there are difficulties in the nebular theory—the general conformity of the movements—details of the uranian movements—the anomaly in the satellite of neptune—where the difficulty lies—the fundamental principle which dynamics offers for our guidance—the immense contrast between the nebula in its original form and its final form—energy that could be obtained by a rearrangement of our system—probable nature of the present change in the plane of the orbits of the satellites of uranus—the similar explanation in the case of neptune.
no one will deny that there are points in connection with the nebular theory which present difficulties which to some seem important. we shall endeavour to estimate the significance of these difficulties in this chapter. they are certain anomalous phenomena presented by the planets uranus and neptune.
the satellites which attend upon the planets exhibit a general conformity with those movements of the planets themselves on which we have dwelt in chapters xiv., xv., xvi. the planes in which the orbits of the satellites are contained are usually not much inclined to the plane of the ecliptic, and the directions in which the satellites revolve also agree with the general direction of the planetary movement. we find these conditions in 338the one satellite of the earth, in the two satellites of mars, in the five satellites of jupiter, in the eight or nine satellites of saturn; but, when we come to uranus and neptune, the two outermost planets, we observe a striking but most instructive violation of the laws which we have found so consistently prevailing in the other parts of the solar system.
let me first mention the special circumstances of uranus. it is now known that this planet has four satellites. of these, titania and oberon were both discovered by sir william herschel on january 11th, 1787. the two remaining satellites, named ariel and umbriel, were not discovered for more than half a century later by mr. lassell, on october 24th, 1851. it is, however, just possible that they were previously seen by sir william herschel.
the innermost of the four satellites, ariel, accomplishes a revolution in a day and a half, umbriel goes round in four days and three hours, titania in eight days and seventeen hours, and oberon in thirteen days and eleven hours. we have already mentioned how the investigations of newcomb show that these four satellites of uranus revolve in the same direction and in the same plane; but this plane, instead of lying in or near the ecliptic, is very nearly perpendicular thereto, the actual angle being eighty-three degrees. this is one of the features in which the satellites of uranus are in startling disobedience to the laws which have been so rigidly observed in most other parts of the system. but there is also a second anomaly. the direction in which the satellites move, when projected on the plane of the ecliptic, is found to be opposite to the universal direction in which all the other 339movements in the solar system are performed. of course the fact that the plane of the orbits of the satellites lies so nearly at right angles to the plane of the ecliptic detracts somewhat from the significance of this circumstance. if the two planes were absolutely at right angles, there would be, of course, no projection at all, and, in the actual circumstances, the moment of momentum, when projected, loses nineteen-twentieths of its amount. it follows that in the actual position of the plane the abnormal direction in which the satellites are moving is not very material.
it must be admitted that, in the position of the plane of their orbits and the direction of their movements, the satellites of uranus are in contrast to what a hasty consideration of the nebular theory might have led us to expect. if the orbits of those satellites had all lain close to the plane of the ecliptic, and if the direction in which the satellites revolved had also conspired with that of the revolution of uranus round the sun, and with all the other hundreds of movements which are in the same direction, there can be no doubt that we should in this place have been appealing to the satellites of uranus as confirmatory evidence of the truth of the nebular theory. the fact that they move in a manner so totally at variance with what might have been expected cannot therefore be overlooked.
neptune, the outermost planet of our system, presents us also with difficulties of an analogous character. so far as the orbit of neptune itself is concerned, it agrees entirely with the general planetary convention; the inclination of that orbit to the plane of the ecliptic is no more than six degrees, and the direction in which the outermost planet revolves round the 340frontier of our system is not different from the directions in which all the other planets revolve. we know nothing about the axis of rotation of neptune except that it may be reasonably presumed to be in the same plane as the movement of its satellite. on october 10th, 1846, lassell, with the help of his great telescope, suspected the existence of a satellite to neptune, and he announced it definitely on july 7th, 1847. we are indebted to newcomb for a careful investigation of the orbit of this satellite. it moves in a track which is practically circular, and it requires about five days and twenty-one hours to accomplish each revolution. its inclination to the ecliptic is not so anomalous as in the case of uranus, the inclination being in this case not more than thirty-five degrees. this is not much greater than the inclinations of the orbits of some of the asteroids, and it might have passed without much comment had it not been for the circumstance that the direction of motion of the satellite in this track is antagonistic to all the other movements in the solar system. this is indeed a more startling fact in some respects than the movements of the satellites of uranus, for, as we pointed out, the plane of the orbits of the satellites of uranus is so nearly perpendicular to the plane of the ecliptic that the direction of the movement could not be held to be of much significance. the satellite of neptune, having an orbital inclination barely more than a third of a right angle, exhibits a retrograde movement which is in some respects the most anomalous feature in the solar system.
