Chapter 2
When the Earth Stood Still
A necessary prerequisite, for understanding the Galileo affair, is acquaintance with its intellectual background. And a key element of this background is provided by the world view that for the preceding two thousand years prevailed in the fields of cosmology, physics, and astronomy. This is the world view which, as we have seen, may be labeled geocentric, geostatic, Ptolemaic, Aristotelian, or Pythagorean.
The geocentric view was not a simple and monolithic entity, but rather was a theory that underwent two thousand years of explicit historical development, comprising about five centuries before and fifteen centuries after the birth of Christ (not to speak of its prehistory). It follows that there are many versions of the theory; for example, Aristotle’s and Ptolemy’s versions differ not only in emphasis but also in matters of substantive detail. The version expounded below is not a synopsis of any one treatise, but rather a reconstruction of the most widely held beliefs at the beginning of the sixteenth century, in a form useful for the understanding and appreciation of the Galileo affair. My account has been inspired primarily by Galileo’s own Treatise on the Sphere, or Cosmography, a short elementary textbook of traditional geostatic astronomy which he wrote and used in the early part of his teaching career, but never published.1
Cosmology
It is useful to begin with the question of the Earth’s shape. The geostatic view held that the Earth is a sphere, so that its surface is not flat but round; this is, of course, true. In fact, the evidence and the arguments proving this fact were already known to Aristotle, and they can be found in his writings. Although uneducated people at the time of Aristotle or Galileo may have believed that the Earth is flat, scientists and philosophers had settled the question much earlier. The Copernican controversy had nothing to do with the shape of the Earth, but rather with its behavior, status, and location in the universe.
Similarly, the maritime voyages and geographical discoveries of Christopher Columbus (1441–1506) and others at the end of the fifteenth century and thereafter may have provided additional confirmation of the Earth’s spherical shape; but this was only a more direct, experiential proof of the Earth’s roundness. On the other hand, those voyages did provide new evidence about the Earth’s size, structure, and relative amounts of land and ocean; and this evidence did have an effect on cosmological and astronomical thinking.
The questions of size and shape which became part of that controversy concerned those of the whole universe. In fact, the old view held that the universe was a sphere much larger than the Earth, but of finite size, the size being only slightly larger than the orbit of the outermost planet; that is, the distance from the outermost planet to the stars was of the same order of magnitude as the distance between one planet and another. The stars were all at the same distance from the center, being attached to the surface of the so-called stellar or celestial sphere; this stellar sphere enclosed the whole universe, and outside this sphere there was nothing physical. In other words, the size and shape of the universe were defined in terms of the size and shape of the sphere on which were attached the approximately 6000 fixed stars visible with the naked eye. This contrasts with the modern view that the universe is infinite, space goes on without end, and stars are scattered everywhere in infinite space; so that it does not make much sense to speak of the shape, size, or center of the universe.
Nevertheless, the finite spherical universe was based on the same set of observations which led to the belief that at the center of the celestial sphere was located the motionless Earth. This was the phenomenon of apparent diurnal motion: the Earth feels to be at rest; the whole universe appears to move daily around the Earth in a westward direction; this is most obvious for the case of the Sun, whose rising in the east and setting in the west generates the cycle of night and day; but the Moon can also be easily seen to do the same; and thousands of stars visible with the naked eye at night appear to undergo no change in size or brightness, but seem to be at a fixed distance from us; they appear to move in unison, so that their relative positions remain fixed; they appear to move in circles which are larger for stars lying closer to the equator and smaller for those lying closer to the poles; in short, the stars appear to move as if they were attached to a sphere which was rotating daily westward around a motionless Earth at the center. Given the plausible principle that what appears to normal observation corresponds to reality, here was the basic argument in support of the key tenets of the geostatic world view.
