Epitome Astronomiae Copernicanae: Liber IV, part 8
Book IV, Part III. Of the real motion of the planets and its true inequality, and the causes of it.
Whence have the planets their name, which in Latin means “wanderers”? From that manifold variety of their proper motions, which, if you follow the judgment of the eyes, has no law, no fixed circle, no definite time, when the comparison is made with the fixed stars.
In how many ways do the planets seem to wander? In three. 1. In longitude, along the sphere of the fixed stars, which we have said extends along the ecliptic. 2. In breadth, or to the two sides of the ecliptic toward its poles. 3. In height, that is, on a straight line stretched from the centre of sight into the depth of the ether. Though this variety is not detected by the eyes alone, but reasoning is added from the changed apparent magnitude of both bodies and arcs.
What is to be held concerning these wanderings of the planets: do they truly wander in all that variety, or is sight only deceived? Although that motion is not wholly, as it falls upon the eyes, in the bodies of the planets themselves, and much deception of sight here insinuates itself, yet when these deceptions have been removed by the mind, there still remains some inequality of motions, and it is truly in all the planets.
What then is that true motion of the planets as to its circumstances? It is constant indeed as to whole periods, and tends about the Sun, the centre of the world, perpetually in the order of the signs, and never stays in one place like one standing still, and much less ever becomes retrograde; yet it is unequal in swiftness by parts, and makes the planet in one certain part of its circuit run out farther from the Sun, and in the opposite part come nearest the Sun, where the farther it runs out the slower it is, the nearer it approaches the swifter; finally in one part of the circle it goes out to the north of the ecliptic, in the other to the south; and so a real inequality still remains to it, threefold, in length, in breadth and in height, which astronomers prove by suitable evidence, of which in Book VI.
I. The causes of the true inequalities.
Say what the ancients thought of the causes of this inequality. The ancients wished this to be the task of the astronomer, that he should bring forward such causes of this apparent inequality as bear witness of the true motion of the planet or of the orbs, that it is most regular, most equal and most constant, and of the simplest figure, namely exactly circular; and they judged that he was not to be listened to who should place any inequality in the real motions themselves of these bodies.
Do you judge that this axiom must be retained? I answer in three ways. 1) That the motions of the planets are regular, that is, ordered and described according to a fixed and unchangeable law, is beyond controversy. For if this were not so, there would be no astronomy, nor could the heavenly motions be predicted. 2) It follows, then, that there is some conformity among whole periods. For that law of which I spoke is one and perpetual through the innumerable turns or measurings of the heavenly course. But if the same law rules them all, all the turns are therefore like to one another and equal in the course of time. 3) But it is not yet granted that even in the different parts of each circuit the motion is in truth equal. For astronomy testifies that if we remove in mind all the deceptions of sight from that confusion of the apparent planetary motion, there is left a circuit of the planet in whose different parts, in truth equal, the swiftness of the planet is unequal, no less than in angles at the Sun equal in cause of time there is an apparent inequality. And Ptolemy himself, having set up different centres as the rule of motion of eccentrics and epicycles, makes those circles of his move at one time more swiftly, at another more slowly. Finally astronomy, treated with fitting subtlety, testifies also of this, that the single journeys or circuits of the planets are not ordered exactly into a perfect circle, but become elliptical.
By what arguments, however, did the ancients establish their opinion contrary to this of yours? Chiefly four: 1) from the nature of the movable bodies, 2) from the nature of the moving power, 3) from the nature of the place in which that motion is, 4) from the perfection of the circle.
Say their argument from the nature of the bodies. They reasoned thus: those bodies are not composed of the elements, and so neither generation nor corruption, nor any alteration has any right in them. The experience of all the ages testifies to this: for the same bodies are always seen, and nothing is found changed in bulk, in number, or in form. Now the motions of the elementary bodies are varied and inconstant for this very reason, that the elements are variously mixed for their constitution and in the mixed bodies fight among themselves. In the heavenly bodies, therefore, where there is no such mixture and no fight of elements in mixtures, there is no place for turbulence, none for inequality.
