Summary, and 20-20 Hindsight
Let’s recap.
- Ptolemy’s deferents and epicycles result from simple geometric transformations to the heliocentric system.
- Inner planet: deferent = Sun’s orbit, epicycle = planet’s orbit.
- Outer planet: epicycle = Sun’s orbit, deferent = planet’s orbit.
- Scaling confuses things further.
- Ptolemy’s eccentric circles approximate Kepler’s ellipses.
- Ptolemy’s equant speed law approximates Kepler’s area speed law.
- The planets lie nearly in the plane of the ecliptic. We’ll see later how Ptolemy handled the discrepancies.
I’ve been defending Ptolemy so far: after a fashion, his system is “nearly equivalent” to the Copernican system or even to Kepler’s. But heliocentrism is still better!1 Kepler tallied its advantages in his first major work, the Mysterium cosmographicum (1596). At that point, ellipses lay in Kepler’s future. But even the simple heliocentric system of post 2—circular orbits, constant speed, centered on the Sun, all in the same plane—explains several mysterious features of the Ptolemaic system:
- The deferent of each inner planet revolves in one Earth year; moreover, its epicycle’s center remains in a straight line with the Sun.
- The epicycle of each outer planet revolves in one Earth year; moreover, the line from the planet to its epicycle’s center remains always parallel to the line from the Earth to the Sun.
- Outer planets always display retrograde motion when they are opposite to the Sun (along the zodiac).
- For outer planets, as the deferents get bigger, the epicyles get smaller in angular size (as viewed from Earth), and hence their retrograde motion appears smaller.
As Koyré puts it, “[Kepler’s diagrams] reveal the (Copernican) reality underlying the (Ptolemaic) appearances; they explain the latter and substitute comprehension for astonishment.”
(1) and (2) follow immediately from the three figures of post 2, and (3) from the account of retrograde motion as a kind of optical illusion: as the Earth overtakes Mars (or Jupiter or Saturn) in its orbit, Mars appears to go backwards. But that happens precisely when the Sun and Mars are on opposite sides of the Earth. (4) follows once we realize that the epicycle of an outer planet is the Sun’s orbit (or Earth’s orbit) in disguise. As we go from Mars to Jupiter to Saturn, we see the epicyle from farther and farther away, so it looks smaller and smaller. Now that’s assuming no scaling, so the epicycles are the same size. But scaling does not affect angular (i.e., apparent) size.
In the Ptolemaic system, none of these regularities are “built in”: why can’t Jupiter’s epicycle rotate with a period of 4.86 years, for example? Especially puzzling is that the period of one Earth year is imposed on the deferent periods of the inner planets, but on the epicyclic periods of the outer planets. But the inner epicyclic and outer deferent periods do what they like! To be sure, there are trends, but nothing like the rigid rules of (1) and (2).
The ancients noticed some of these patterns. Most obviously, Mercury and Venus hug the Sun. This suggested to some ancient Greek (c. 4th century BCE) that they revolved about it. (This came to be known as the Heracleidean or Egyptian system, probably a misattribution.) Later on, Aristarchus of Samos (c. 270 BCE) proposed a fully heliocentric system. Unfortunately none of his heliocentric writings have come down to us; we know of his theory only indirectly.
Viewing the ancient geocentrists with 20-20 hindsight, it’s easy to ask them: How could you be so deluded? Koestler expressed this forcefully in The Sleepwalkers, in a chapter titled “The Divorce from Reality”:
There is something profoundly distasteful about Ptolemy’s universe; it is the work of a pedant with much patience and little originality, doggedly piling “orb in orb”. …
[The Ptolemaic system] was a monumental and depressing tapestry, the product of tired philosophy and decadent science. …
…mental snow-blindness…
A modicum of split-mindedness and double-think was perhaps not too high a price to pay for allaying the fear of the unknown.
…the universe was put into deep freeze, science was paralyzed…
The frightened mind, always on the defensive, is particularly aware of yielding an inch to the devil.
This is the dark side of the presentism. We know how the story ends; we know how to give each clue its proper weight. The people living through it lacked this perspective.
I recommend reading Koestler to get the full force of his argument, and reading Evans and Kuhn as a corrective. Koestler has the liveliest prose.
From the standpoint of kinematics (i.e., moving geometry), heliocentric and geocentric models are fully equivalent. The difference comes from dynamics. Direct physical evidence of the Earth’s motion calls for fairly delicate tests. Foucault’s pendulum experiment (1851) is often cited as the first instance of this, although other indications had accumulated following Newton’s Principia. Back in Ptolemy’s day, everyday experience left the matter wide open. Psychological preconceptions naturally voted for a stationary Earth. Even today, one says, “Don’t just stand there, do something!”, not “Don’t just spin around the Earth’s center and revolve around the Sun…”
On the other hand, we shouldn’t give Ptolemy a total pass. As we’ve just seen, heliocentric kinematics enjoys much greater simplicity and explanatory power than its geocentric counterpart. Heracleides proposed a spinning Earth over 400 years before Ptolemy; Aristarchus’s fully heliocentric system pre-dates Ptolemy by more than 300 years. So-called impetus dynamics, which refutes the naive arguments against a moving Earth, appeared with John Philoponus (c.490–c.570CE), or perhaps earlier.
Heliocentrism sets the scale of the solar system: all outer planet epicycles and inner planet deferents must be assigned the same diameter, since they all represent the Sun’s orbit. (This is the import of regularity (4).) For Kepler, this advantage was crucial, as we will see.
[1] Modern historians dislike this sort of value judgement, calling it ‘presentism’ or ‘whiggism’. But they recognize that modern astronomy beats Ptolemaic astronomy hands down by almost any scientific criterion; also that the Copernican and Keplerian systems mark two important milestones on the road to modern astronomy. They just don’t like the word ‘better’, preferring to say it in a more roundabout way, as I have done in this footnote. They have a point: more on this shortly.
Diagonal Argument 