In the spherical finite universe, position or location or place had an absolute meaning. The geometrical center of the stellar sphere was a definite and unique place, and so was its surface or circumference; and between the center and the circumference, various layers or spherical shells defined intermediate positions. The part of the universe outside the Earth was called heaven in general, and to distinguish one heavenly region from another they spoke of different heavens (in the plural). For example, the stellar sphere could be regarded as the highest heaven, which meant the most distant one from the Earth, and which was also called the firmament; whereas the closest heaven was the spherical layer to which the nearest heavenly body (the Moon) was attached, and so the lunar sphere or sphere of the Moon was the first heaven. Between the lunar and the stellar spheres, six other particular heavens or heavenly spheres were distinguished: one was for the Sun, and then there was one for each of the other five known planets (Mercury, Venus, Mars, Jupiter, and Saturn). A heavenly sphere was not the same as a heavenly body: a heavenly sphere was one of the eight nested spherical layers surrounding the central Earth, each of which was the region occupied by a particular heavenly body or group of heavenly bodies, and to each of which these heavenly bodies were respectively attached; whereas a heavenly body was a term referring to the Sun, Moon, a planet, or one of the thousands of fixed stars. The two terms may be confusing because heavenly bodies were considered to be spherical in shape, and so they were spheres in their own right; however, the term “heavenly sphere” referred only to one of the spheres concentric with the center of the universe to which the Sun, Moon, planets, and fixed stars were attached.
The terrestrial region too had its own layered structure. This is related to a three-fold meaning for the term earth. In saying earlier that the Earth is a sphere, I was referring to the terrestrial globe consisting of land and oceans. This globe is a sphere, not in the sense of a perfect sphere, but only approximately, because the land is above the water and is full of mountains and valleys. Such an approximation is, of course, very good because the height of even the tallest mountain is insignificant compared to the Earth’s radius. However, it was only natural to distinguish water from earth, taking the latter term in the sense of just land, rocks, sand, and minerals; when so understood, “earth” is obviously only a part of the whole globe. Next, it was also natural to count the air or atmosphere surrounding the globe as part of the terrestrial region of the universe; and so by earth one could also mean the whole region of the universe near the terrestrial globe, up to but excluding the Moon and the lunar sphere. In short, the term earth had three increasingly broader meanings: it could refer to just the solid part of the terrestrial globe; or it could refer to the whole globe consisting of both land and oceans; or it could refer to the whole terrestrial region of land plus oceans plus atmosphere.
Terminology aside, the substantive point is that the Earth (namely, the place where mankind lives) is not a body of uniform composition, but has three main parts; it contains a solid part, a liquid part, and a gaseous part. These three parts (namely, earth, water, and air) were labeled elements to signify their fundamental importance. In regard to the arrangement of these terrestrial substances, the element earth sinks in water, and so earth must extend to the central inner core of the world and must make up most of what exists below the surface; on the other hand, most of the surface of the globe is covered with water, and the element water mostly surrounds the element earth. This was expressed theoretically by claiming that the natural place of the element earth was a sphere immediately surrounding the center of the universe, and that the natural place of the element water was a spherical layer surrounding the innermost sphere. For the case of the air, simple observation tells us that it surrounds the spheres of the first two elements, and so its natural place was a third sphere surrounding the first two.
There was a fourth terrestrial element, to which the name fire was given; but it required a more roundabout explanation. Just as we see earth sink in water, and water fall down (as rain) through air, we see flames shoot upwards through air when something is burning; we also see currents of heat move upwards through air during hot summer days, and smoke generally rise; and we see trapped fire escape upwards in volcanic eruptions. Such observations were taken as evidence that the natural place of fire was a fourth spherical layer above the atmosphere and just below the lunar sphere.
The existence of the element fire was also derived from some considerations about basic physical qualities. There were two fundamental pairs of physical opposites: hot and cold, and humid and dry. The element earth was a combination of cold and dry; the element water was a combination of cold and humid; and the element air was a combination of hot and humid. So there had to be a combination of hot and dry, and that was what constituted the element fire.
In summary, from the point of view of location in the geostatic finite universe, there were twelve natural places, each consisting of a sphere or spherical layer with a common center. The four terrestrial spheres were the natural places of the four terrestrial elements (earth, water, air, and fire). The eight heavenly spheres were the natural places of the heavenly bodies; they ranged from the lunar sphere to the stellar sphere, with six intermediate spheres for the Sun and the five planets. The stellar or celestial sphere enclosed everything else, while the Earth was the center of everything else.
Like position, direction had a definite and absolute meaning in the finite universe. There were three basic directions: toward the center of the universe, which was called downward; away from the center of the universe, called upward; and around the center of the universe. Thus, one important way of classifying motions was in these cosmological terms: bodies could and did move toward, away from, and around the center of the universe.