What do you think should be answered to this argument? If the argument speaks of disorderly turbulence of motions, there is indeed none such in the heaven; there are no heavenly tumults, such as in thunderclaps of flames fighting among themselves and of dripping water: for the composition of the bodies of the world is of a very different kind. But if it is opposed to every regular inequality also, then not all, and certainly not that regular intensification and remission of motions, is from the fight and mixture of the elements in the bodies moved, nor from the fact that they are mutable. For some inequality of motions arises from this very thing, that they are bodies, both those which are moved and those which impart motion, and because they consist of their own matter, their own quantity, their own figure, within as without, and according to quantities and figures are also endowed with their natural power, which can do less on a distant movable body than on a near one: where the faculties of the mover and the moved rather yield to each other than fight. So the magnet attracts iron with one part of its body, repels it with the other, not at all on account of any mixture of elements, but on account of an inner rectilinear figuration, according to which it has an inborn power; so the same magnet attracts iron more strongly when near than when far, not because, when nearer, it has more fire or earth, but because its power is weakened by the very distance. The heavenly bodies (that is, those of the world) nevertheless remain perennial and unchangeable as to their whole masses (for the changes that befall their surfaces can bring no weight to disturb the motions of the whole masses), and on this perennity of the whole globes, and on the fact that there is nothing disorderly in the world to hinder their motions, depends also that regularity of circuits and perpetual likeness, and the constant equality of the inequality in single parts through whole turns.
Recount the second argument of the ancients, drawn from the moving cause. They said that the moving powers of the heavenly bodies are the simplest substances, namely divine and most pure minds, which what they do they do constantly, perpetually alike, using the most equable exertion of strength, never wearied, because they feel no labour. There is therefore no cause why at different times they should move their globes differently, and so also the figures of the motions, by this very nature of the minds, are most perfect circles.
What do you oppose to this? Although the moving power is neither any god nor a mind, yet it must be conceded, as the argument wishes, partly also of that moving cause which the truer philosophy suggests, namely the natural power of bodies, that wherever and in so far as such power is solitary, it moves most equably and in a perfect circle, and that by the sole necessity of its effort and the perennial simplicity of its essence. So it happens in the rotation of the bodies of the Sun (and perhaps also of the Earth), which is from one moving cause alone, whether that be a quality of the body or an offspring of the soul born with the body. For the axis with its two opposite poles remains, and the body revolves about the axis most equably and most circularly. So also it would be if some planetary globe were always at the same interval from the Sun; for it would be carried by the Sun in a most perfect circle most equably through the emitted immaterial form of the solar body, established in the most equable motion of turning, with which same most equable motion that form of the body also goes round in the breadth of the world’s space, like a stirred whirlpool.
But although we have so far granted the argument of the ancients, there does not yet follow from it a complete equality of motions. For to the motion there concur not only the moving power and the movable body, but also the inner rectilinear figuration of the movable body, which according to its diverse situation toward the Sun is diversely affected in the motion also, being driven out from one region, drawn inward from another; there concurs the rest of the magnetic axis of the movable body in a parallel situation, from which inner rest and from the carrying about coming from outside there arises that change of situation of the parts of the planet toward the Sun; there concurs finally the interval between the Sun and the planet, which is varied by that expulsion and attraction; but the interval being changed, and the planet coming into a denser or a rarer power, its motion also must needs be intensified or remitted, and the figure of the journey become elliptical. Thus, in respect of the concurrence of so many requisites, the power moving the planet cannot be called simple, because it moves in one degree and another of its form.
What was the ancients’ argument from place? They gathered thus: the elementary region is about the centre of the world, the heaven at the surface; to the elementary bodies therefore belongs rectilinear motion, which has a beginning and an end, and which, dispensed by the contrary principles of heaviness and lightness, brings each of those bodies back to its place, whence it comes that according to nearer and nearer approach to the natural place, as to a goal, the swiftness also is different and different, and finally mere rest. But the heavenly bodies are turned perpetually in the circular space of the world, which is an argument that they are neither heavy nor light, nor are they moved for the sake of rest or of occupying a place, as one in which they would always be turned, but are moved only that they may be moved; and so both their motion must be equable, and the form of the motion other than rectilinear, namely one fitted to the eternity of motion, that is, returning into itself.
