The Essential Galileo

by Galilei, Galileo, Finocchiaro, Maurice A.

  Regarding the impediment of the newly acquired downward motion, first it is clear that these two motions (namely, the circular around the center and the straight toward the center) are neither contrary nor incompatible nor destructive of each other; for the moving body has no repugnance toward such motion; you yourself already granted that its repugnance is to motion which takes it farther from the center, and that its inclination is to motion which brings it closer to the center; so it follows necessarily that the moving body has neither repugnance nor propensity to motion that takes it neither farther from nor closer to the center, and consequently there is no reason for any decrease in the power impressed on it. Moreover, the cause of motion is not a single one, which might diminish on account of the new action; instead there are two distinct causes, of which gravity attends only to drawing the body toward the center, and the impressed power to leading it around the center; therefore, there is no reason for an impediment.

  [§8.6 Day III: Heliocentrism and the

  Role of the Telescope]48

  [346] SALV. We ought to leave this question and go back to our main subject; here the next point to consider is the annual motion, which is commonly attributed to the sun, but which was taken away from the sun and given to the earth first by Aristarchus of Samos and later by Copernicus. Against this position I see Simplicio comes well equipped, in particular with the sword and shield of the booklet of mathematical conclusions or disquisitions;49 it would be good to begin by proposing its attacks.

  SIMP. If you do not mind, I would like to leave them to the end, as they are the last to have been discovered.

  SALV. Then, in accordance with the procedure followed until now, you must [347] advance in a systematic manner the contrary reasons—those of Aristotle as well as those of the other ancients; I will also contribute to this, so that nothing is left out without being carefully considered and examined; likewise, Sagredo will bring forth the thoughts that his lively intellect will awaken in him.

  SAGR. I will do it with my usual frankness; you will be obliged to excuse it since you made this request.

  SALV. Our obligation will be to thank you for the favor, not to excuse you. However, let Simplicio begin to advance those difficulties that prevent him from being able to believe that the earth, like the other planets, can move in an orbit around a fixed center.

  SIMP. The first and greatest difficulty is the repugnance and incompatibility between being at the center and being away from it; for if the terrestrial globe should move in the course of a year along the circumference of a circle, namely, along the zodiac, it would be impossible for it to be simultaneously at the center of the zodiac; but Aristotle, Ptolemy, and others have proved in many ways that the earth is at this center.

  SALV. You speak very well; there is no doubt that whoever wants the earth to move along the circumference of a circle must first prove that it is not at the center of this circle. Therefore, it follows that we should determine whether or not the earth is at this center, around which I say it turns, and at which you say it is fixed; and before doing this, we must also see whether or not you and I have the same conception of this center. So tell me what and where you understand this center to be.

  SIMP. By this center I understand the center of the universe, of the world, of the stellar sphere, of the heavens.

  SALV. I could very reasonably dispute with you whether there is such a center in nature since neither you nor others have ever proved whether the world is finite and bounded or infinite and boundless; however, granting for now that it is finite and bounded by a spherical figure, and hence that it has a center, we must decide how credible it is that the earth, rather than some other body, is located at this center.

  SIMP. That the world is finite, bounded, and spherical is proved by Aristotle with many demonstrations.50

  SALV. All these, however, reduce to one, and this single one to [348] nothing; for he proves that the universe is finite and bounded only if it is in motion, and so all his demonstrations fall to pieces if I deny his assumption that the universe is in motion. However, in order not to multiply the disputes, let us concede for now that the world is finite and spherical and has a center. Since such a shape and center have been proved on the basis of its mobility, it will be very reasonable to proceed to the particular investigation of the exact location of such a center on the basis of the same circular motions of the heavenly bodies; indeed Aristotle himself reasoned and proceeded in the same manner, making the center of the universe that point around which all the celestial spheres turn and at which he saw fit to place the terrestrial globe. Now, tell me, Simplicio: suppose Aristotle were forced by the clearest observations to change in part his arrangement and structure of the universe, and to admit he was wrong in regard to one of the two following propositions (that is, either in placing the earth at the center or in saying that the celestial spheres move around such a center); which of the two alternatives do you think he would choose?

