Immanuel Kant

Universal Natural History and Theory of Heaven

Part Two

Section Four

Concerning the Origin of Moons and the Axial Rotation of the Planets

The striving of a planet to develop from the quantity of basic materials is at the same time the cause of its axial rotation and produces the moons which are to orbit around it. What the sun with its planets is on a large scale a planet with a sphere of attraction extending far out is on a small scale, namely, the major part of a system whose pieces have been set in motion through the force of attraction of the central body. Since the developing planet activates for its development the particles of the basic material from the total extent of its power of attraction, it will produce from all these sinking motions, thanks to their reciprocally interacting effects, circular movements. And these will finally settle upon a single common direction. Some of these motions will get moderated appropriately for free circular movement and in this limited area will be located close to a common plane. In this space, as with the main planets around the sun, the moons will develop around the planets, when the extent of the power of attraction of such cosmic bodies offers favorable conditions for their production. Furthermore, what was said in connection with the origin of the solar system can be applied equally well to the system of Jupiter and Saturn. The moons will arrange their orbital circles in one direction almost in a single plane. This will be set up for the same reasons as those in the large-scale analogy. But why do these satellites move in their common direction far more in the direction in which the planet moves than in any other? The moons' orbits are not produced through the circular movements of the planets. They acknowledge as cause only the power of attraction of the main planet, and, so far as this force is concerned, all directions are equally good. Mere contingency will select the direction out of all possible directions, according to which the sinking movement of the material changes into circles. In fact, the circular path of the main planet does nothing at all to impress upon the material out of which the moons are to develop orbital motion around it. All the particles around the planet move with it in the same motion around the sun and are, in relation to the planet, at rest. The power of attraction of the planet achieves everything by itself. But since all directions are in themselves equally suitable to the power of attraction, the orbital movement which arises out of that requires only a small external stimulus for the orbital movement of the moons to end up in one direction far more than in another. This small degree of steering the orbital movement acquires from the forward movement of the elementary particles which run simultaneously around the sun at a higher speed and in the sphere of the planet's power of attraction. For this requires the particles closer to the sun which orbit at a higher speed already from a considerable distance to abandon the direction of their path and to move up over the planet in an extended curve. Because these particles have a higher velocity than the planet itself, when they are drawn down by the planet's power of attraction, they produce in their perpendicular descent and also in the descent of the other particles a deviation from west to east. It requires only this slight steering to see to it that the orbital movement in which the descent, initiated by the power of attraction, finishes up takes on this direction far more than any other. Thus, all the moons will coordinate their orbital direction with the direction of the main planet's orbit. However, the plane of their path also cannot deviate far from the plane of the planetary orbits, because the material out of which they develop, for the very reason which we have referred to concerning orbital direction in general, is organized precisely in this way, namely coordinating itself with the plane of the principal orbits.

From all this we clearly see what the circumstances are in which a planet may be able to acquire satellites. The power of attraction of the planet must be large and, as a result, the extent of the sphere in which this power is effective must extend far out, so that the particles moved to the planet through a long descent, without regard to the effects of resistance, at length are able to attain the velocity for a free orbital momentum. As well there must be present sufficient material for the development of moons in this region, something which cannot occur with a slight power of attraction. Thus, only planets with large masses and at a great distance from the sun are endowed with satellites. Jupiter and Saturn, the two largest and most distant planets have the most moons. Earth, much smaller than these planets, is assigned only one. And Mars, which on account of its distance might have merited some share of this advantage, goes without because its mass is so small.

