Immanuel Kant

Universal Natural History and Theory of Heaven

Part Two

Section Five

Concerning the Origin of Saturn's Ring and the Calculation of the Daily Rotation of the Planet from the Relationships to this Ring

Thanks to the systematic arrangement in the cosmic structure, its parts are linked together by a ladder of alterations in their characteristics, and we can assume that a planet located in the remotest region of the world will have approximately the character which the nearest comet would possess, if through a diminution of its eccentricity, it were raised into the family of planets. With this in mind, we will examine Saturn as if it had gone through several orbits with a greater eccentricity, in a manner similar to the motion of a comet, and had been gradually brought into a path like a circle (14). The heat which the planet incorporates in its approach to the sun caused the material on its outer surface to rise up. As we know from previous sections, this material in the case of the most distant celestial bodies is excessively volatile, so that with low levels of heat it undergoes diffusion. After the planet was brought in several orbits to the position where it is now suspended, in such a moderate climate it gradually lost the heat it had absorbed, and the vapours from its outer layer, which still constantly spread around it, gradually stopped moving up into tails. New material did not move upward any longer in such accumulations to supplement the old ones. In short, the vapours already going around Saturn remained, for reasons which we will refer to presently, suspended in a constant state of rest around the planet and gave it the reminder of its previous comet-like character in a permanent ring, while Saturn's body exuded the heat and finally became a calm and cleansed planet. Now we will point out the secret which in this celestial body could have held the vapours which had come up from it in free suspension, indeed, which changed these vapours from an atmosphere spread out around the planet into the form of a ring standing completely apart from it. I assume that Saturn had an axial rotation. Nothing more than this is necessary to reveal the entire secret. No mechanism other than this single one produced a ring for the planet through the immediate mechanical result of the phenomenon mentioned above. I am sufficiently confident to assert that in all of nature only a few things can be reduced to such a comprehensible origin as this strange characteristic of Heaven can be derived from the raw state of the planet's first development.

The vapours rising up from Saturn had their own movement and established themselves freely at the altitude to which they rose. This motion they acquired as parts of the planet from its axial rotation. The particles which moved up from close to the equator of the planet must have had the fastest motions, and those further away right up to the poles that much slower motions, according to the distance from the equator from which they arose. The relationship to the specific gravity established different altitudes for the ascending particles. But the only particles which could maintain their locations at that distance in a constant free circular momentum were the ones which could attain their own velocity from the axial rotation at a level which the centripetal force required for equilibrium at those distances. The remaining particles, to the extent that the interaction with the others could not bring them this precise velocity, must either through their excess motion leave the planetary sphere or through their lack of motion necessarily sink back onto the planet. The particles scattered throughout the total extent of the vapour sphere, thanks to the same central law in the motion of their curved momentum, would intersect the extended equatorial plane of the planet from both sides. And in coming together on this plane from both hemispheres, they would stop each other and accumulate there. Since I assume that the above-mentioned vapours are the very ones which the planet in its cooling sent back up, all the scattered vapour material will collect close to this plane in a space not very wide and leave the space on both sides empty. In this new and changed orientation, however, the materials will continue exactly the same movement which they maintained while suspended in free concentric circular orbits. In such a manner, the circle of vapours alters its shape, which was completely spheroidal, into the form of an extended plane matching precisely Saturn's equator. But this plane must also, for exactly the same mechanistic reasons, finally assume the form of a ring, whose outer edge will be determined by the effect of the sun's rays, which with their force scatter and disperse those particles which have distanced themselves a certain way from the mid-point of the planet, as they do with comets. In this way the sun's effect designates the outer limit of their circle of vapours. The inner edge of this emerging ring will be determined by the relationship to the velocity of the planet at its equator. For that distance away from the mid-point where this velocity attains an equilibrium with the power of attraction for that location is the closest approach to the planet where the particles which have arisen from its body are able to describe circular orbits from their own movement acquired from the planet's axial rotation. Because the particles closer than that require a higher velocity for such an orbit, which they cannot have because the movement even on the equator is not faster, they will maintain eccentric orbits which intersect each other, weaken each other's motions, and finally will fall back down onto the planet from which they arose. Now, there we see a wonderfully strange phenomenon, the sight of which since its discovery has always astonished astronomers and whose cause we could not ever entertain even a probable hope of discovering. Now we see that phenomenon arise in an easy mechanistic way, free of all hypotheses. What happened to Saturn, as can be easily seen from this, would happen just as regularly to a comet with a sufficient axial rotation, if it were set at a constant height in which its body gradually could cool down. Nature, left to its own forces, is fertile in excellent results, even in chaos. The development following from this produces such wonderful relationships and harmonies for a creature's common needs that it enables us to recognize with unanimous certainty in the eternal and unchanging laws of their essential characteristics the Great Being in whom they are all united, thanks to their common dependency in a collective harmony. Saturn derives important advantages from its ring. It lengthens its day and under so many moons illuminates its night to such an extent, that the absence of the sun is easily forgotten. But must we then, on that account, deny that the common development of material through mechanical laws, without the need for anything other than their universal efficacy, could have produced the relationships which created advantages for reasoning creatures? All beings have a common dependency on a single cause: the Divine Understanding. They can therefore produce no other consequences after them except those which bring with them an image of the perfection of exactly the same Divine Idea.