Geometrically speaking, motion could be simple or mixed. Simple motion was motion along a simple line. A simple line was defined as a line every part of which is congruent with any other part. Thus, there were supposedly only two such lines, circles and straight lines; and there were two types of simple motion, straight and circular motion. Mixed motion was motion which is neither straight nor circular.
Another way of classifying motions was in terms of the motions characteristic of the various elements, those which the elements undergo spontaneously. Earth and water characteristically moved straight downwards, while air and fire characteristically moved straight upwards. Now, since heavenly spheres and heavenly bodies moved characteristically with circular motion around the center, this meant that they must be composed of a fifth element; the term aether or quintessence was used to refer to this heavenly element.
Finally, another important classification was in terms of the opposition between natural and violent motions. Violent motion was motion caused by some external action; natural motion was motion which a body underwent because of its nature, so that the cause was internal. For example, the downward motion of earth and water, the upward motion of air and fire, and the circular motion of heavenly spheres and heavenly bodies were all cases of natural motion; on the other hand, rocks thrown upwards, rain blown sideways by the wind, a cart pulled by a horse, and a ship sailing over the sea were all cases of violent motion.
More fundamentally, motion was the opposite of rest. Rest was the natural state of bodies, and so all motion presupposed a force in some way. Natural motion was essentially the motion of a body toward or within its proper place; only when displaced from its proper place by some force would a terrestrial body engage in natural motion up or down; and only if started by some mover would a heavenly sphere rotate around the center of the universe, thus carrying its planet or stars in circular motion. On the other hand, violent motion was motion which was not toward the body’s proper place, and such motion could only happen by the constant operation of a force.
From what has already been said, it is apparent that Earth and heaven were very different; indeed, this radical difference was enshrined in an idea which needs to be made explicit and which deserves a special label. The key term is the Earth–heaven dichotomy; but one could equivalently speak of the dichotomy between the earthly or terrestrial or sublunary or elemental region of the universe, on the one hand, and the heavenly or celestial or superlunary or aethereal region on the other.
We have already seen that one difference between the two regions was location, which was absolute in the finite spherical universe: terrestrial bodies occupied the central region of the universe below the Moon, while heavenly bodies occupied the outer region from the lunar to the stellar sphere. Similarly, we have also seen that there was another difference in regard to natural motions: earthly bodies moved naturally straight toward or away from the center of the universe, whereas celestial bodies moved circularly around the same center. We have also seen that the two regions differed in regard to the elements of which bodies were composed. Sublunary bodies were made of earth, water, air, or fire, or a mixture thereof. On the other hand, in the superlunary region things were made of aether, or various concentrations thereof; that is, aether in low concentration made up the heavenly spheres, which were actually invisible; whereas aether in a highly concentrated state generated the Moon, Sun, planets, and stars, which were the heavenly bodies we actually saw.
Now, just as the natural places and the natural motions of the two regions obviously corresponded to each other, the elements in the two regions also corresponded to the natural places and motions. That is, the natural places and the natural motions of terrestrial bodies could be conceived as the essential properties of the terrestrial elements, while the natural places and motions of celestial bodies could be conceived as the essential properties of aether.
Other differences between Earth and heaven could be defined in terms of additional properties of the different elements. For example, whereas superlunary substances had no weight, sublunary bodies obviously did. Or to be more exact, whereas aether was weightless, the sublunary bodies subdivided into two classes: earth and water had weight or gravity, and so they were called heavy bodies; but air and fire had levity, namely the tendency to go up, and so they were called light bodies. Moreover, aether was regarded as intrinsically luminous, capable of giving off its own light, while earthly elements were dark. Even fire did not emit an inherent light of its own, but only temporarily produced light when in the process of escaping from lower regions to move to its natural place just below the lunar sphere.
Of the various differences between Earth and heaven, two deserve special attention: natural motion and susceptibility to qualitative change. Natural motion has always been regarded as one of the essential or defining characteristics of a physical body. This is something that seems to have remained unchanged even by the Copernican Revolution; from this point of view, what changed was the natural motion which is attributed to bodies. Since the geocentric theory attributed different natural motions to terrestrial and to celestial bodies, it ought to come as no surprise that it believed in the Earth–heaven dichotomy.