We observe with pleasure how the same force of attraction which brought the material for building moons and at the same time determined their movement extends to the very body of the planet itself in giving it an axial rotation (by means of exactly the same action through which the planet develops) in the common direction from west to east. The particles of the descending basic material, which, as mentioned, acquire a common rotational movement from west to east, fall for the most part onto the surface of the planet and are mixed into its cluster, because they do not have the appropriate velocity to maintain themselves in freely suspended orbital motion. Since they now come into collision with the planet, they must, as parts of it, continue just the same rotational movement and in exactly the same direction which they had before they were united with the planet. And it is easy to infer from the foregoing that generally the number of particles which the lack of necessary movement drives down to the central body must be very much greater than the number of those capable of attaining the appropriate level of velocity. Thus, we can easily grasp why this central body will not in its axial rotation possess nearly the velocity sufficient to achieve an equilibrium between the gravity on its surface and the centrifugal force. Nevertheless, the axial rotation of planets with a large mass and at a considerable distance from the sun will be much faster than with the small ones close to the sun. In fact, Jupiter has the fastest axial rotation that we know about, and I do not know what system would allow us to be able to reconcile this fact with a body whose cluster exceeds all the others, unless we can see that its very movements are themselves the effect of that power of attraction which this celestial body exerts in accordance with the mass of its cluster. If the axial rotation were an effect of an external cause, then Mars would have to have a more rapid axial rotation than Jupiter. For the very same power of movement affects a smaller body more than a larger one. We would quite correctly wonder about this, since all the movements diminish with distance from the mid-point, but the speeds of the rotations increase with distance. With Jupiter the rotational movement could be two and a half times faster than its annual motion around the sun.

Thus, we must recognize in the daily rotations of the planets the very same cause which is generally the common origin of movement in nature, namely, the force of attraction. This style of explanation, therefore, will successfully prove its truth through the natural quality of the basic concept and through an unforced consequence of that.

But if the development of a body itself produces the axial rotation, then all the spheres of the cosmic structure must have it. Why, then, does the moon not have it? Some people erroneously think that the moon has a kind of rotation by which it always has the same side turned toward the Earth much more from some overbalancing of one hemisphere rather than from a real rotational impulse. Must the moon really have rotated on its axis in at an earlier period more quickly and through some unknown cause or other have gradually reduced this movement until it was brought to this slight and measured remainder? We need to resolve this question only in connection with one of the planets. Then the application to all planets will follow of itself. I am postponing this solution to another occasion, because it has a necessary connection to the assignment which the Royal Academy of Sciences in Berlin has established for the prize in the year 1754.

The theory which is to explain the cause of the axial rotations must also be able to produce from exactly the same causes the orientation the planetary axes in relation to their orbital plane. We have reason to wonder why the equator of the daily rotation is not in the same plane as the one in which orbit the moons moving around that same planet. For this same movement which directs the orbit of a satellite, through its extension to the body of the planet, produced its axial rotation, and it should give the satellite exactly the same determinate direction and orientation. Celestial bodies which have no planets orbiting closely around them nevertheless had their axial rotation set by exactly the same movement of the particles which served them as material and through the same law which limited each one to the plane of its periodic orbit. Consequently, this axial rotation, for the same reasons, had to be coordinated with the direction of the orbital plane. Hence, the axes of all celestial bodies would have had to be oriented perpendicularly to the common interconnecting plane of the planetary system, which does not deviate far from the ecliptic. But the axes are only perpendicular with the two most important parts of the cosmic structure, with Jupiter and the sun. With the others whose rotation we know the axes are at an angle in relation to the plane of their orbits, Saturn more than the others, but the Earth more than Mars, whose axis is almost perpendicular to the ecliptic. The equator of Saturn (so far as we are able to ascertain it from the arrangement of its ring) is inclined at an angle of 31 degrees to the plane of its orbit. However, the Earth is only inclined towards the plane at an angle of 23.5 degrees. We can perhaps attribute the cause of this deviation to the inequality in the movement of the material which came together to build the planet. In the arrangement of the plane of its orbit, the preponderant movement of the particles was around the planet's mid-point. And then the interconnecting plane was in place around which the elementary particles accumulated to make the movement there circular, where possible, and to pile up material for the development of the satellites, which for this reason never deviate far from the plane of the planet's orbit. If the planet developed for the most part only out of these particles, then its axial rotation in its first growth would be as little offset from that plane as the satellites which orbit around it. But the planet develops, as the theory has established, more from particles which sank down on both sides and whose number or velocity appears not to have been so totally balanced, so that one hemisphere would be able to acquire a small excess of movement with respect to the other and thus some displacement of the axis.