these circumstances connected with the satellites of uranus and neptune have been sometimes brought forward as arguments against the nebular theory. 341what laplace would have said to them we can only conjecture, for, at the time he brought out his theory, neptune was entirely unknown, and none of the satellites of uranus had been observed. but it has sometimes been urged that the movements of these two systems are inconsistent with the principles of the nebular theory, and that, therefore, the nebular theory must be abandoned. i have no desire to minimise the difficulties, but i think the considerations to which i now invite attention may help to lessen them even if they do not altogether remove them. i trust, at least, we may be able to show that even those anomalous movements are not incompatible with the acceptance of the account of the origin of our solar system given by the nebular theory.
the prim?val nebula may be regarded as chaotic in its earliest stages; perhaps it was like the nebulous wisps in fig. 51. it was chaotic in the arrangement of the material of which it is formed, and in the movements of that material. before a disorganised nebula can become evolved into a nebula with any definite form like that in fig. 52, or into anything resembling a solar system, an immense period of time must elapse, and during that time the operation of the laws of dynamics gradually impresses certain well-marked features on the nebula, and disposes it to assume an orderly form. we have explained that no matter how the nebula originated, or no matter what may have been the irregularities in its extent or distribution, and no matter how diverse may have been the agitations of its various parts, the principles of dynamics assure us that each such nebula must, for all time, stand in some special relation to a certain particular plane. the 342moment of momentum which the nebula has with respect to this plane, exceeds the moment of momentum that it has with respect to any other plane. we have pointed out how, notwithstanding the vicissitudes and transformations to which, in the course of illimitable ages, the nebula must submit, its moment of momentum relatively to this plane will remain absolutely unaltered. we have shown how the energy of the nebula becomes gradually exhausted. the collisions between various particles, the frictions that will necessarily arise, and the actions which we may sufficiently describe by saying that they are of a tidal character, will all result in the transformation of energy into heat. this heat is radiated away and lost, and there is a corresponding decline in the energy of the system. to preserve its moment of momentum unaltered in the course of ages, notwithstanding the continuous reduction of energy, the materials of the nebula will ever find themselves more and more approximating to the plane, and will ever find themselves more and more compelled to revolve in the same direction. if the original size of the nebula be compared with the area of the atlantic ocean, the condensed form which the nebula may ultimately assume may be no larger than a coral island. if the nett moment of momentum, diffused over the space as large as the ocean, has still to be preserved in the space as large as the island, we need not be surprised that the spin of the system in its condensed form is its dominating characteristic.
in the evolution of our solar system from the prim?val nebula, this operation of reducing the movements to the same plane and of requiring that all the movements shall take place in the same direction, 343having had play for unmeasured ages, has in the main accomplished its end. all the important bodies of the system do go round in the same direction; that much, at least, has been attained. all of them also go round in planes which are nearly coincident, but, as we have already noted, they are not yet absolutely coincident. the greatest planets have, however, very nearly become reconciled, so far as the planes of their orbits are concerned, to the condition which dynamics imposes. the same is true of the rotation of the sun on its axis. that axis is inclined at an angle of eighty-three degrees to the plane of the ecliptic, so that the sun’s equator would have to be shifted only through an angle no greater than seven degrees, if it were to be placed in the plane in which it should be situated, if the condition of the smallest quantity of energy for a given amount of moment of momentum was to be realised. we find a greater discrepancy in the plane of the earth’s equator. this is inclined by about twenty-three degrees to the plane of the ecliptic. here there is some energy which might yet be expended without a diminution of the amount of moment of momentum in the system; for if the earth’s axis were to be made perpendicular to the plane of the ecliptic, then the velocity of rotation of the earth about its axis might undergo a corresponding abatement, and yet keep up the requisite moment of momentum. we thus see that even with the older planets the conditions which would be enforced, if the moment of momentum was to be sustained with the least quantity of energy, are not absolutely complied with; which simply means that there has not yet been time enough for our system to arrive at the perfect state, to which it must be approximating.