The geostatic universe was not a trichotomy, even though there were three visible kinds of natural motions (downward for earth and water, upward for air and fire, and around the center of the universe for aether). One reason was that the downward and upward natural motions were conceived as two minor subspecies of the same fundamental geometrical kind, namely straight or rectilinear motion.
However, this geometrical reason was not the only justification why the essential distinction was the two-fold one between straight and circular natural motions, rather than the three-fold one between upward, downward, and around. There was also the cosmological reason that, unlike circular natural motion, straight natural motion could not be everlasting or perpetual. For once a rock had reached the center of the universe, its nature would make it remain there rather than continue moving past the center, which would constitute upward and thus unnatural motion for the rock. Similarly, once a fiery object had reached the region above the terrestrial atmosphere just below the lunar sphere, it had reached its natural place and had nowhere else to go; for to continue moving would bring it into the first heavenly sphere, which was reserved for the aethereal Moon, and where the element fire could not subsist.
Finally, there was a theoretical reason why upward and downward natural motions could belong to the same fundamental region of the universe, but were essentially different from natural circular motion. The theory in question was the theory of change and contrariety, according to which all change derives from contrariety, and no change can exist where there is no contrariety; contrariety in this context meant oppositions such as those between hot and cold and between dry and humid. Now, up and down, together with the related pair of light and heavy, was another fundamental contrariety. It followed that a region full of bodies, some of which moved naturally downwards and some upwards, was bound to be full of all sorts of qualitative changes; and indeed observation obviously revealed that the terrestrial world is full of births, growth, decay, generation, destruction, weather and climatic changes, and so on. On the other hand, the circular natural motion of the heavenly bodies was thought to have no contrary; consequently, the heavenly region lacked an essential condition for the existence of change.
Add to this that the opposition between hot and cold and between dry and humid belonged only within the four terrestrial elements, and one could claim that the region of aether lacked any of the proper conditions for change. And observation confirmed that too because no physical or organic or chemical changes are easily detected in the heavens, and none were said to have ever been seen. The only essential phenomenon in the heavens was motion, but all heavenly motion was fundamentally regular: it involved the rotation of concentric spheres, which thus remained in place, so that there was not even change of place; what changed was only the relative position of the various bodies attached to the different celestial spheres.
Natural motion and qualitative change, then, provided the basis for the Earth–heaven dichotomy. There were many differences between Earth and heaven, but two interrelated differences were especially important: in the terrestrial world bodies moved naturally with rectilinear motion and underwent all sorts of qualitative changes, whereas in the celestial region things moved naturally with circular motion and were not subject to qualitative change.
To summarize our discussion so far, the Aristotelians and Ptolemaics believed that the Earth was spherical, motionless, and located at the center of the universe; that the universe was finite, bounded at the outer limit by the stellar sphere, and structured into a series of a dozen nested spheres, all inside the stellar sphere and surrounding the central sphere of the solid element earth; that there was a fundamental division in the universe between the earthly and the heavenly regions; and that these regions consisted of bodies with very different properties and behavior, such as different natural places, natural motions, elemental composition, and possibilities for qualitative change. Two things must now be added to this general cosmological picture: the details of the physics of the motion of terrestrial bodies and the astronomical details of the heavenly bodies. Let us begin with the former.
Physics
In the terrestrial region, the natural state of bodies was rest. To be more exact, it was rest at the proper place, depending on the elemental composition of the body: at the innermost core for the element earth; just above that for water; above water for air; and above air for fire. This meant that, whereas no cause was sought to explain why a body rested at its proper place, when a body was in motion or at rest outside its proper element, then an explanation was required.
Now, the explanation for why a body was in motion could be that it was going to rest at its proper place; this was the case of natural motion like rocks and rain falling or smoke rising though air. Or the explanation could be that the body was being made to move by an external agent; this was the case of violent motion like a cart pulled by a horse, or a boat sailing over the water, or rain blown by the wind, or weights being lifted from the ground to the top of a building. Both natural and violent motions required a force; the only difference was that in natural motion the motive force was internal to the body, whereas in violent motion the force was external. For example, falling bodies fell because of their inherent tendency to go down, to go to their natural place if they were not already there; the term gravity was used to refer to this internal force, and it was measured by the weight of an object. On the other hand, for a sailboat the wind was obviously the external force, and for a cart the horse.
