English 233: Astronomy: the appearances, Ptolemy's theory, Copernicus's theory

English 233: Introduction to Western Humanities -- Baroque & Enlightenment

Explaining the astronomical appearances:

how the Ptolemaic and Copernican theories propose to do it.

A model of the universe is a complex hypothesis about how objects really stand in space such that they present the appearances they do to an observer placed at a particular spot within the overall imagined system (e.g., to an astronomer on earth).

Let's review some of these appearances and then see how Ptolemy and his followers proposed to explain them. Since it is vitally important that we keep distinct in our minds the observed look of things that we are trying to explain and the imagined look of things that we postulate "behind experiences" to explain them, I will put descriptions of appearances in green type, descriptions of Ptolemaic hypothetical machinery in purple type, and descriptions of Copernican machinery in red type. It is the job of both the Ptolemaic and the Copernican theoretic models to explain the same appearances.

Every night the constellations wheel through the sky at a constant rate -- 15 degrees of arc per hour. "Diurnal" in the diagram below means "daily.")

Figure 1.

On successive nights, a given constellation will become visible a little further along its path than it did the previous night, and fade out correspondingly further along.

If we look northwards, and "connect the dots" for successive observations of stars during a given 2-hour period on the same evening, we would see something like what's in the diagram below. (You have seen time-delay photos that yield a similar effect, but of course the astronomers before photography had to imaginatively "connect the dots.") Some points to consider in interpreting this diagram:

The heavy circle that is drawn touching the horizon separates the stars that are always visible (the "circumpolar" stars) from those that rise and set. Which of these latter are visible at a given hour of the night (say, midnight) depends on the season of the year. (The "zodiac" is made up of constellations that behave this way.)
Exactly what point on this diagram would appear directly overhead to you would depend on where on earth you were standing. If you were at the earth's north pole, then the pole star would be directly overhead. If you were standing at a place on earth where the appears 45-degrees above the northern horizon, then what would be directly overhead for you would be a star at the top of the circle drawn here. This is the way it is for someone situated at 45-degrees North latitude -- for example, near Bordeaux (France), Turin (Italy), or Minneapolis, Minnesota (USA).

Figure 2.

If we look in other directions, we see the same wheeling, but differently oriented towards the horizon.

Figures 3(a) and 3(b).

The above diagrams show the sorts of things that happens to the "fixed stars" on a given night. Remember: these are designated as "fixed" because their relative positions with respect to each other remain constant. (Of course, as described above, they move -- but all together, as "constellations" -- through the night sky on a given night.)

But other heavenly bodies behave differently. On successive nights (registered at the same moment each night) they show up in a slightly different position with respect to the fixed stars. They were termed "planets," from the Greek word meaning "to wander."

Remember: the term "planet" so far is being used in a purely phenomenal sense, to designate how it behaves in appearance to an observer situated on the earth. It is quite a different thing to conceive of it as a "planet" in the theoretical sense of "satellite of earth," as is done in the Ptolemaic theory, or in the theoretical sense under which it refers to those bodies (including Earth) that are hypothesized to orbit the sun, as is done in the Copernican theory.

Here, for example, is where the sun shows up at sunset on successive evenings for just over a month in late Spring, when it is "journeying through" the constellations of Aries ("the Ram") and Taurus ("the Bull").

Figure 4.

The Ptolemaic theory explains these data (phenomena, appearances) by postulating that in real space (i.e., "behind" appearances)

the center of the cosmos coincides with the center of the earth;
the fixed stars are mounted permanently on a huge black sphere, at a great distance from, but whose center also coincides with, the center of the cosmos; and
this sphere of the fixed stars rotates westwards almost (but not quite) daily around its center;
the slight increment beyond a day that the sphere of fixed stars rotates serves, in the course of the year, to put any given constellation slightly westward of where it was at any given moment (say, sunset or sunrise) during the previous day, so that in the course of a year that constellation at that given time, passes over a different point on the earth's surface, and after a year at that same moment stands over the exact point that it was over at that moment the previous year;
the sun is attached to another sphere, whose center is also at the center of the earth, but which is crystalline (not only rigid but translucent), at a distance in between the earth and the sphere of the fixed stars;
the sphere to which the sun is attached rotates westwards once a day around the center of the cosmos, thus carrying the sun in a daily circular orbit around the earth, so that each day the sun stands between a given point on the earth and a different point on the stellar sphere (i.e., moves with respect to the constellations).

The Copernican theory explains these same data by postulating a different scenario going on in real space:

the center of the cosmos coincides with the center of the cosmos;
the fixed stars are mounted permanently on a huge black sphere, at a great distance from, but whose center also coincides with the center of the cosmos; but
this sphere is fixed (motionless) in space;
the earth is (somehow) carried by a crystalline sphere that rotates eastwards once a year around the sun, thus carrying the earth in an annual circular orbit around the sun; with the result that
every day the line from the center of the earth through the center of the sun extends to a slightly different point on the stellar sphere than the day before (as gauged by the constellations afixed to it), until after a year the earth, sun, and stellar sphere are once again so alligned that this line intersects the same point on the stellar sphere.
the earth rotates eastwards at a constant rate once a day on its axis, so that directly above any given point on the its surface is a different point, at any moment, on the stellar sphere.