Regardless of these reasons, I consider this explanation only as a supposition which I do not have the confidence to establish. My true view is as follows. The axial rotation of the planets in the original state of their first development was quite accurately aligned with the plane of their annual rotation. Causes were present which pushed these axes out of their first position. A celestial body which is moving out of its first volatile condition into a firm state undergoes, when it develops in this way, a large change in the regularity of its outer surface. This surface becomes firm and hardens while the deeper material has not yet sufficiently sunk down according to the appropriate distribution of its specific gravity. The lighter types of material intermixed in its cluster, after separating out from the rest, finally move under the outermost crust, which has become firm, and creates holes. The largest and widest of these holes, for reasons which are too detailed to discuss here, occur under or near the equator. The crust finally sinks down into these depressions and produces various inequalities, mountains and rifts. Now, since in something like this manner, as must apparently have happened with the Earth, the Moon, and Venus, the outer crust became uneven, the planet could not achieve an equilibrium any more on all sides in the momentum of its axial rotation. A few prominent sections of considerable mass, which had nothing equal to them on the opposite side which could act as an effective counterweight to the impetus, must have then shifted the axial rotation and sought to place it in a condition around which the material was equally poised. Thus, exactly the same cause as in the example of the complete development of the celestial body changes its outer crust from a smooth state into broken up inequalities. This general cause has made it necessary to change somewhat the original orientation of the planet's axis. We perceive this to be the case with all the celestial bodies which the telescope can reveal sufficiently clearly. But this change has its limits, so that the deviation is not excessive. The inequalities, as already mentioned, show up more near the equator of an orbiting celestial body than at a distance from it. In the region of the poles they disappear almost entirely. The discussion of the causes of this I am postponing to another time. Thus, the most prominent masses rising above the even surface will be found near the equinoctial circle. Since the masses strive to bring themselves close to this circle because of the major influence of their momentum, they will be able to shift the axis of the celestial body at the most only a few degrees out of its perpendicular orientation with the orbital plane. As a consequence, a celestial body which has not yet fully developed will still have this perpendicular orientation of its axis to its orbital path. The angle will perhaps be altered only with the long succession of centuries. Jupiter appears to be still in this condition. The preponderance of its mass and size and the lightness of its material have required Jupiter's material to reach the firm and stable condition a few centuries later than other celestial bodies. Perhaps the inside of its cluster is still in motion, as the parts composing it sink toward the centre according to the determination of their gravity, and in the separation of the thinner varieties from the heavy ones it is acquiring a firm condition. In such circumstances, Jupiter cannot yet appear calm on its outer surface. Collapses and ruin govern there. The telescope itself has confirmed that for us. The shape of the planet is constantly changing, while the Moon, Venus, and the Earth itself remain unaltered. Indeed, we can also with justice estimate that the completion of the development is several centuries later in the case of a celestial body which exceeds our Earth in size by a factor of more than twenty thousand and which has a smaller density by a factor of four. When its outer surface reaches a tranquil composition, then undoubtedly much larger inequalities, like the ones which occur on the surface of the Earth, combined with the velocity of its rotational impulse, will in a relatively short period give its axial rotation the constant orientation which the equilibrium of its forces will require.

Saturn, which is three times smaller than Jupiter, because of its greater distance from the sun can perhaps have a much faster development than Jupiter. At least Saturn's much quicker axial rotation and the large ratio of its centrifugal force to the gravity on its outer surface (which is to be presented in the following section) see to it that the inequalities which have thus presumably developed there have been given very quickly through a displacement of the axis a shift to the side of the excess weight. I freely concede that this part of my system concerning the position of the planetary axes is still incomplete and quite far from being subject to geometrical calculation. I preferred to reveal this candidly rather than through some devious but apparently competent reasons do damage to the rest of the theory and give it a weak part. The section which follows can provide confirmation of the credibility of the entire hypothesis. There we will explain the movements of the cosmic structure.

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