Sometimes “violent motion” was equated with “forced motion,” but in such cases it was understood that by “forced motion” one meant motion caused by an external as distinct from internal force. Since all motion was forced, the term “forced motion” was sometimes regarded as redundant if taken to mean caused motion, and it was found useful only if taken to mean externally caused motion. In other words, the term force was ambiguous and could mean either any cause of motion or an external cause of motion; this may cause some confusion, but the context usually clarifies the meaning.
All motion, then, whether natural or violent, was caused by a motive force, whether internal or external. There was, however, another condition which was required by all motion, namely resistance. That is, in a sense motion was the overcoming of resistance. This was so in part because all space happened to be filled and there was no vacuum or void, so that whenever a body was moving it could only move through some medium, be it air, water, oil, molasses, sand, or soil. Even the heavenly region, interplanetary and interstellar space, was not devoid of matter; it was filled with (invisible) aether.
Moreover, it was argued that if there were no resistance to overcome, then a motive force (however small) would make a body move instantaneously, namely with infinite speed; and this was an absurdity since it meant that the body would occupy different places at the same time, and indeed many different places at the same time; it followed that there could not be a void, vacuum, or zero resistance. This argument depended on the idea that speed is inversely proportional to resistance, for this idea would provide the justification of why motion without resistance would be instantaneous; that is to say, not only was resistance required for motion to occur, but motion was correspondingly slower with greater resistance and faster with lesser resistance.
This quantitative relationship between speed and resistance was apparently taken seriously for the extreme case of zero resistance and used as just indicated in the above argument. However, the relationship was not taken equally seriously for the other end of the spectrum, for very strong resistance. That is, when the resistance was very strong, rather than saying that a given force would cause some motion, perhaps at very slow speed, it was held that there was a threshold for motion to occur at all; the force had to be sufficient to overcome the resistance in the first place, and if that was the case then the speed was inversely proportional to the resistance. Here, the typical example was that of a single man trying to pull a ship into dry dock by himself; it is clear that he will not be able to move the ship at all, not even 100 times slower than a team of the one hundred men required to accomplish the task.
The relationship between force and speed (when the resistance was constant) was also sometimes expressed quantitatively. The formula was that at constant resistance, the speed is directly proportional to the force. Here the paradigm example was the fall of heavy objects through a fluid like water; heavier objects do sink faster than lighter ones, and do so more or less in proportion to the weight; and weight in this case is the (internal) motive force.
In a modern conceptual framework and using modern terminology, we could combine the two relationships and obtain the following formula: given that the force can overcome the resistance, the body moves at a speed which is directly proportional to the force and inversely proportional to the resistance, that is, speed = constant × ( force/resistance).
These ideas had great plausibility and were largely in accordance with observation, except for situations like free fall through air and violent projectile motion. For free fall, the Aristotelian theory implied that a lead ball fell much faster than a rock, so that when dropped from the same height the lead would reach the ground much earlier than the rock; moreover, for a given object its speed of fall should not increase with time because it depended only on its fixed weight and the fixed resistance of the air. The problem of projectiles involved the motion of such things as arrows shot from bows, the question being where was the force making them move after the projectiles had left the ejector. The Aristotelians were aware of these problems and tried to solve them, but their solutions were found to be increasingly unsatisfactory. Indeed, it was the discussion of these problems that provided one line of development in the rejection of the old physics and the construction of the new one. However, this was not the only line of development, and, as we shall see later, Galileo’s new physics was concerned not only with the problem of falling bodies, but also with the problem of the Earth’s motion.