What do you answer to this third argument? Not all inequality of motions is from heaviness and lightness, the properties of the elements, but some also from change of interval, as is plain in the lever and the balance, and this cause begets the intensification and remission of the heavenly motions, as has been explained so far. Meanwhile it must be borne in mind that there is nevertheless some kinship between the principles of heaviness and lightness in the elements and the natural inertia of the planetary globe toward motion, but through which no inequality of motion is excused. As to the figure of the motion, the argument concludes no more than we ourselves can grant: that the motion is reflected into itself, of which sort is not only the circular but also the elliptical, and so the assumptions are not denied. For truly the bodies which revolve about their axes are moved in this only, that by their perennial motion they may serve some necessity of their globe, and some also, that they may carry the planets about them in perennial rounds.
Say the fourth argument of the ancients, sought from the circular figure. They philosophized thus: of all the motions returning into themselves the circular is the simplest and the most perfect, while in all the others, as the oval and the like, something of straightness is mixed; this circular motion therefore is most familiar to the simplest nature of bodies, to the divine moving minds (as one whose beauty and perfection is something of the mind), and finally to the heaven, which has a spherical figure.
How is this to be dissolved? To this I answer thus: first, if the heavenly motions were the work of a mind, as those ancients believed, it would be concluded very handsomely that the journeys of the planets are perfectly circular. For then the form of the motion, conceived by the mind, would be for the power a rule and a goal to which the motion would be referred. But the heavenly motions are not the work of a mind, but of nature, that is, of the natural power or soul of bodies, acting uniformly according to those corporeal powers, which is proved by nothing more strongly than by this very observation of the astronomers, who, the deceptions of sight being lawfully separated, find that there remains in the real and truest motion of the planet an elliptical figure of the circuit, which bears witness of the natural corporeal power and of the emanation and quantities of its form. Next, even if we grant them intelligences, they still do not obtain what they wish, namely the complete perfection of the circle. For if it were a question of the beauty of the circle alone, the circle would be most rightly discerned by the mind, and would adorn the bodies themselves, whatever they are, most of all the heavenly, since they are partakers of quantity, a most beautiful quantity. But since besides the mind there would also be need of natural and animal faculties for moving, those would follow their own genius too, and would not do all things from the dictate of the mind, which they would not perceive, but many things from material necessity; it is no wonder, then, if these faculties, mixed together, could not wholly attain perfection. The ancients themselves grant to the planets eccentric journeys, which seems a much greater deformity than the elliptical path, and yet by the foresight of their minds they could not avoid this deformity.
I have often warned, however, that when I deny that the heavenly motions are the work of a mind, I am not then speaking of the creating Mind, to which all things are fitting, whether circular or elliptical, whether to be administered and represented through minds, or compelled by material necessity from principles once laid down.
II. Of the causes of the inequality in longitude.
What causes, then, do you give why, although all the journeys of the primary planets are ordered about the Sun, yet the angles (under which, as from the centre of the Sun, the different parts of the journey of one planet are viewed) are not completed by the planet in proportional times? Two causes concur, one optical, the other physical, each of nearly equal effect. The first cause is that the journey of the planet is not drawn round the Sun at an equal interval everywhere, but one part of it is near the Sun, the opposite part so much farther from the Sun. Of equals, moreover, the near is viewed under a greater angle, the remote under a smaller; and what are viewed under an equal angle, the near are smaller, the remote greater. The other cause is that the planet is in truth slower at the greater distance from the Sun, swifter at the less.
The two causes being then put together into one, it is easily plain that of two arcs equal to the sight the greater arc by itself requires a greater time, and much greater indeed because of the real slowness of the planet in that more remote arc.