Now we will calculate the time of the axial rotation of this celestial body from the relationships of its ring, according to the hypothesis of its development mentioned above. Because all the movement of the ring's particles is a motion derived from axial rotation of Saturn, on whose outer surface they were located, the fastest movement which these particles possess among themselves will be the same as the fastest rotation which occurs on Saturn's outer surface. In other words, the velocity at which the particles of the ring orbit on its inner edge is equal to the velocity of the planet at its equator. But we can easily find that when we look for it in the velocity of one of Saturn's satellites. For we assume that it is proportional to the square root of the distances from the mid-point of the planet. From the velocity we have discovered, the time of Saturn's axial rotation is immediately given: it is six hours, twenty-three minutes, and fifty-three seconds. This mathematical calculation of an unknown movement for a celestial body, which is perhaps the only prediction of its kind in the real theory of nature, awaits confirmation from the observations of future ages. The telescopes known up to this time do not enlarge Saturn sufficiently, so that we can discover the spots (which we can presume are on its outer surface) in order to perceive its axial rotation through their forward displacement. But the telescopes have perhaps not yet reached that perfection which we can expect of them and which the hard work and skill of the craftsmen seem to promise us. If we once succeed in providing visible confirmation of our conjectures, how certain the theory of Saturn would be and what an overwhelming credibility the entire system which is built upon the same principles would derive from that. The time of Saturn's daily rotation establishes the relationship of the centrifugal force away from the mid-point to the force of gravity at the outer layer. The former is to the latter as 20 is to 32. Thus, the force of gravity is only around 3/5 greater than the centrifugal force. Such a large proportion as this brings about necessarily a very observable difference in the diameters of this planet. And we might apprehend that it would have to develop to such an extent that the observation of this planet, although it is only enlarged a little by the telescopes, would have to be all too clearly visible. But in truth this does not happen, and the theory could thus suffer a disadvantageous blow. A proof based on first principles completely removes this difficulty. According to Huygens' hypothesis, which assumes that the gravitational force inside a planet is the same throughout, the difference in the diameters is proportional to the diameter at the equator in a ratio twice as big as the proportion of the centrifugal force to the gravitational force at the poles. For example, in the case of the Earth, the force moving away from the mid-point at the equator is 1/289 of the gravitational force at the poles. Thus, in Huygens' hypothesis, the diameter of the equatorial plane is 1/578th greater than the earth's axis. The cause is as follows: the gravitational force, according to what has been assumed, inside the Earth's cluster in all regions close to the mid-point is as great as it is on the outer surface, but the centrifugal force diminishes as one moves close to the mid-point. Thus, the centrifugal force is not always 1/289th of the gravitational force. For these reasons, the loss in weight of a liquid column on the plane of the equator amounts, not to 1/289th but half of that, i.e., to 1/578th. On the other hand, according to Newton's hypothesis, the centrifugal force, which initiated the axial rotation, on the entire equatorial plane right to the mid point has the same relationship to the gravitational force at a specific location. For the gravitational force inside the planet, assuming the planet has the same density throughout, decreases with the distance from the mid-point in the same proportion as the centrifugal force decreases, so that the latter is always 1/289th of the former. This creates a lightening of the liquid columns at the equatorial plane and a rise in them of 1/289. This difference of the diameters in this theory is increased even more by the fact that the shortening of the axis involves bringing the parts closer to the mid-point, and with that an increase in the gravitational force; the increase in length of the equatorial diameter involves moving parts further from the very same mid-point and thus lessening the gravitational force. For this reason, the flattening of the Newtonian spheroid increases to the point where the difference in the diameters increases from 1/289th to 1/250th.