  SIMP. I believe that in this case the Peripatetics …51

  SALV. I am not asking about the Peripatetics, but about Aristotle himself; for I know very well what they would answer. As the most submissive and slavish servants of Aristotle, they would deny all experience and all observation in the world and even refuse to use their senses, in order not to have to make the confession; they would say the world is as Aristotle said and not as nature wants; for if they lose the support of this authority, with what would you want them to appear in the field? So tell me what Aristotle himself would do.

  SIMP. Really, I could not decide which of the two inconveniences he would regard as the lesser one.

  SALV. Please do not use this term; do not call inconvenient what could turn out to be necessarily so. To want to place the earth at the center of the heavenly revolutions was indeed inconvenient. However, since you do not know which way he would be inclined to go, and since I regard him as a man of great intellect, let us examine which of the two choices is more reasonable, and let us take that one to be what Aristotle would choose. Let us resume our earlier discussion, then, [349] and let us assume (with Aristotle) that the universe has a spherical shape and moves circularly, so that it necessarily has a center in regard to both its shape and its motion; although we have no observational information about the size of the universe other than that deriving from the fixed stars, we are certain that inside the stellar sphere there are many orbs, one inside the other, each with its own heavenly body, and that they also move circularly; we are inquiring about which is more reasonable to believe and say, either that these nested orbs move around the same center of the universe, or that they move around some other center very far from there. Now, Simplicio, tell us your opinion about this particular detail.

  SIMP. If we could limit ourselves only to this issue and be sure not to encounter any other difficulty, I would say it is much more reasonable to claim that the container and the contained parts all move around a common center than around several.

  SALV. Now, if it is true that the center of the universe is the same as that around which the orbs of the heavenly bodies (namely, of the planets) move, then it is most certain that the sun rather than the earth is found placed at the center of the universe; thus, as regards this first simple and general point, the place in the middle belongs to the sun, and the earth is as far away from the center as from the sun itself.

  SIMP. But what is the basis of your argument that the sun rather than the earth is at the center of the revolutions of the planets?

  SALV. I conclude this from observations that are very evident and hence necessarily binding. The most palpable of these observations that exclude the earth from this center and place the sun there is the fact that all planets are found to be sometimes closer to the earth and sometimes farther; these differences are so large that, for example, when Venus is farthest it is six times farther from us than when it is closest, and Mars recedes almost eight times more in one position than in the other. So you can see whether Aristotle was wrong b
y a small amount in thinking that they are always equally distant from us.

  SIMP. What, then, are the indications that their motions are around the sun?

  SALV. For the three superior planets (Mars, Jupiter, and Saturn) this is inferred from their being always found closest to the earth when they are in opposition to the sun and farthest when they are near conjunction; [350] this variation in distance is so significant that when Mars is closest it appears sixty times greater than when it is farthest. Then, in regard to Venus and Mercury, we are certain of their revolving around the sun from their never receding much from it and from our seeing them sometimes beyond it and sometimes in between; the latter is conclusively proved by the changes in the apparent shape of Venus. For the case of the moon, it is indeed true that it cannot be separated from the earth, for reasons which will be given more clearly as we proceed.

  SAGR. I expect to hear more marvelous things that depend on this annual motion of the earth than was the case for those that depend on the diurnal rotation.

  SALV. You are absolutely right. For, the action of the diurnal motion on the heavenly bodies was and could be nothing but to make the universe appear to us to be hastily running in the opposite direction; but this annual motion, by mixing with the particular motions of all the planets, produces very many oddities that so far have made all the greatest men in the world lose their bearings. Now, returning to the first general considerations, I repeat that it is the sun that is the center of the heavenly revolutions of the five planets (Saturn, Jupiter, Mars, Venus, and Mercury); and it will also be the center of the earth’s motion if we can manage to place it in the heavens. Then, as regards the moon, it has a circular motion around the earth, from which (as I said) it cannot be separated in any way; but this does not mean that it fails to go around the sun together with the earth in the annual motion.