Could not one cause suffice, so that, since the orbit of the planet altogether recedes farther from the Sun on one side than on the opposite, we might make the remoteness so great that all this apparent inequality should be excused by this unequal distance of the parts of the orbit alone? The observations do not suffer us to make the inequality of distances as great as is the inequality of the time in which the planet completes equal angles at the Sun, but they bear witness that the inequality of the intervals suffices to excuse at least half of this inequality: the remainder is therefore from a real acceleration and retardation of the planet.
What are the laws and examples of this swiftness and slowness? A genuine example is in the balance: for as there, when the arms are in equilibrium, the proportion of the weights hung from each arm to one another is the inverse of the proportion of the arms; for the greater weight, hung from the shorter arm, makes an equal to the lesser weight hung from the longer arm: so as the short arm is to the long, so is the weight of the longer to the weight of the shorter; and if we now remove in mind one arm and in place of its weight conceive an equal power in the beam itself of lifting the remaining arm with its weight, then it appears that this power of the beam cannot do so much on a weight at a distance as it can on the same weight near: so also astronomy testifies of the planet that the Sun cannot do so much to move it and carry it about when the planet is farther from the Sun in a straight line as when the interval is lessened; and in a word, if you take equally long arcs of the planet’s orbit, the proportion between the withdrawals of the two arcs from the Sun is the same as the proportion of the times which the planet spends in those arcs. Thus the centre of the Sun or of the world is represented by the beam of the balance, and its moving power by the other arm and its weight, which we were just now bidden to disregard and reduce in mind into the beam itself; the planet is represented in the weight of the remaining arm, the interval between the Sun and the planet in the arm of that weight.
Let AC be a balance, with weights D and B hanging from C and A, the beam EF, the angles FEC and FEA right; then as CE is to EA, so will the weight B of EA be to the weight D of EC. Remove EA in mind, and let the power of the weight B, formed through EA, be the power of the beam E itself; this power of the beam E will then hold the weight D, hung from C, in equilibrium at the horizontal, that is, so that FEC is a right angle. But if the same weight, drawn away from C, passes as far as G, the same power of E will be able to do more on this weight and will lift it above the line EC.
Let E now be not a beam but the Sun, and D the planet, EC and EG different distances of the planet from the Sun. The observations therefore testify that as EC is to EG, so is GK, the advance of the nearer planet in G, to GI or CH, the advance of the more remote in C.
Do you then ascribe weight to the planet? It was said above that in place of weight we must consider that natural and material resistance or inertia against leaving a place once occupied, which snatches the planet as it were out of the hands of the rotating Sun, so that it does not exactly follow that holding power.
What is the cause why the Sun does not hold the planet as strongly from afar as from near? The very attenuation of the form of the solar body, greater in a longer outflow than in a shorter: which attenuation, although in the proportion of the intervals it is duplicate, that is, both in length and in breadth, yet works only in the simple proportion, that is, according to length alone; the causes were stated above.
III. The causes of the inequality in height.
But what thrusts the planet out into the more remote spaces and brings it back toward the Sun? The same which holds the planet, namely the Sun, through the power-bearing form of its body, sent out through all the spaces of the world. For the thrusting out and the attraction are, as it were, certain elements of this holding. For the thrusting out and attraction are made by power-bearing lines issuing from the centre of the Sun, and since these lines go round together with the Sun, the planet also, which is thrust and drawn, must needs follow these lines, in proportion to their strength against the resistance of the body of the planet. Thus the contrary motions of thrusting out and attraction in a manner compose this holding.
You ascribe contrary operations, attraction and expulsion, to the simple body of the Sun and its immaterial form, and so not simple ones. There is one action or natural energy, of moving the body of the planet for the sake of assimilation, or of restoring it to its primal situation; but it seems diverse, on account of the diversity of the object. For the body of the planet has a kinship with the body of the Sun on one side at least, and on the other is at variance. Now it belongs to the same simple work to embrace like things and reject unlike. This opinion is supported by the example of magnets, which, though they are not heavenly bodies, yet in them this twofold power is not from a composition of elements but from a simple corporeal form.
The body of the planet itself, then, will be composed of contrary parts. Not even this: for it follows only that the planetary globe is figured within with straight lines or fibres, such as the magnetic are, which happen to be terminated in two contrary regions, in one of which, not on account of the body itself but on account of its situation toward the Sun, kinship with the Sun reigns, in the other discord.