Astronomy
The main astronomical details of the geostatic world view can be visualized in terms of Figure 3.2
Figure 3. Celestial sphere
Imagine a large sphere (NS) surrounding a small one (NʹSʹ) at its center, and let the small sphere represent the Earth and the large one the stellar or celestial sphere. The diurnal motion was conceived as the daily rotation of the large sphere around a line, called the axis of diurnal rotation, which went through the north and the south celestial poles (N and S); this line also intersected the Earth’s center and two points on its surface, the north and the south poles of the Earth (N´ and Ś). From an observational viewpoint, the celestial poles were the two points in the heavens that appeared to be motionless (the north celestial pole to observers in the Earth’s northern hemisphere, and the south celestial pole to observers in the southern hemisphere); and the circular paths of the fixed stars appeared to be centered at the respective poles. On the surface of the celestial sphere, midway between the poles was a great circle of special importance, called the celestial equator; it too had a terrestrial counterpart (the Earth’s equator), which could be defined as the intersection of the plane of the celestial equator with the Earth’s surface, or as the great circle on the Earth’s surface halfway between the north and south terrestrial poles.
One reason for the importance of the celestial poles and equator was that they yielded a fixed frame of reference to define the position of the heavenly bodies, and correspondingly the position of points on the Earth’s surface. One could measure the angular position of a star north or south of the celestial equator, which was called declination (AB); correspondingly, the angular distance from the terrestrial equator of a point on the Earth’s surface is called latitude. For each declination or latitude one could conceive a plane parallel to the equator whose intersection with the surface of each sphere generated circles (called parallels) that became smaller as one moved toward a pole. On the other hand, the east–west position of a star (B) required first the drawing of a meridian, namely, a great circle (partially shown as NBA) through the star and the poles; then one would measure the ascension, namely, the angular distance from this meridian to some particular meridian (for example, A to VE); it was analogous for positions on the Earth’s surface, except that this east–west angular distance is called longitude.
There were two kinds of heavenly bodies, called fixed stars and wandering stars. A fixed star was a heavenly body that moved daily around the Earth in such a way that its position relative to most other heavenly bodies did not change (it was “fixed”); for example, its declination remained constant, and so did its angular distance from any other fixed star. A wandering star was a heavenly body that not only moved daily around the Earth, but also changed its position relative to other heavenly bodies; that is, the wandering stars were those heavenly bodies which, besides undergoing the diurnal motion, appeared to move in other ways (namely, “wandered” about). There were only seven wandering stars, which were also called planets; indeed, the word planet originally meant literally “wandering star.” Because wandering stars were often called simply planets, fixed stars were often called simply stars. So although one broad meaning of the word star was synonymous with the term heavenly body, one narrow meaning of star was identical to the term fixed star; the term fixed was often dropped when the context made it clear that one was indeed referring to fixed stars.
Thousands of fixed stars were visible on a clear night with the naked eye; they were catalogued both in terms of apparent brightness (called magnitude) and in terms of shapes or patterns formed by groups of stars close to each other (called constellations). The naked eye could be trained to distinguish six magnitudes; stars of the first magnitude were the brightest, and those of the sixth magnitude were the faintest. The brightest star was named Sirius or the Dog Star; it was located near the equator and was part of the constellation of Canis Major. One particular star of the second magnitude was especially important because it was so close to the north celestial pole that, for practical purposes (such as navigation), it could be regarded to be the pole; it was called Polaris or the North Star and was part of the constellation of Ursa Minor.
Both the Sun and Moon were planets because they moved (“wandered”) in relation to the fixed stars. Because of their brilliance and their relatively large size, they were called the two luminaries. The other known planets were named Mercury, Venus, Mars, Jupiter, and Saturn. We now know that there are other planets circling the Sun in orbits beyond Saturn, but they were unknown not only to the ancients but also to Copernicus and Galileo, and so they played no role in the Copernican Revolution.
The most important point about the planets was that, out of the thousands of heavenly bodies, there were seven that circled the Earth westward once a day like all others, but did not do so in unison with them; these seven bodies also revolved slowly eastward, so that from day to day their position shifted. Whereas a fixed star revolved around the Earth in such a way that after twenty-four hours it returned to the same position (relative to other stars), after twenty-four hours a planet did not quite return to the earlier position but usually had fallen behind somewhat, being located slightly eastward. This can be seen most easily for the case of the Moon by observing its position on succeeding nights at midnight; relative to the fixed stars, it appears to move eastward. In other words, the planets seemed to behave as if their motion were a combination of two circular motions in opposite directions: they circled the motionless Earth westward with the universal diurnal motion, and in addition they simultaneously moved slowly eastward.