According to these principles, the diameters of Saturn would have to be in an even larger ratio to each other than 20 to 32. They would have to reach a proportion almost equal to 1 to 2, a difference which is so large that the slightest attentiveness would not miss it, no matter how small Saturn may appear through the telescopes. But from this one should notice that the assumption of the uniform density, which seems to be quite correctly applied to the case of the earth's sphere, in the case of Saturn deviates far too widely from the reality. This is inherently probable in the case of a planet whose cluster consists, for the greatest part of its content, of the lightest materials and which leaves the heavier sorts of material much freer to settle down toward the mid-point, according to the effects of the gravitational pull, than do those celestial bodies whose much denser material delays the settling down of the material and allows it to harden before the settling can occur. When we also assume in the case of Saturn that the density of its material in the interior increases as one moves closer to the centre, then the gravitational force no longer declines in this ratio, but the growing density compensates for the deficiency in those parts which are set at heights above the point located in the planet and which contribute nothing by their power of attraction to the planet's gravitational power there (15). When this preponderant density of the deepest material is very large, thanks to the laws of attraction, the density changes the gravitational force which in the interior declines toward the centre into something almost uniform and establishes the ratio of the diameters according to Huygens' proportion, which is always half the ratio between the centrifugal force and the gravitational force. Consequently, since with respect to each other, these were as 2 to 3, then the difference in the diameters of Saturn will not, not 1/3, but 1/6 of the equatorial diameter. Finally, this difference will still be concealed because Saturn, whose axis makes a constant angle of 31 degrees with the axis of its orbital plane, never orients the position of its axis perpendicular to its equator, as happens with Jupiter. According to the planet's appearance, this lessens the previous difference by almost one third. Under such circumstances, and especially considering Saturn's great distance away, we can believe that the flattened shape of its body will not be so easily visible as we have really come to think. However, astronomy, whose progress depends particularly on the perfecting of the instruments, with their help will perhaps be in a position to discover such a remarkable characteristic, if I do not flatter myself excessively.

What I say about the shape of Saturn can, to some extent, serve as a general remark about the theory of heaven. According to an exact calculation, Jupiter has a ratio of the gravitational force to the centrifugal force at its equator of at least 9.25 to 1. If its cluster were of uniform density throughout, in accordance with Newton's theories, this planet should show a difference between its axis and the equatorial diameter even greater than 1/9. But Cassini found it to be only 1/6, Pound 1/12 and sometimes 1/14. At least all these different observations, which in their difference confirm the difficulty of this measurement, agree in that they establish the difference as much smaller than it would be in Newton's system, or rather, according to his hypothesis of the uniform density. And if we therefore change the assumption about the uniform density, which permits such a wide discrepancy between theory and observation, into the much more probably assumption that the density of the planetary cluster is arranged so that it increases towards the centre of the planet, then we will validate the observations not only of Jupiter but also of Saturn, a planet much harder to measure, so as to be able to understand clearly the cause of the smaller flattening of its spherical body.

From the development of Saturn's ring, we have taken the opportunity to venture on the bold step of determining through calculation the time of its axial rotation, something which the telescopes are not capable of discovering. Let us add to this attempt at a physical prediction yet another concerning the very same planet, something whose witnessed validity is to be anticipated from the more perfect instruments of future ages.