Some of these "wanderers," however, exhibit paths that are more complicated. Here are the positions that the planet Mars takes on successive nights in the late Spring. (The dash represents the path of the sun through the same region during the same season, as registered (for instance) at the moment just after sunset when the stars become visible).

Figure 5.

Clearly it will not do to try to explain this pattern of observed behavior by the same hypothetical mechanism Ptolemy resorted to in order to explain the way the sun appears to move among the fixed stars (in Figure 4., above). Here we have a kind of "loop," by which, over time, the planet proceeds on an apparent arc among the fixed stars and then slows down, turns around and goes back in the opposite direction for a while, after which it reverses its path once more and proceeds again in the original direction, along the same kind of apparent arc as before (though by now in a different region of the fixed stars). And, in fact, this pattern repeats itself several times until, after some definite time (but more than a couple of years), the planet returns to its original position with respect to the constellations.

And, indeed, the case is worse: this same pattern of "retrograde motion" is exhibited by all the heavenly bodies except the sun, the moon, and the fixed stars.

Below, in (a), is the kind of epicycle/deferent system that astronomers working in the Ptolemaic framework postulated as the real relative motion of an "superior" planet in space, with respect to the Earth and the sphere of fixed stars. (A "superior" planet in Ptolemy's scheme is one whose orbit around the Earth lies beyond that of the sun; these are Mars, Jupiter, and Saturn. The "inferior" ). Such a motion would produce the appearances (above) for observers on Earth, whose surface Ptolemy supposed as concentric with both the sphere of fixed stars (rotating daily) and the deferent, whose period of rotation must differ slightly so as to make the planet advance.in general through the fixed stars (from April 1 to June 1 and from October 1 to October 15 in the picture above). The job of the epicycle, when carried sideways (deferred by the deferent on which it is mounted), is to make the planet trace some such actual path through space as indicated in (b). This motion in actual space would show up to an observer located on Earth as the kind of path drawn in (c), which corresponds to the sort of observed path (with retrograde motion) recorded in the previous diagram.

Figure 6.

And here is the sort of arrangement in actual space hypothesized by Copernicus to account for the same apparent retrograde motion, in this case of an "superior" planet -- Mars, Jupiter or Saturn -- whose orbits Copernicus places successively further out from the sun than that of Earth (the motion seen in Figure 4).

Figure 7.

The Earth moves on its orbit from E1 to E7. During the same time, the superior planet (e.g., Mars) moves more slowly in its orbit from P1 to P7. The planet's apparent position against the fixed stars on the stellar sphere (which Copernicus postulates as motionless) slides eastward from position 1 to 7, but as Earth catches up and passes the more distant planet there will show up against the constellations a brief westward retrogression from 3 to 5. This corresponds to the kind of path observed for Mars in the record summarized in the first diagram.

Ptolemaic astronomy had to postulate epicycle/deferent systems for all the inferior and superior planets (i.e., for all the theoretical planets except the Sun and the Moon). And indeed, it was necessary to postulate epicycles on epicycles, and to resort to other complications (eccentrics and equants, which we will not discuss here).

The resulting complicated system (necessary to account for the observed data within the Ptolemaic geocentric framework) struck Copernicus as too senselessly complicated to be imagined as the work of a perfect Creator.

The beauty of the Copernican system was that same kind of the planetary mechanism in real space that it postulated to account for the observed motion of the Sun (Figure 4, above) accounts for the apparently very different observed motion of both the inferior and exterior planets (which, in Copernicus' scheme, of course, are, respectively, those whose orbits are inside the orbit of the earth and those whose orbits are outside of that of the the earth). And: these single-orb mechanisms themselves are intrinsically simpler than the compound machinery of epicycle-and-deferent.

The Copernican scheme for explaining the same appearances is thus impressively simpler than the traditional model in two distinct ways. And this was one major reason why Copernicus decided to propose it in the book he published (On the Revolutions of the Heavenly Bodies) in 1543: such a heavenly structure impressed him as much more consonant with the sort of thing a perfect divine engineer would have constructed.

And there were additional reasons that this structure seemed to Copernicus to be the sort of one that a perfect Creator would have decided upon.

It is remarkable, then, that this astronomical hypothesis, which was soon to raise such protest in orthodox Christian circles both Protestant and Catholic, and whose eventual triumph in the 17th Century was to have such a dire effect on the religious faith of so many intellectuals in the 18th Century, was put forward, in the 16th Century, by a Christian monk, for the most pious of reasons.

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