The individual planets moved eastward at different rates. The Moon took about a month to return to the same position relative to the fixed stars; the Sun took one year; Mars about two years; and Saturn about twenty-nine years. Thus, the planets moved not only relative to the Earth and the fixed stars, but also relative to each other; each planet had its own distinctive motion, besides the universal diurnal motion. Since the westward diurnal motion was common to all, when one spoke of planetary motions one usually referred to the distinctive individual motions of the planets. Note that, while all the individual planetary motions were usually eastward, this direction was opposite to that of the diurnal rotation, which was westward.
The planetary motion of the Moon, which took about a month, was the most readily observable one since it was connected with the cycle of its phases; a full moon is easily seen and the period from one full moon to the next is an obvious unit of time that can be used as the basis for a calendar. The planetary motion of the Sun was also easy to observe since it is related to the cycle of the seasons of the year; hence, as we have already mentioned, it was called the annual motion.
Everyone can easily observe that, in the course of a year, the rising or setting Sun slowly moves in a north–south direction. Sometimes it rises near due east and sets near due west, which is to say that it is seen on the celestial equator; this happens around March 21, which is the time of the vernal equinox; it also occurs around September 23, the time of the autumnal equinox. Sometimes it rises and sets about 23.5 degrees north of due east and due west, respectively (namely north of the celestial equator); this happens in the northern hemisphere around June 22, the time of the summer solstice. Sometimes it rises and sets about 23.5 degrees south of due east and due west, respectively (south of the celestial equator); this occurs in the northern hemisphere around December 22, the time of the winter solstice. One can also observe from a given location on the Earth’s surface the elevation above the horizon of the Sun at noon; in the course of a year this elevation changes daily and ranges about 47 degrees, being highest around June 22 and lowest around December 22 (in the northern hemisphere).
This annual northward and southward motion of the Sun indicates that its position relative to the fixed stars changes along a north and south direction since the fixed stars remain at a constant distance from the celestial equator. In other words, the declination of the Sun changes by about 47 degrees during a year, while the declination of a fixed star does not change; so this north–south motion of the Sun is part of its “wandering” among the fixed stars.
Although this apparent northward–southward solar motion was the one most easily observed, it was different from its planetary motion which was eastward. The two were related as follows. The Sun’s eastward revolution in its planetary orbit did not take place in the plane of the celestial equator but in a plane inclined to it by 23.5 degrees. The point was that the Sun’s motion among the fixed stars was not exactly eastward, but mostly eastward; its trajectory was slanted north and south. The Sun moved eastward and southward for six months, and eastward and northward for the other six months. The obvious difficulty in observing the Sun’s eastward motion among the fixed stars stems from the fact that they cannot be seen when the Sun is visible. What one can do is to observe some star located near the celestial equator and rising in the east soon after the Sun sets in the west; this means that the Sun and star are diametrically opposed, or about 180 degrees apart. Next, observe the position of the same star just after sunset about a month later; it will be seen to be not just rising, but high in the sky and about 30 degrees west of its previous position; that means that the Sun is now only about 150 degrees away, which is to say that Sun has moved eastward about 30 degrees closer to the star. About six months after the first observation, the star will appear and immediately set in the west just after sunset. Twelve months later, the star will again rise in the east when the Sun sets in the west.
The planetary motion of the Sun may be pictured as in our diagram (Figure 3). Imagine looking at the large sphere from above the north celestial pole, and picture the large sphere rotating clockwise around the motionless small central sphere to represent the westward diurnal rotation of the stellar sphere around the Earth. Next, imagine a great circle on the stellar sphere in a plane cutting the equatorial one at an angle of 23.5 degrees, to represent the Sun’s geocentric orbit projected onto the stellar sphere; in accordance with standard terminology, let us use the term ecliptic to refer to this geocentric orbit, or the corresponding great circle on the stellar sphere, or the plane on which they both lie. The intersection of the ecliptic and the equator on the stellar sphere defines two special points, called the vernal equinox (VE) and the autumnal equinox (AE); and halfway around the ecliptic between the equinoxes are two other special points, the summer solstice (SS) at the northern end, and the winter solstice (WS) at the southern end; these four points thus divide the ecliptic circle into four equal quadrants. Now, imagine the Sun moving counterclockwise around the ecliptic at a rate that makes it traverse the whole circumference in one year; then the Sun will be at VE around March 21, at SS around June 21, at AE around September 21, and at WS around December 21.