According to our assumption, Saturn's ring is an accumulation of particles which, after they arose as vapours from the outer layer of this celestial body, thanks to the momentum which they receive and continue from the planet's axial rotation, maintain themselves at the altitude of their distance away in free circular movement. These particles do not have the same periodic orbital times at all their distances, but rather hold to these times according to the square root of the cube of their distance from the planet, if they are to keep themselves suspended according to the laws of the central forces. Now, the time in which, according to this hypothesis, the particles of the inner edge complete their orbit is about ten hours, and the orbital time for the particles on the outer edge is, according to the appropriate calculations, about fifteen hours. Thus, when the lowest parts of the ring have completed three orbits, the furthest parts have completed only two. Even if we estimate that the interference which the particles create for each other in the plane of the ring through their great dispersal is as insignificant as we like, it is nevertheless probable that the slower movement of the particles further away in each of their orbits gradually delays and retards the more quickly moving lower parts. On the other hand, the lower parts would have to impart to the upper parts some of their motion, so as to create a more rapid rotation. If this reciprocal interaction were not finally interrupted, this process would last until such a time as all the particles in the ring, both the low ones and those further away, were brought to rotate in the same time, in which state they would be at rest relative to each other and would have no effect in displacing each other. But such a condition, if the movement of the ring ended up like this, would destroy it completely. For if we take the middle of the plane of the ring and establish that the movement remain what it was before and what it must be to be capable of sustaining free orbital movement, the lower particles would not hold themselves suspended at their altitude, because they would be held back considerably, and they would intersect each other in oblique and eccentric motions. The more distant particles, however, through the impulse of a motion greater than it should be for the central force at their distance from the planet, would move away from Saturn further than the outer boundary set by the effect of the sun and would, of necessity, be scattered behind the planet by the sun's effect and carried away.

But we need not fear all this disorder. The mechanism of the developing ring involves an arrangement which, thanks to the very causes which should destroy the ring, establish it in a secure state by means of which it is divided up into several concentric circular bands which, because of the intervening gaps which separate them, have no more common interaction with each other. For while the particles orbiting on the inner edge of the ring with their faster motion push forward the particles above somewhat and accelerate their orbit, the higher level in velocity provides these particles with an excess of centrifugal force and moves them further away from the place where they were suspended. But if we assume that while these particles strive to separate themselves from the lower ones, they have to overcome a certain interconnection which, although indeed they are scattered vapours, nevertheless appears to be not entirely insignificant for them, then this increased level of momentum seeks to overcome the interrelationship mentioned above, but does not do so by itself, so long as the excess in the centrifugal force causing them to move around in the same orbital time as the lowest particles does not exceed the central force of their position and their interdependency. And for this reason, the upper particles must undergo a certain tendency to pull themselves away from the lower ones in a band of a certain width in this ring. However, the interconnection remains, but not in a large width, because the velocity of these particles orbiting in equal times increases with the distances more than it should according to the central laws. Thus, when it has gone beyond the level which can sustain the interconnection of the vapour particles, they must tear themselves away and take up a distance away from the planet appropriate to the excess momentum of the orbital forces over the centripetal force at that location. In this way, the intervening space will be set up, keeping the first band of the ring away from the rest. And in much the same way, the accelerated motion of the particles above, through the rapid rotation of those below and their interconnection with them, which seeks to hinder the separation, will make a second concentric ring, from which the third arises around a moderate intervening gap. We could calculate the number of these circular bands and the width of the intervals between them, if we knew the extent of the interconnection linking the particles to each other. But we can be satisfied that we have generally found out with a good degree of probability the composition of Saturn's ring, which prevents its destruction and keeps it suspended through free movements.

The conjecture gives me no little satisfaction thanks to the hope of seeing it confirmed in future through effective observations. A few years ago there was a report from London that when people observed Saturn with a new Newtonian telescope, an improved model by Bradley, its ring happened to be essentially a combination of many concentric rings, separated by intervening spaces. This report has not been taken further since that time (16). The observational instruments have opened up for our understanding the knowledge of the most distant boundaries of the cosmic structure. If now it is particularly up to them to undertake new steps in this business, from the attentiveness of our time to all those things which can expand human ideas we really have probable grounds for hoping that they will turn particularly in a direction which presents them with the greatest expectation of important discoveries.

If Saturn, however, has been so fortunate as to make a ring for itself, why then has no other planet shared this advantage? The reason is clear. The ring must arise from the ascending vapours of a planet, which it gives off in its raw condition. The planet's axial rotation must give these vapours their momentum which they only have to continue when they have reached the altitude where they can attain an exact equilibrium between the planet's gravitational power and the motion they have been given. Thus, we can easily determine by calculation the altitude to which the vapours from a planet must rise, if they are to maintain themselves in a free circular motion by means of the motions which they had at the planet's equator, provided we know the diameter of the planet, the period of its axial rotation, and the gravitational force on its outer surface. According to the law of central movement, the distance of a body which can go freely in circles around a planet at a velocity equal to the planet's axial rotation is in exactly that ratio to the semi-diameter of the planet as the centrifugal force away from the centre at the equator is to the gravitational force. On the basis of these principles, the distance of the inner edge of Saturn's ring is equal to 8, when we assume that the half-diameter of the planet is 5. These two numbers are in the same ratio as 32 to 20, which, as we have previously noted, expresses the ratio of the gravitational force to the centrifugal force at the equator. On the same basis, if we establish that Jupiter is to have a ring developed in this way, the smallest half-diameter would have to exceed the half-diameter of Jupiter by a factor of 10. That would exactly match the distance where its most remote satellite orbits around it. For these reasons and also because the vapours rising up from a planet cannot expand so far out from it, it is impossible for Jupiter to develop a ring. If we want to know why the Earth has acquired no ring, we will find the answer in the size of the half diameter, which the inner edge of the ring would have to have had. This would have to have been 289 Earth diameters. With the slowly moving planets the possibility for the development of a ring gets even more remote. Thus, there is no example left where a planet could have acquired a ring in the manner which we have explained, other than the example of the planet which really has one. This is not an insignificant confirmation of the credibility of our manner of explanation.

