THE THIRD CONCORD.
Rotations of the Planets on their Axes.—The Older Planets—No Information
about Uranus or Neptune or the Asteroids—The Speed of Rotation is
Arbitrary so far as Kepler’s Laws are concerned—The Third Concord—A
Remarkable Unanimity—Kant’s Argument—Illustration of the Rotation of
the Moon on its Axis—How the Nebular Theory explains the
Rotation—The Moon’s Evolution—Special Action of Tides—The Evolution
of the other Satellites—The case of Mars—Jupiter and Saturn as
Miniatures of the Solar System—Uranus and Neptune offer
Difficulties.
WE have seen in the last chapter how the rotation of the sun beat time,
as it were, for the planets, by giving to them an indication of the
direction in which the revolutions round the sun should be performed,
and we have observed with what marvellous unanimity the planets follow
the precept thus given. We have now to consider yet another concord,
which has perhaps not the great numerical strength of that last
considered, but is, nevertheless, worthy of our most special attention.
The earth revolves about an axis which is not very far from being
perpendicular to the principal plane to which the movements of the solar
system are related. From a dynamical point of view it would, of course,
have been equally possible for the earth to revolve on its axis in the
same direction as the rotation of the sun, or in the opposite direction.
There is nothing so far as the welfare of man is concerned to make one
direction of rotation preferable to the other, but, as a matter of fact,
the earth does turn round in the same way as the sun turns.
Jupiter also turns on its axis, and Jupiter again, like the earth, might
turn either with the sun or it might turn in the opposite direction.
Here, again, we find a unanimity between the earth and Jupiter; they
both turn in the same direction, and that is the direction in which the
sun rotates. The same may be said of Mars, and the same may be said of
Saturn. In the case of the planets Mercury and Venus we cannot speak
with equal definiteness on the subject of their rotations about their
axes. The circumstances of these planets are such that there are great
difficulties attending the exact telescopic determination of their
periods of rotation. The widest variations appear in the periods which
have been assigned. It has, for instance, been believed that Venus
rotates in a period not greatly differing from the period of twenty-four
hours in which our earth revolves. But it has been lately supposed that
the period of Venus is very much longer, and is in fact no less than
seven months, which is, indeed, that of the revolution of Venus about
the sun. According to this view, Venus rotates round the sun in a period
equal to its revolution. If this be so, then Venus constantly turns the
same face to the sun, and the movement of the planet would thus resemble
the movement of the moon around the earth. As a matter of observation,
the question must still be considered unsettled, though there are sound
dynamical reasons for believing that the long period is much more
probable than the short one. We do not now enter into this question, or
into the still more difficult matter of the rotation of Mercury; it
suffices to say that whichever period be adopted for either of these
planets is really not material to our present argument. In both cases it
has never been doubted that the direction of the rotation of the planets
is the same as the direction in which Jupiter and Mars and the earth
rotate, these being also the same as the direction of the solar
rotation.
As to the rotations of Uranus and Neptune about their respective axes,
the telescope can show us nothing. The remoteness of both these planets
is such that we are unable to discern objects on their discs with the
definiteness that would be required if we desired to watch their
rotations. We have also no information as to the rotation of the several
asteroids. No one, I think, will doubt that each of these small planets,
equally with the large planets, does rotate about its axis; but it is
impossible for us to say so from actual knowledge.
But undoubtedly the five old planets, Mercury, Venus, Mars, Jupiter, and
Saturn, as well as the earth, all rotate in the same direction as the
sun. Each planet might rotate twice as fast, or half as fast, as it does
at present. They might all rotate in the opposite direction from that in
which they do now, or some of them might go in one direction, and some
in the other, with every variety in their diurnal periods, while the
primary condition of Kepler’s Laws would have still been complied with.
We may also note that the _direction_ in which the rotation takes place
seems quite immaterial so far as the welfare of the inhabitants on these
planets is concerned.
The fact that the planets and the sun have this third concord demands
special attention. The chance that the earth should rotate in the same
direction as the sun is, of course, expressed by one-half. It is easy to
show, that out of sixty-four possible arrangements of the directions of
rotation of the five planets and the earth, there would be only one in
which all the movements coincided with the direction of the rotation of
the sun. If, therefore, it had been by chance that the direction of
these motions was determined, then Nature would have taken a course of
which the probability was only one sixty-fourth. No doubt this figure is
by no means so large as those which expressed the probabilities of the
other planetary concords; it is, however, quite sufficient to convince
us that the direction of the rotation of the planets on their axes has
not been determined merely by the operation of chance.
We are to see if there is any physical agent by which the planets have
been forced to turn round in the same direction. And here comes in one
of those subtle points which the metaphysical genius of Kant suggested.