But it is incredible that the heavenly bodies are vast magnets. Let the magnetic philosophy of William Gilbert the Englishman, then, be read, in which book, although the author did not believe that the Earth is carried among the stars, he yet ascribes to it a magnetic nature by very many arguments, and teaches that its magnetic fibres or filaments extend in straight lines from south to north. That which is one of the primary planets, namely the Earth, to be any one of the primary planets is by no means absurd or incredible.
Granted that the planet has an inner rectilinear magnetic figuration: what then is it that makes it turn one region of its body after another toward the Sun? Does it itself turn its fibres? By no means: rather we must ask what it is that holds the body of the planet, so that it does not abandon its magnetic axis in its situation, which it once received, with respect to the parts of the world, although the body revolves about the axis (like the body of the Earth) and at the same time is removed from its place and carried in a circle about the Sun. For from this direction of the magnet toward the same region of the world through the whole circuit and from the transport of the body from place to place about the Sun, as from two elements, this effect is composed, that the globe of the planet exchanges the situation of its regions toward the Sun. Look at diagram 62.
What are examples of this exchange? A familiar example again is in the magnetic compass, whose iron needle is imbued with the magnet. For into whatever region it is carried, the needle of the compass always looks to the north. And so, if you go round some castle bearing a compass, it will come about that now the head, now the tail of the needle looks to the castle, by the very fact that the head always, in every part of the circuit, looks to the north.
Another astronomical example was given above in Book III, when we said that the axis of the rotation of the Earth, while the Earth is carried about the Sun, remains perpetually in the same parallel situation, fol. 231.
What causes, then, do you give for the direction of the magnetic fibres of the planetary body toward the same region of the world through the whole circuit of the planet? The same which were indicated above in Book I, fol. 174, by which the axis of the rotation of the Earth is made firm. For first, the parallel situation of the fibres represents a certain identity, which is rest rather than motion. The cause of it, therefore, does not seem to be any positive or active natural power, but rather a privation of all motion. And so that natural inertia of matter toward motion seems to have an inner rectilinear figuration, and to be extended along these fibres, or by the condensation of the parts in a straight line to be made stronger and more insuperable.
But if this is not probable, let there be two distinct things: the first an inability of all matter, considered without inner figuration, which brings it about for the planet that it does not leave its place unless drawn out from without, namely by the Sun; the second of the planetary body, as it is figured within with straight fibres, by which those fibres are made safe from being inclined or removed from their position by the carrying round of the body. Finally let it be free to those who philosophize to define this very thing which I have just said, whether it is an inability only, or a power.
You define this inability or power by the mere maintaining of its position; what if something else lay beneath, and that power looked to certain parts of the starry heaven? Above, in Book I, fol. 174, when the question was of the axis of rotation of the Earth, similarly immovable, it was answered why such a thing is not to be thought: namely because there would be no cause why it should be directed to an empty point of heaven rather than to some star, and why to this part rather than to that; and because these fibres of the planets, no less than the axis of rotation of the Earth above, are found in the succession of ages to incline a little, and so to desert the former fixed stars and to nod to others that succeed, so far as can generally be judged. For that motion is very slow, so that within the 1400 years from Ptolemy to us this cannot be affirmed with sufficient safety of all the planets.
Perhaps those axes of the rotation of the bodies, of the fibres which you introduce here in place of librations, sustain the office? The axis of the diurnal turning of the Earth, of which in the spherical doctrine, is stretched, in respect of longitude, perpetually toward the beginnings of Cancer and Capricorn. For this axis produced on each side marks the poles of the world, as is in Book II, fol. 189. But the arc drawn from the pole of the world at right angles to the ecliptic passes also through the poles of the ecliptic; it is therefore the colure of the solstices, marking the beginnings of the said signs. But the fibres by which the Earth is repelled or allured by the Sun pass from sign to sign. For the aphelion of the Earth was once in Sagittarius, now it is in the sixth degree of Capricorn. Therefore the axis of the rotation of the Earth and the fibre which changes the interval differ from each other.