What makes me almost certain that the ring going around Saturn has not come about in the common way and was not built up through the universal laws of development governing throughout the entire system of planets, which also produced Saturn's satellites, and certain, I say, that no external material provided the material for this ring but that it is a creation of the planet itself, which moved its most volatile parts upward up by its heat and gave them a rotational momentum from its own axial rotation, is this fact: unlike the other satellites of this planet and, in general, all orbiting bodies which accompany a main planet, the ring is not oriented on the common interrelated plane of planetary motions, but deviates from it considerably. This is a certain proof that it did not develop from the common basic material and acquire its motion from the sinking down of this material, but arose from the planet long after its complete development and through the orbital force implanted in the planet, as a part separated from it. It acquired from the planet's axial rotation a related motion and direction.

The pleasure of having grasped one of the strangest peculiarities of Heaven in the full extent of its nature and development has involved us in an extensive discussion. With the permission of our indulgent readers, let us keep going to excess, if that is agreeable, so that after we have permitted ourselves pleasantly arbitrary opinions with a sort of freedom from restraint, we will turn back with that much more caution and return to the truth.

Could we not imagine that the Earth, like Saturn, once had a ring. It might have arisen from its outer layer exactly as Saturn's did and have maintained itself a long time, until the Earth had gone from a much faster rotation than the present one to the existing rate for who knows what reasons. Or we could attribute the building of it to the common basic material sinking down according to the rules which we explained above, which we must not take so strictly if we will indulge in our liking for the unusual. But what a store of beautiful explanations and consequences such an idea offers us. A ring around the Earth! How beautiful the sight for those who were made to live on Earth as a paradise. How much comfort for those whom Nature greeted with a smile on all sides. But this is still nothing in comparison with the confirmation which such a hypothesis can derive from the ancient lore of the creation story, no small recommendation for approval among those people who believe they are not dishonouring revelation but endorsing it when they use it to ennoble the excess displays of their wit. The waters of the firmament, which the Mosaic account talks of, have already caused interpreters no small problem. Would it not be possible for us to use this ring to assist ourselves out of this difficulty? This ring consisted undoubtedly of vapours rich in water. And in addition to the advantage which it could provide for the first inhabitants on the earth, we have the fact that it was, when necessary, capable of breaking apart in order to punish the world, which had made itself unworthy of such beauty, with deluges. Either a comet, whose power of attraction brought the ring's parts into total confusion, or the cooling in the region where it was positioned united its scattered vapour particles and hurled them down upon the earth in the most horrifying of all inundations. We understand readily what the consequences of this were. The whole world went under water and absorbed, in addition to the foreign and volatile vapours of this unnatural rain, that slow poison which brought all creatures closer to death and destruction. The shape of the pale light bow vanished from the horizon at that time, and the new world, which no longer could remember what it looked like without experiencing terror before this fearful instrument of the divine revenge, saw perhaps with no less dismay in the first rainfall that coloured bow which seems to develop its shape like the first one, but which through the covenant of a forgiving heaven was to be a sign of grace and a memorial to the lasting establishment of the newly changed Earth. The similarity in the form of this memorial sign to the narrated event could make such a hypothesis appealing for those people who follow the prevailing inclination to bring the wonders of revelation into one system with the ordinary laws of nature. I find it more advisable completely to sacrifice the transitory approval which such agreement can arouse for the true pleasure which comes from the perception of regular interconnections when physical analogies reinforce each other in the designation of physical truths.


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