Let us take any two planets—say, for instance, the earth and Jupiter—and
let us endeavour to see what the nature of the agent must have been
which has operated on these planets so as to make them both rotate in
the same direction. Kant urged that there must have been some material
agent working on the materials in Jupiter, and some material agent
working on those of the earth, and that to produce the like effect in
each planet there must have been at one time a material connection
existing between that body which is now Jupiter and that body which is
now the earth. In like manner Kant saw this material connection existing
between the other planets and the sun, and thus he was led to see that
the whole material of our solar system must once have formed a more or
less continuous object. The argument is a delicate one, but it seems
certainly true that in the present arrangement of the orbits it is
impossible for us to conceive how, with intervals of empty space between
the tracks of the planets, a common influence can have been exerted so
as to give them all rotations in the same direction.
The nebular theory at once supplies the explanation of the unanimity in
the rotation of the planets, just as it supplied the explanation of the
unanimity in the directions of their revolutions. To explain the
rotation of a planet on its axis, let us imagine that one portion of the
contracting nebula has acquired exceptional density. In virtue of its
superior attraction it absorbs more and more material from the adjacent
parts of the nebula, and this will ultimately be consolidated into the
planet, though in its initial stages this contracting matter will remain
part of the nebula. We have shown that the law which decrees that the
moment of momentum must remain constant will require that, after a
certain advance in the contraction, all the parts of the nebula shall
rotate in the same direction. Thus we find that the sun, or rather the
parts of the nebula that are to form the sun, and the parts that are to
form the planets are all turning round together.
[Illustration: Fig. 51.—AN ELONGATED IRREGULAR NEBULA
(n.g.c. 6992; in Cygnus). (_Dr. W. E. Wilson, F.R.S._)
(_From the Astronomical and Physical Researches at Daramona
Observatory._)]
At this point we may consider a geometrical principle which, though
really quite simple, is not always easily understood. It has indeed
presented considerable difficulty to many people. Suppose that an
ordinary card is laid on a flat board, and that, with a bradawl, a hole
is made through the card into the board. The hole may be at the centre,
or at one of the corners, or a little way in from one of the edges, or
in any other position whatever on the card. Now suppose that a postage
stamp is stuck upon the card anywhere, and that the card is then moved
around the bradawl. How are we to describe the motion of that postage
stamp? It would certainly be revolving around the bradawl; but this
motion we may consider as composed of two others. At any instant we may
accurately represent the movement of the postage stamp by considering
that its centre was moving in a direction perpendicular to the line
joining that centre to the hole made by the bradawl, and that it also
had a rotation around its centre, the period of that rotation being just
the same as the time the card would take to go round the bradawl. Thus
we see that the movement of the postage stamp contains at any moment a
movement of translation and a movement of rotation.
We may illustrate the case we have supposed by the movement of the moon
around the earth. If the centre of the earth be considered to be at the
centre of rotation the moon may be considered to be in the position of
the postage stamp. As our satellite revolves, the same side of the moon
is continually turned towards the earth, but this is due to the fact
that the moon, at each moment, really possesses two movements, namely, a
movement of translation of its centre, in a direction perpendicular to
the line from the moon’s centre to the earth’s centre, coupled with a
slow rotation of the moon round its axis.
The contracting nebula we may liken to our piece of cardboard, the stamp
will represent the spot in which the nebulous material has contracted to
form the planet, and the position of the bradawl is the centre of the
sun. As we have seen by our illustration, the nebulous planet is endowed
with a certain movement of rotation, the period of its rotation on its
axis being equal to that of its revolution around the centre; and it is
important also to notice that both these movements take place in the
same direction.
Thus we see from the nebular theory how the primæval nebula, in the
course of its contraction, originated a planet, and how that planet was
also endowed with a movement of rotation; its period of rotation being
originally equal to the period of rotation of the whole nebula. This
explains how the planet, or rather the materials which are to form the
future planet, derived from the nebula their movement of rotation, which
must have been extremely slow in the beginning. As the contraction
continued, the materials of the gradually growing globe drew themselves
together, and tended to become separate from the surrounding nebula. At
length the time arrived when the planet became sufficiently isolated
from the rest of the nebula to permit the conservation of moment of
momentum to be applied to it individually. Thus, though the rotation was
at first excessively slow, yet, as the contraction proceeded, and as the
parts of the forming planet drew themselves closer together, in
consequence of their mutual attractions, it became necessary that the
speed with which these parts accomplished their revolutions should be
accelerated. At last, when the planet had become consolidated, and when
consequently the mutual distances of the several particles constituting
the planet had been reduced to but a fraction of what those distances
were originally, the speed of the planet’s rotation had become
enormously increased. In this manner we learn how, from the very slow
rotation which the nebulous material had at first, a solid planet may be
made to rotate on its axis as rapidly as the planets in the solar system
do to-day.
We thus find that the third concord, namely, the agreement in the
directions of the planets’ rotations, is a further strong corroboration
of the nebular theory. The unanimity of all these various movements is
the dominant characteristic of the solar system.
But this third concord, derived from the rotation of the planets, may be
yet further strengthened. The movements of the satellites, which
accompany so many of the planets, must also find their explanation from
the primæval nebula. The circumstances of the satellites are, however,
different in the different cases.