344if we have found that in the rotations of the earth and of the sun, and in the revolutions of the planets round the sun, the conditions ultimately aimed at have not yet been reached, why should we feel surprised that in the outer planets of our system, uranus and neptune, the conditions which evolution tends to produce have not yet been fully attained? that the operation of the conservation of moment of momentum is in progress in the internal economy of the uranian system, we have already had occasion to explain in chapter xi. the fact which newcomb demonstrated, that the four satellites revolve in the same plane, can only be accounted for by the supposition that in that system the conservation of moment of momentum, with declining energy, has gradually imposed this condition on the system belonging to uranus. with reference to the position of the plane of the satellites, in the case of uranus and neptune, we would say, that though at present their arrangement appears anomalous, it will probably not always remain so. the fact that the satellites of uranus are in a plane nearly perpendicular to the plane of the ecliptic really implies that there is a certain amount of energy still disposable in our system, if by readjustment of the plane of the uranian satellites the necessary moment of momentum in the system is still preserved.
fig. 52.—two-branched spiral (n.g.c. 7479; in pegasus).
(lick observatory.)
the laws of dynamics tell us that the orbits of planets must be gradually, if with excessive slowness, tending still further to the same plane. in this process energy can be expended by the system, while the moment of momentum is unabated. we can at least suggest what seems to be at this moment in progress in the system belonging to uranus. it will readily be 345admitted that there may be a difficulty in seeing how the movement of a planet, which is going in the wrong direction, could be stopped and turned into the right direction. but we need not suppose that so violent a change as this would imply is to be expected in our system. we are quite accustomed to find the planes of the orbits of all planets in gradual movement. the plane containing the orbits of the four satellites of uranus is at this moment probably moving gradually upwards. it will in due course become actually at right 346angles to the ecliptic, and we may then reasonably assume that it will advance further in the same direction. at the moment the right angle is passed, this continuous movement will have the effect of changing the directions of the satellites’ movement from retrograde to direct. the present anomaly will then tend to become evanescent, for, as the exhaustion of the energy continues, the planes of the satellites of uranus will gradually come into conformity with the plane of the ecliptic.
we make no doubt that there may be a similar explanation of the movements of the satellite of neptune. the inclination of the plane of the orbit of the satellite to the ecliptic is probably now increasing. it will ultimately come to be at right angles thereto, and then the next advance of the plane will convert, by a continuous action, the retrograde motion of the satellite, at present so disconcerting, into a direct motion. the change of the plane will still continue until it, too, may ultimately coalesce with the ecliptic.
the fact appears to be, that though an enormous quantity of energy must have been lost by radiation from our system during the illimitable ages through which the evolution has been running its course, the disposable energy is not yet quite exhausted. there are certain adjustments in our system which may still be made and which will allow of yet further radiation of energy, while still preserving sufficient to keep up the necessary moment of momentum. it seems obvious that the system is tending towards a condition in which the planes of all the orbits shall be coincident, and in which all the directions shall be absolutely unanimous. if we were at once to alter the system by moving all the 347orbits into the plane of the ecliptic, but making no change in the dimensions of those orbits, or the velocities concerned; if we were also to adjust the rotations of the earth, as well as of the other planets, so that all the axes of rotation should be perpendicular to the plane of the ecliptic; if we were to turn the plane of the satellites of uranus through that angle of 97°, which would suffice at the same time to bring it into coincidence with the ecliptic, and lay the movements of the satellites in the right direction; if we were also to turn the orbit of the satellite of neptune through 145°, thus bringing that orbit to coincide with the plane of the ecliptic, in such a manner that the direction of the movement of the satellite of neptune conspired with all the other movements of the system, then this rearrangement of the system would increase the moment of momentum, while the quantity of energy was not altered. but this is the same thing as saying that some energy yet remains to be disposed of, while the system still preserves the requisite moment of momentum.
the conclusion we come to may be thus expressed: the movements of the satellites of uranus and neptune do not disprove the nebular hypothesis. they rather illustrate the fact that the great evolution which has wrought the solar system into form has not yet finished its work; it is still in progress. the work is very nearly done, and when that work shall have been completed, the satellites of uranus and neptune will no longer be dissociated from the general concord.