Let us now combine the clockwise rotation of the whole stellar sphere with the counterclockwise revolution of the Sun along the ecliptic. The result is that the Sun in reality moved in a helical path which in one year looped clockwise around the Earth about 365 times (days of the year), but which in any one day corresponded almost but not quite to one of the parallels on the stellar sphere. I say “almost but not quite” first because the parallel circle was not completely traversed by the Sun, but fell short by about one degree (1/360 of a circle, which approximately equals 1/365 of a year); and second because the end of the daily path rises northward or drops southward relative to the beginning of the same daily path by 1/4 of a degree on the average (namely 23.5 degrees every 3 months, or every 90 days).
The ecliptic was important not only because it represented the yearly eastward path of the Sun among the stars, but also because it was used to define a frame of reference, distinct from the equatorial one mentioned earlier. For example, one could draw a line perpendicular to the center of the ecliptic (called the axis of the ecliptic); one could then speak of the poles of the ecliptic as the points where its axis intersected the celestial sphere; one could define the position of a star in terms of its angular distance from the ecliptic toward one of its poles; and one could also plot the position of a body in terms of east–west position along the ecliptic.
This ecliptic frame of reference was especially important for the other six planets because they are never seen to wander much away from the ecliptic; that is, planets are always observed to be somewhere inside a narrow belt extending 8 degrees above and below the ecliptic. This was the result of the fact that the individual circular paths of the planets took place in planes which, while not identical with the ecliptic, intersected it at small angles no larger than 8 degrees. This narrow belt on the stellar sphere along which the planets revolved was called the zodiac. It was subdivided into 12 equal parts of 30 degrees each, and each part happened to be the location of a group of stars that seemed to be arranged into a distinct pattern. These twelve patterns were the constellations of the zodiac and were named Aquarius, Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, and Capricorn. The Sun, Moon, and other planets were at all times found somewhere in one of these constellations, and they moved from one constellation to the next in the order just listed. This order corresponded to what we have called an eastward direction (from the viewpoint of terrestrial observation), or counterclockwise (in connection with the pictorial diagram just described); the key point, however, was that the order of the signs of the zodiac was a direction of motion opposite to that of the diurnal rotation.
When projected onto the stellar sphere, the eastward motion of the planets could be described in terms of great circles on the surface of that sphere, all of which were within the zodiac and intersected one another at small angles. But the planets were not believed to be attached to the stellar sphere like the fixed stars; unlike the fixed stars, the planets were not regarded to be equidistant from the Earth. The fact that the planets appeared to move relative to the fixed stars, and that this motion took place at different rates for different planets, implied that each planet was attached to its own sphere which rotated eastward at its own rate, while being carried westward daily by the diurnal rotation of the stellar sphere.
Except for the Moon (whose distance was relatively ascertainable because of eclipses), there was no direct way to measure the sizes of the various planetary spheres or orbits, but the relative determination was done on the basis of the length of time required for a given planet to complete one circular journey among the stars. The principle used was that the bigger ones of these nested planetary spheres rotated at slower rates, and the smaller ones at faster rates; that is, the bigger the orbit, the slower the period of revolution. This principle was combined with the observation that the periods of revolution ranged from one month for the Moon to one year for the Sun and twenty-nine years for Saturn. The result was that in order of increasing distance from the Earth, the planets were most commonly arranged as follows: Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. Thus, as mentioned earlier, between the stellar sphere and the Earth, there were seven other nested spheres, whose rotation carried the corresponding planets in their own individual eastward orbits, while they were all being carried in a westward daily whirl by the diurnal rotation of the celestial sphere.
Besides the fundamentals just sketched, the geostatic world view also contained some more specific and technical points, but the discussion of these is best postponed until later, as they become relevant in the context of understanding various parts of the geokinetic, heliocentric, and Copernican world view. For now, let me end this sketch by stressing a very important point: the geostatic and geocentric system of Aristotle, as elaborated more technically by Ptolemy, yielded plausible explanations and useful predictions of celestial phenomena; in short, it worked. For about two thousand years, no one was able to come up with anything better. All this changed with Copernicus, to whom we turn in the next chapter.