  SIMP. I still do not comprehend this arrangement too well; perhaps by drawing a diagram we will understand it better and be able to discuss it more easily.

  SALV. So be it. Indeed, for your greater satisfaction and amazement, I want you to draw it yourself and see that you understand it very well, even though you think you do not grasp it; by merely answering my questions, you will draw it to the last detail. So, take a sheet of paper and a compass, and let this white paper be the immense expanse of the universe where you have to locate and arrange its parts in accordance with the dictates of reason. First, without my teaching it to you, you firmly believe the earth to be located in this universe; so, take a point of your own choosing around which you understand it to be located, and mark it with some symbol.

  [351] SIMP. Let this, which is marked A, be the location of the terrestrial globe.

  SALV. Very well. Second, I know you know very well that the earth is neither located inside the solar body nor contiguous to it, but is separated from it by a certain distance; so, assign to the sun some other place of your choice, as far from the earth as you wish, and mark this too.

  SIMP. It is done; let the location of the solar body be this, marked O.

  SALV. Having fixed these two, I want us to think about accommodating the body of Venus in such a way that its state and motion can satisfy what sensory appearances show us about them. So, recall what, from previous discussions or your own observations, you understand to occur in regard to this star; then assign to it the position you deem appropriate.

  SIMP. Let us suppose the truth of the appearances which you related and which I also read in the booklet of conclusions: that is, that this star never recedes from the sun more than a determinate interval of little more than forty degrees, so that it not only never reaches opposition to the sun, but not even quadrature,52 nor so much as the sextile configuration;53 further, that it appears sometimes forty times larger than at other times, namely, largest when it is in retrograde motion and approaches evening conjunction with the sun, and smallest when it is in direct motion and approaches morning conjunction; moreover, that it is true that when it appears largest it shows a horned shape, and when it appears smallest it is seen perfectly round. Given that all these appearances are true, I do not see how we can escape the conclusion that this star revolves in a circle around the sun; for this circle cannot in any way be said to enclose or to contain within it the earth, nor to be below the sun (namely, between it and the earth), nor to be above the sun. This circle cannot enclose the earth because then Venus would sometimes come into opposition to the sun; it cannot be below the sun because then Venus would appear sickle shaped at both conjunctions with the sun; and it cannot be above the sun because [352] then it would appear always round and never horned. So, for its position I will mark the circle CH around the sun, without making it enclose the earth.

  SALV. Having accommodated Venus, you should think about Mercury; as you know, the latter stays always near the sun and recedes from it much less than Venus does.

  SIMP. There is no doubt that, since it imitates Venus, a very appropriate place for it will be a smaller circle inside that of Venus and also around the sun; a very conclusive argument or reason for this, especially for its vicinity to the sun, is the vividness of its shining, which is greater than that of Venus and the other planets. So, on this basis we can draw its circle, marking it with the letters BG.

  SALV. Where, then, shall we place Mars?

  SIMP. Because Mars reaches opposition to the sun, it is necessary that its circle enclose the earth. But I see that it must necessarily enclose the sun as well; for when this planet reaches conjunction with the sun it would appear horned (like Venus and the moon) if it were not beyond the sun but rather in between; however, it always appears round. Therefore, its circle must enclose both the earth and the sun.

  Moreover, I remember your having said that when it is in opposition to the sun it appears sixty times larger than when it is near conjunction; so, I think these appearances will agree very well with a circle around the center of the sun and enclosing the earth, which I am now drawing and marking DI. Here, at the point D, Mars is closest to the earth and in opposition to the sun; but, when it is at the point I, it is in conjunction with the sun and farthest from the earth.

