Immanuel Kant
Universal Natural History and Theory of Heaven
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Immanuel KantUniversal Natural History and Theory of Heaven |
Part Two
Section Two
Concerning the Different Densities of the Planets and the Relationship of Their Masses
We have shown that the particles of the elementary basic material, distributed equally by themselves in cosmic space, by their sinking downward towards the sun remain suspended in the places where the velocity which they attained in their descent reaches a precise equilibrium in relation to the force of attraction and that their direction would be altered so as to be perpendicular to the radius of the circle, as should be the case with circular movements. However, if we now think of the particles of different specific density at the same distance from the sun, then the ones with a greater specific gravity drive more deeply through the resistance of the other particles toward the sun and will not be diverted from their path as soon as the lighter ones. Thus, their movement will form a circular orbit only at a closer distance to the sun. On the other hand, the elements of the lighter type are diverted from a straight vertical fall earlier and take on a circular movement before they are driven so deep toward the centre. Thus, they remain suspended at a greater distance away. Moreover, they are not able to drive so deeply downward through the space filled with the elements, without the resistance of these elements decreasing their motion, and they will not be able to attain the velocity required for a circular movement closer to the mid-point. And, according to the equilibrium in the movements, the specifically lighter particles will orbit at distances far from the sun; the heavier ones occur, however, at closer distances. The planets which are built out of these elements will therefore be denser when they are nearer the sun than when they are formed from the combination of these atoms far away from the sun.
Thus, there is a sort of statistical law which establishes for the material of cosmic space an inverse relationship between the distance from the centre and the density. In the same way, it is easy to grasp that it is not essential that each distance contain only particles of the same specific density. Of the particles of a certain specific type, some are suspended at a greater distance from the sun and attain the necessary permanent circular motion appropriate to their fall at a greater distance. These have moved down toward the sun from further away. On the other hand, those whose original location in the universal distribution of the materials in Chaos was nearer the sun, regardless of the fact that their density is no greater than the former group, will attain a circular orbit closer to the sun. Moreover, since the locations of the materials in relation to the mid-point of their descent is determined not only by the specific gravity of the material but also by its original place in the first calm state of nature, it is easy to see that very different types of material will combine at every distance from the sun, so as to remain suspended there and that, nevertheless, generally we will find the denser material in greater accumulations closer to the mid-point than further away. In general, the masses must be denser in proportion to their closeness to the sun and less dense when their distances away are greater.
In the matter of this law governing planetary densities, our system manifests an advantageous comprehensiveness in comparison with all those ideas which people have come up with or even could come up with about the cause. Newton, who established the densities of some planets by calculation, thought that the cause of this relationship according to the established distance was to be found in the appropriateness of God's choice and in the fundamental motives of His final purpose, since the planets closer to the sun must endure more solar heat and those further away must receive less heat, which would not seem to be possible, unless the planets near the sun were composed of a denser material and those further away of a lighter material. But to perceive the inadequacy of such an explanation does not really require much reflection. A planet (for example, our Earth) is composed of types of material very different from each other. Of these, it was necessary only that the lighter varieties, which will be more deeply penetrated and affected by the same solar working and whose composition has a relationship to the heat generated by the sun's rays, be spread out on the planet's outer surface. But here the fact that the mixture of the remaining material in the total cluster must have this relationship sheds light on nothing at all. Newton was afraid that if the Earth had been in a lower position in the proximity of Mercury, in the sun's rays it would necessarily burn up like a comet and that the Earth's materials have insufficient protection against fire not to become scattered by this heat. But it is much more pertinent that the sun's own material stuff, which is four times lighter than the material making up the Earth would have to be destroyed by fire. Or why is the Moon twice as dense as the Earth, yet still suspended at just the same distance away from the sun as the Earth? Thus, we cannot attribute the proportional densities to the relationship with the sun's heat, without entangling ourselves in the greatest contradictions. We much sooner see that a cause which distributes the planets according to the density of their clusters must have had a relationship to the inner material and not to the material on the surface. This cause would have to establish the relationship with the density only in the total composition, still permitting a differentiation in the materials in one and the same celestial body, without regard to the consequences which it established. Whether some statistical law or other, like the one which will be presented in our theory, can achieve this satisfactorily I leave to the insight of the reader to judge.
