## LECTURE 5: PTOLEMY TO COPERNICUS

Key Questions:
• What was the Ptolemaic model of the cosmos? What was the role of epicycles in Ptolemy's model?
• What were the strengths and weaknesses of the Ptolemaic model?
• What developments laid the groundwork for the development of the Copernican model?
• What were the main elements of the Copernican model?
• What were the strengths and weaknesses of the Copernican model?
• Should a scientific theory seek to provide a "true" description of nature or just an effective way of predicting observable phenomena?

### THE PTOLEMAIC MODEL

Geocentric theory of planetary motion perfected by Hipparchus (2nd century BC) and Ptolemy (2nd century AD).

Key innovation: the epicycle

• Each planet moves on a circular epicycle.
• Center of epicycle moves in a circular path (the deferent) around Earth.
• Explains why planets are brightest when moving retrograde.

To achieve high accuracy, allow deferent center to be off Earth ("eccentric").
Also fiddle with uniform circular motion.
If necessary, can add epicycles onto epicycles.

### EVALUATION OF THE PTOLEMAIC MODEL

Strengths:

• Explains many complex behaviors with a few basic tricks.
• Gives very accurate predictions of planetary positions. Still pretty good 1500 years later.
Weaknesses:
• Complicated: many "moving parts."
• Some results appear "coincidental" --- e.g., why Mercury and Venus stay near Sun.
• Each planet treated independently; no simple way to figure out order of planets.
• Doesn't make much sense as a physical explanation.

### "SAVING THE APPEARANCES"

A strength or a weakness?

• Model flexible as measurements improve: if predicted position is inaccurate, add another epicycle.
• Allows model to achieve higher accuracy as data improve.
• Makes it almost impossible to test model.
A key philosophical question: Should a theory of the universe seek to explain the motions of the stars, Sun, Moon, and planets in true physical terms, or should it merely try to predict them accurately ("save the appearances")?

### LOSS AND REDISCOVERY

• Greek discoveries lost to Europe after fall of Rome ~400 AD.
• Preserved by Arab scholars, who also made major advances in mathematics.
• Greek texts, including Aristotle and Ptolemy, re-entered Europe via Spain in 12th century.
• Thomas Aquinas revived Aristotle, re-introduced study of physics and astronomy, but also entrenched geocentric view.

### PAVING THE WAY FOR COPERNICUS

Nicolaus Copernicus (1473-1543), Polish lawyer, physician, and church canon, first developed his heliocentric model around 1510.
After 1500 years of Ptolemy, what paved the way for a change of view?
Numerous changes in the 14th and 15th centuries.

``Scientific'' developments:

• Revived emphasis on empirical investigation (i.e., using experience and experiment) as a tool for understanding nature.
• Occam's razor: The simplest explanation consistent with the known facts is the most likely to be true. (William of Occam, 14th Century.)
• ``Impetus'' theory of motion developed by English and French scholars. A body can retain its motion without outside force. Undermined authority of Aristotle and the key argument against Earth rotation.

• Calendar reform: since day is 365.24 days instead of 365.25, Julian calendar (instituted by Julius Caesar) had slipped 11 days relative to seasons.
• Problem rooted in imperfection of Ptolemaic model. Important religious and practical significance. Eventually resolved by Gregorian Calendar in 1582.
• Reform movements within the church.
• Rise of humanism, belief in ability of humans to understand and master nature.
• Development of perspective in visual art, raising issues of illusion vs. objective reality.
• Rise of universities as centers of scholarship, somewhat independent of the church.

### THE COPERNICAN MODEL

Motivations:

• A conservative revolutionary, Copernicus holds strongly to idea of uniform circular motions in the heavens.
• Rejects Ptolemaic model because it fiddles with this assumption ("equants") --- not Aristotelian enough!
• Motivated by "philosophical" considerations of elegance, not by failure of Ptolemy's model to match data.
Basics:
• Reinvents (independently) the heliocentric model of Aristarchus.
• Daily motions reflect Earth's daily rotation.
• Moon orbits around Earth; Earth and other planets orbit around Sun.
• Order of planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn.
• Retrograde motion caused by planets overtaking each other.
Epicycles:
• To achieve accurate predictions of planetary positions, Copernicus adds epicycles to planetary orbits around Sun.
• Unlike Ptolemy, he does not use epicycles to explain retrograde motions of planets.
• Epicycles are less fundamental to the Copernican model, but still necessary.
• They will eventually be eliminated by Kepler (a century later), who shows that planetary orbits are ellipses, not circles.

### SUCCESSES OF THE COPERNICAN MODEL

Copernicus takes heliocentric model much further than Aristarchus, finding many powerful applications.

• Explains why Mercury and Venus stay close to Sun in sky.
• Also explains other "coincidences" in Ptolemaic model.
• Allows calculation of planetary orbital periods around Sun.
• Allows geometric calculations of planetary distances from Sun.
• These show nice regularity: more distant planets have longer periods, move slower.
• Easier to calculate planetary positions than with Ptolemaic model.

### EVALUATION OF THE COPERNICAN MODEL

Strengths:

• All of the "successes" listed above. Also:
• In basic form (circular orbits around Sun), explains major phenomena more simply than Ptolemaic theory.
• Treats solar system as a system, not just one planet at a time.
Weaknesses:
• Copernicus has rather weak counter to the "falling object" argument against Earth's daily rotation.
• Counters parallax argument against orbital motion of Earth by saying stars are too far away to see change in position. This argument is correct, but might be unconvincing to a skeptic.
• Accurate version of theory requires many epicycles, no simpler than Ptolemaic model.
• Somewhat less accurate than Ptolemaic model in predicting planetary positions.
From a modern perspective, Copernicus gets to largely the right answer for partly the wrong reasons (insistence on circular motions).
Not just luck: required guts, creativity, calculational skill, years of hard work.

### RECEPTION OF COPERNICAN THEORY

• Copernicus worried about reaction to his theory.
• Didn't publish in complete form until 1543, year of his death.
• Dedicated De Revolutionibus Orbium Coelestium (On the Revolutions of the Celestial Spheres) to Pope Gregory III.
• His publisher, Osiander, wrote a new preface and substituted it for Copernicus' own preface.
• Says, in essence, that model is proposed as a basis for calculation but needn't be taken seriously as a physical explanation.
• Not what Copernicus thought, though Osiander's preface may have eased the reception of De Revolutionibus.
• Catholic church reception tolerant-to-favorable until early 1600s. Copernican tables used for Gregorian calendar reform.
• Protestant leaders (Luther, Calvin) condemned as arrogant, counter to scripture.
• Mixed reception by scholars. Some enthusiastic. Some opposed. Many used for astronomical calculations without accepting as physical model.
Again the key question: Should an astronomical theory seek objective truth, or merely an adequate description of what is observed?