OBJECTIONS TO THE NEBULAR THEORY.
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 the 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 movements 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 frontier 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. What 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 primæval 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 moment 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 primæval 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, having
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.
If 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.
[Illustration: 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 admitted 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 angles 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
orbits 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.
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