The relationship of the planetary densities brings with it one more circumstance which corroborates the validity of our theory by completely endorsing the previously proposed explanation. The celestial body standing at the mid-point of other spheres orbiting around it is commonly of a lighter sort than the bodies orbiting most closely to it. The Earth with respect to the Moon and the Sun with respect to the Earth manifest such a relationship vis-а-vis their densities. According to the proposal which we have laid out, such a condition is necessary. For the lower planets were built up mainly from the excess elementary material which, thanks to the advantage of its density, could have driven right to an area close by the mid-point with the required velocity. By contrast, the body at the very mid-point was put together from totally heterogeneous materials which did not attain the velocity required by the law. Among these, the lighter materials make up the greatest portion. Thus, it is easy to see that, because the celestial body orbiting closest to the mid-point or the one nearest to it has within it, as it were, a selection of the denser forms of material but that the central body has a mixture of all types, without distinction, then the former will be denser than the latter. In fact, the moon has twice the density of the Earth, and the Earth is four times denser than the sun. According to all assumptions, the even deeper planets (i.e., closer to the sun), Venus and Mercury, will exceed these with an even higher density.
We now turn our attention to the relationship which, according to our theory, the masses of the celestial bodies should have in comparison to their distances from the sun, in order to test the results of our system against Newton's infallible calculations. It does not require many words to comprehend that the central body must always be the major part of its system. Consequently, the sun must be preponderantly greater than the planets collectively, just as the same point will hold for Jupiter and Saturn in relation to their nearby planets. The central body is created from the downward sinking from the entire extent of the sphere of its power of attraction of all particles incapable of attaining the most precisely established circular movement and a close relationship to the common plane. These must undoubtedly be a number uncommonly larger than those which attain orbital movement. To apply this observation in particular to the sun: if we wish to estimate the spatial extent in which orbiting particles which have served as basic material for the planets have deviated furthest from the common plane, then we can assume that it is, as an approximation, somewhat larger than the width of the greatest deviation of the planetary orbits from each other. Now, while they deviate from the common plane on both sides, their greatest angular difference with respect to each other is hardly 7.5 degrees. Thus, we can picture all the material out of which the planets were developed as having been distributed in the space which we imagine between two planes extending out from the sun at the centre and creating an angle of 7.5 degrees. However, a zone 7.5 degrees wide extending in the direction of the largest circle is a bit more than the seventeenth part of the spherical surface. Thus, the physical space between the two planes, which cut out a part of planetary space in the width of the above mentioned angle, is somewhat more than a 17th part of the physical contents of the entire sphere. Thus, according to this hypothesis, all material used for planetary development would comprise approximately the seventeenth part of the material which the sun assembled for its composition on both sides out as far as the furthermost planet is located. But this cluster of the central body has a preponderance over the combined content of all the planets which is not 17 to 1 but 650 to 1, as Newton's calculations have established. However, it is easy to see that in the higher regions beyond Saturn, where planetary development either ceases or is rare, where only a few comet bodies have arisen and especially where the movements of the basic material did not happen to acquire the equilibrium with the centripetal force as required by law (as in the regions closer to the centre) and ended up in an almost universal sinking toward the mid-point, it is easy, I say, to see that for these reasons the sun would have to acquire such a preponderantly large mass.
However, in order to compare the planets with each other with respect to their masses, we first observe that, in accordance with the method of development, the quantity of material which combines in the composition of a planet depends particularly on the extent of its distance from the sun, for the following reasons: (1) Because of its power of attraction, the sun limits the sphere of the planet's power of attraction; however, for the same reason, the more distant planets are not so narrowly restricted as the close ones. (2) The circle from which all the particles have come together to make a more distant planet will be described with a larger radius and contain more basic material than the smaller circles. (3) For the reasons just mentioned, the width between the two planes of the greatest deviation at a constant angle is greater at a greater distance than at a small distance. On the other hand, this advantage for the more distant planets over the ones lower down will be limited by the fact that the particles nearer the sun will be of a denser type and, everything considered, will be less scattered than at a greater distance away. But we can easily conclude that for planetary development the first advantage is far greater than the limitation just mentioned. Generally the planets which develop a long way distant from the sun would have to acquire larger masses than the ones close to the sun. This happens in such a manner insofar as we imagine a planet's development with only the sun present. But if we admit the development of several planets at different distances, then one planet will restrict the extent of the power of attraction of another planet through the sphere of its own centripetal force. This brings about an exception to the previous principle. For the planet which is near another one of exception mass will lose a great deal from the sphere of its developmental material and thus will be much smaller than the relationship of its solar distance by itself requires. On the whole, the planets have a greater mass as they are further from the sun. Saturn and Jupiter, the two main parts of our system, are thus the biggest because they are furthest from the sun. However, deviations from this analogy do occur. But in them the mark of their common development is always manifest: the principle which we hold to, namely, that a planet of exceptional size deprives the nearest ones on both sides of the mass appropriate to them, given their distance from the sun. For it attracts to itself a portion of the material which should go into the development of both of them. In fact, because of its location, Mars should be bigger than the Earth. But Mars has a diminished mass because of the force of attraction from Jupiter, which is so large and close by. Although Saturn itself has an immediate advantage over Mars because of its distance, nevertheless Saturn has not been entirely free from suffering a considerable loss thanks to Jupiter's power of attraction. And it seems to me that Mercury owes its exceptionally small mass not only to the force of attraction of the powerful sun, which is so close by, but also to the fact that Venus is a neighbouring planet. If we compare the presumed density of Venus with its size, Venus must be a planet of considerable mass.
