provides a natural way to measure the distances of the planets from the Sun.

Inner Planets:

Use geometry of maximum elongation (see figure below)

(Click on the image to view at full scale [Size: 9Kb])

Outer Planets:

Measure time from opposition to quadrature
More complicated but quite tractable.

By contrast, you cannot estimate planetary distances with the Ptolemaic system by simple means. You have to find them some other, arbitrary way, if at all.

Results:

Planet Copernicus Actual

Mercury 0.376 0.387

Venus 0.719 0.723

Earth 1.00 1.00

Mars 1.52 1.52

Jupiter 5.22 5.20

Saturn 9.17 9.54

The distances from the Sun are only measured relative to the Earth-Sun distance (the Astronomical Unit).

The problem was, neither Copernicus nor anybody else at the time knew how big an AU (the mean Earth-Sun distance) was in everyday units to any degree of precision. That is a another story for another day...

Opposition to Copernicus

The Copernican Heliocentric System met with almost immediate opposition.

Religious Objections:

Luther, Calvin, & Melancthon objected on the ground that a moving Earth contradicted scriptures.
The Catholic Church was officially silent at first.

More detail about this may be found in A Brief Note on Religious Objections to Copernicus. These were of less immediate consequence and concern to Copernicus than the scientific objections.

Scientific Objections

A rotating and revolving Earth was deemed an absurdity by strict Aristotelians:

Both motions require very large speeds:

Speed of rotation at Columbus: 1280 km/hour
Orbital Speed: 107,000 km/hr = 30 km/sec!

There was no observational evidence of Earth's orbital motion:

Stellar Parallaxes were not observed.
Stars weren't brighter at opposition.

There was no observational evidence of Earth's rotation:

Daily motions are as easily explained by a fixed earth.
The motions do not require a rotating earth.

Copernicus was aware of these problems, but lacked the observational tools to address them definitively.

The most important was the non-observation of Stellar Parallaxes.

Stellar Parallaxes

Parallax is the apparent back-and-forth motion of nearby stars with respect to more distant stars caused by the changing perspective of the Earth at is orbits around the Sun.

(Click on the image to view at full scale [Size: 7Kb])

The reason it was not observed is that the stars are much farther than people thought at the time. We'll discuss this more in detail in an upcoming lecture.

This was a powerful objection to the Heliocentric system. One that had to be addressed to finally settle the issue.

The Power of Ideas

In detail, the Copernican System was flawed and unwieldy. It was arguably only an incremental improvement over the Ptolemaic system, insofar as it made somewhat better predictions of the positions of the planets than the Ptolemaic calculations of the day, and it was somewhat easier to use mathematically because it eliminated the difficult artiface of the equant.

In practice, however, it made up for this by offering a considerable measure of conceptual simplicity: many of the contrivances of the geocentric system needed to explain retrograde motions and the differences in the motions between inferior and superior planets were eliminated.

In a world of increasing change, the idea behind it was to prove powerful, and truly revolutionary.

Return to [ Unit 3 Index | Astronomy 161 Main Page ]

Planet	Copernicus	Actual
Mercury	0.376	0.387
Venus	0.719	0.723
Earth	1.00	1.00
Mars	1.52	1.52
Jupiter	5.22	5.20
Saturn	9.17	9.54