  Finally, the same appearances are observed in regard to Jupiter and Saturn, although with much less variation for Jupiter than for Mars, and still less with Saturn than with Jupiter; so, I think I understand that these two planets will also be very adequately accommodated by means of two circles also around the sun. The first one is for Jupiter and is marked EL; the other larger one is for Saturn and is labeled FM.

  SALV. So far you have conducted yourself splendidly. Now, as you can see, the variation in distance for the three superior planets is measured by an amount twice the distance between the earth and the sun; hence, [353] the variation is greater for Mars than for Jupiter since Mars’s circle DI is smaller than Jupiter’s circle EL; similarly, because EL is smaller than Saturn’s circle FM, the variation is even less for Saturn than for Jupiter; this corresponds exactly to observation. What remains for you now is to think about the place to assign to the moon.

  SIMP. Let us use the same argument, which seems to me to be very conclusive. Because we see the moon reach both conjunction and opposition with the sun, it is necessary to say that its circle encloses the earth; but we must not say that it encloses the sun because then near conjunction it would not appear horned but always round and full of light; furthermore, it could never produce, as it often does, an eclipse of the sun by coming between it and us. Therefore, it is necessary to assign to it a circle around the earth, such as this marked NP; thus, when positioned at P, from the earth A it appears in conjunction with the sun and so can eclipse it sometimes; and when located at N it is seen in opposition to the sun, and in this configuration it can come into the earth’s shadow and eclipse itself.

  SALV. What shall we do now with the fixed stars, Simplicio? Do we want to spread them in the immense space of the universe, at different distances from any determinate point? Or do we want to place them on a surface extending
spherically around its center, such that each of them is equidistant from the same center?

  SIMP. I would rather follow an intermediate path. I would assign them an orb constructed around a determinate center and contained between two spherical surfaces, namely, a very high concave one and another convex one below it; and I would place the countless multitude of stars between them, but at different heights. This could be called the sphere of the universe, and it would contain inside it the orbs of the planets we have already drawn.

  SALV. So far, then, Simplicio, the heavenly bodies have been arranged just as in the Copernican system, and you have done this yourself. Moreover, you have assigned individual motions to all except the sun, the earth, and the stellar sphere; to Mercury and Venus you have attributed a circular motion around the sun, without enclosing the earth; you make the three superior planets (Mars, Jupiter, and Saturn) move around the same sun, encompassing the earth inside their circles; then the moon can move in no other [354] way but around the earth, without enclosing the sun; and in regard to these motions you again agree with Copernicus.

  Three things now remain to be assigned to the sun, earth, and stellar sphere: that is, rest, which appears to belong to the earth; the annual motion along the zodiac, which appears to belong to the sun; and the diurnal motion, which appears to belong to the stellar sphere and to be shared by all the rest of the universe except the earth. Since it is true that all the orbs of the planets (namely, Mercury, Venus, Mars, Jupiter, and Saturn) move around the sun as their center, it seems much more reasonable that rest belongs to the sun than to the earth, inasmuch as it is more reasonable that the center of moving spheres rather than any other point away from this center is motionless; therefore, leaving the state of rest for the sun, it is very appropriate to attribute the annual motion to the earth, which is located in the middle of moving parts; that is, between Venus and Mars, the first of which completes its revolution in nine months, and the second in two years. If this is so, then it follows as a necessary consequence that the diurnal motion also belongs to the earth; for if the sun were standing still and the earth did not rotate upon itself but only had the annual motion around the sun, then the cycle of night and day would be exactly one year long; that is, we would have six months of daylight and six months of night, as we have stated other times. So you see how appropriately the extremely rapid motion of twenty-four hours is taken away from the universe, and how the fixed stars (which are so many suns) enjoy perpetual rest like our sun. Notice also how elegant this first sketch is for the purpose of explaining why such significant phenomena appear in the heavenly bodies.