It seems, then, that the Earth should nevertheless be farthest distant at the beginning of Capricorn. For if the whole body of the Earth is rotated about that axis, the fibre also will be rotated, however it may differ from it in situation, and will describe as it were two cones, meeting with their vertices at the centre of the Earth; and only for a single moment of the day will it look to its proper place, in the rest of the day it will go round the beginning of Capricorn, shown by the axis of the Earth, and so will gather all its force into this axis and will draw the Earth away from the Sun by a kind of spiral line always toward the region of the axis. Indeed in this way, and by the cohesion of the fibre with the axis of the diurnal motion thus consolidated, what is said would happen, and the apsis of the Earth would never depart from the beginning of Capricorn. We are therefore forced to concede either that a globe within the outer crust, so that the latter is rotated with the diurnal motion, that globe, having the fibres, is not rotated, and the usual magnetic power belongs to the outer crust, because it always shows the poles of the diurnal turning, not however the apsis of the Sun or of the Earth. Let some natural philosopher help here J. C. Scaliger, disputing on the origin of rivers and on the flow and ebb of the sea, and see whether these separate bowels of the Earth could succour that labouring man. Though to me the Moon and the soul of the Earth suffice.
If the planetary globes have an inner rectilinear magnetic figuration, why do you not ascribe to those very fibres rather that they flee from the Sun and approach the Sun, according to the diversity of the regions of their body, as was done in the Commentaries on Mars? 1. Because astronomy testifies that the departure from the Sun and approach to it are made on a line as if extended toward the Sun, in so far as the intermixed circulation does not vary it; but the magnetic fibres are rarely stretched toward the Sun. 2. Because two very different things would be ascribed to those magnetic fibres. For first they would direct themselves to the same region of the world, which is something like rest, then they would move their body from its place, now from the Sun, now toward the Sun. But this by way of expulsion and attraction is more simply reconciled with the holding and carrying round of the bodies which the Sun effects. 3. Nay, it is more probable that the power-bearing form of the solar body is continued as far as the planets, than that of these as far as the Sun, so that they flee it, repelling, and seek it, drawing. For the Sun is a vast body, those of the planets small; the light and heat of the Sun reach us manifestly, the Sun carries the planets. Of the other powers of the Sun, then, we were sure before, of the extension of the planetary power as far as the Sun we have not such and so evident testimonies. 4. It will appear below that the fibres of the body suffer from the Sun some slight inclination: it is therefore probable that the libration also of the whole body is adventitious to it from the Sun rather than inborn; that it is, namely, a suffering from another, not an action or motion from itself.
But you would at least set up this power as common between the Sun and the planets, and a force of expulsion and attraction passing to and fro mutually, as is common between two magnets. Nay, this very thing is the fifth reason why this expulsion and attraction is not ascribed to the planets themselves, that it be not mutual by the very institution of the Creator, who does nothing in vain; therefore if the power of the planet were stretched as far as the Sun, the Sun would have to be moved by the planets, in the proportion of the bodies, out of its situation, which it has in the centre of the world, or at least to totter, drawn now hither now thither, as many planets, with a like faculty among themselves, fall upon the Sun from one side.
You seem not even so to escape this inconvenience: for the Sun, by the power-bearing form of its body, leaning as upon a pole in thrusting the planets, will thrust itself out proportionally, and drawing the planet as with a hook, will draw itself a little toward the planet. In every way we escape this by denying the mutual attraction and expulsion. For first the form and disposition of the bodies will not be directed hither if the power of the planet is not extended to the Sun; next, neither in the very act does any such thing follow, as if apart from the counsel of the Creator, from material necessity alone. For so great is the mass, so great the density in the matter of the solar body, so great its power of attracting and driving, so great in turn the smallness both of the planet and of its resistance, that the Sun is in no peril as to its state. So when a ship sticks in the sand and can be pulled off and moved from its place only by two hundred horses, a hundred horses, although they are half the power required, do not nevertheless move half of the single task, because between motion and non-motion there is no halving, since these are contradictory.