Everything agrees as splendidly as we might wish in order to confirm the adequacy of a mechanical theory for the origin of the cosmic structure and the celestial bodies. Now, as we estimate the space in which the material stuff before the development of the planets was distributed, we wish to consider how diffuse the material was which filled this space and how free of obstacles the particles suspended all around were to established their rule-governed motions. If the space holding in itself all the planetary material was contained in that part sphere extending out to Saturn which was between two imaginary planes extending at an angle of 7.5 degrees to each other from the mid-point of the sun out into the full reaches of space (and which therefore comprised one seventeenth of the entire space which we can describe with a radius equal to the distance of Saturn), then in order to calculate the diffusion of the basic planetary material, we will set the distance of Saturn at 100,000 Earth diameters. Thus, the entire sphere of Saturn's orbit will exceed the volume of Earth by a factor of 1000 billion. If we take instead of the seventeenth part only the twentieth part of the space in which the elementary basic stuff was suspended, this must exceed the volume of Earth by a factor of 50 billion. Now, if, following Newton, we set the mass of all the planets along with their satellites at 1/650 of the mass of the cluster of the sun, then the Earth, which is only 1/169282 of this mass, will be related to the collective mass of all the planetary material in the ratio of 1 to 276.5. And if we then made all this material the same specific density as the Earth, we would produce a body which would take up a space 277.5 times greater than the Earth. Assuming that the density of the entire cluster of the Earth is not much greater than the density of the firm material which we encounter under Earth's outermost layer, as is required by the characteristics of the shape of the Earth, and assuming that this outer material is about 4 or 5 times denser than water and that water is 1000 time heavier than air, then, if all the planetary material is expanded to the density of air, it would take up a space almost 1,400,000 times larger than the Earth. This space is 30 million times smaller than the space in which, according to our theory, all the planetary material was spread out. Thus, the scattering of the planetary material in this space is much more thinly distributed than the particles of our atmosphere. In fact, the thin density of this scattered distribution, as inconceivable as it may appear, was neither unnecessary nor unnatural. It must be as thin as possible, in order to permit the suspended particles all freedom of movement, almost as in an empty space, and infinitely to reduce the resistance which they could have created for each other. They could, however, have assumed such a thinly distributed state on their own. We cannot doubt this point if we know a little about the diffusion which matter undergoes when it is transformed into vapour or when, to stay on the subject of the heavens, we consider the thinning out of the material in the tail of a comet, whose diameter, of an unheard of thickness, exceeds the diameter of the earth by a factor of a hundred and yet it is so transparent that the small stars can be seen through it, something which our air, when it is illuminated by the sun at a height many thousand times smaller, does not allow.
I conclude this part by bringing out an analogy which in and of itself can raise the present theory of the mechanical development of the celestial bodies above a probable hypothesis to a formal certainty. If the sun is composed of particles of the same basic material from which the planets have developed and if the difference between them consists only in the fact that in the sun undifferentiated material of all sorts accumulated, while in the planets the density of their of their types was distributed according to the different distances, then if we consider the material of all the planets as a collective unity, from their complete intermixing the result would have to be a density almost equal to the density of the sun. Now, this necessary consequence of our system finds fortunate confirmation in the comparison which Buffon, that worthily celebrated philosopher, set out between the densities of the total aggregate of planetary material and the material of the sun. He found a similarity between the two in the ratio of 640 to 650. When unbiased and necessary consequences of a theoretical conception encounter such fortunate confirmation in true natural relationships, can we really then believe that mere contingency has effected this agreement between theory and observation?
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