As regards the moon, the theory of its evolution is now well known,
mainly by the researches of Professor George Darwin. In the moon there
appear to have been causes at work of a somewhat special kind. We must
just refer to what is well known with regard to the history of the moon.
Here, again, we observe the importance of the principles of the
conservation of moment of momentum. As the moon raises tides on the
ocean surrounding the earth, and as those tides flow around the globe,
they cause friction, and that friction involves, as we have so often
pointed out, the loss of energy to the system. Thus, the energy of the
earth-moon system must be declining, while the moment of momentum
remains constant. Now there are only two sources from which the energy
can be derived. One of those sources is that due to the rotation of the
earth on its axis. The other is due to the moon, and consists of two
parts, namely, the energy arising from the velocity of the moon in its
orbit, and the energy due to the distance by which the earth is
separated from the moon. As the moon’s velocity depends upon its
distance, we cannot view these two portions as independent. They are
connected together, and we associate them into one. So that we say the
total energy of the earth-moon system consists partly of that due to the
rotation of the earth on its axis, and partly of that due to the
revolution of the moon around the earth. It might also seem that we
ought to add to this the energy due to the rotation of the moon around
its own axis; but this is too inconsiderable to need attention. In the
first place, the moon is so small that even if it rotated as rapidly as
the earth the energy due to the rotation would not be important. Seeing,
however, that the moon has for the rotation on its axis a period of
between twenty-seven and twenty-eight days, its velocity of rotation is
so small that, for this reason also, the energy of rotation would be
inconsiderable. We are, therefore, amply justified in omitting from our
present consideration the energy due to the rotation of the moon on its
axis.
The energy of the earth-moon system is on the decline: the lost energy
might conceivably be drawn from the rotation of the earth, or it might
be drawn from the revolution of the moon, or it might be drawn from both
If it were drawn from the revolution of the moon, that would imply that
the moon would lose some of its speed or some of its distance, or in any
case that the moon would get nearer to the earth and revolve more
slowly, the speed of the earth being on this supposition unaltered. In
this case, the moment of momentum of the earth would remain the same as
before, while the moment of momentum of the moon would be lessened; the
total moment of momentum would therefore have decreased, but this we
have seen to be impossible. It therefore follows that the energy
withdrawn from the earth-moon system is not to be obtained at the
expense of the revolution of the moon.
The energy must therefore be obtained at the expense of the rotation of
the earth on its axis. But if this be the case, the speed with which the
earth rotates must be diminished; that is to say, the length of the day
must be increased. And if the speed of the earth’s rotation be reduced,
that means that the amount of moment of momentum contributed by the
earth is lessened. But the total quantity of moment of momentum must be
sustained, and this can only be done by making the moon go further away
and describe a larger orbit. We thus see that in consequence of the
tides the length of the day must be increasing, and the moon must be
gradually retreating. Thus we find that at earlier periods the moon’s
distance from the earth must have been less than it is at present, and
the further we look back through remote periods the less do we find the
distance between the earth and the moon. Thus we see that there must
have been a time when the moon or the materials of the moon were in
actual contact with the materials of the earth. In fact, it seems quite
possible that the moon may have been a portion of the earth, broken off
at some very early period, while the earth was still in a liquid state,
if indeed it had condensed to even that extent. Thus the revolution of
the moon round the earth is hardly to be used as an argument in favour
of the nebular hypothesis. The moon is indeed a consequence of the
earth’s rotation.
The satellites of Mars offer conditions of a very different kind, though
here, again, tidal influences have been so important, that it is perhaps
questions relating to tides that are illustrated by these satellites
rather than the nebular theory.
A remarkable circumstance may be noted with regard to the movements of
the satellites of Mars. The inner satellite has a period of about seven
and a half hours, which is not a third of the period that the planet
itself takes to go round on its axis. This leads to a somewhat curious
consequence. The tides raised on Mars by this inner satellite would
certainly tend rather to accelerate the rotation of the planet than to
retard it; for these tides must course round the planet in the direction
of its rotation, but with a speed in excess of that rotation. Any tidal
friction, so far as this satellite is concerned, will tend to augment
the velocity of the planet’s rotation, just as in the opposite case,
where the moon raises tides on the earth, it is the lagging of the tides
behind the movement due to the rotation that acts as a brake, and tends
to check that speed. If, therefore. Mars is accelerated by this
satellite, it will do more than its original share of the moment of
momentum of the Martian system; it is therefore imperative that the
satellite shall do less. Accordingly, we find that this satellite must
go in towards the planet. No doubt this effect is much complicated by
the influence of the other satellite of the same planet, but the
illustration may suffice to show that if the satellites of the earth and
Mars do not convey to us much direct evidence with regard to the nebular
theory, this is largely because the effect of the tides has been a
preponderating influence. The Martian system as we now see it has
acquired its characteristic features by tidal influence, so that the
more simple influences which would immediately illustrate the nebular
theory have become hidden.
As to the satellites of Jupiter and Saturn, the circumstances are again
quite different from those that we find in the earth and in Mars. There
is little more to be said with regard to them than that everything that
they present to us is consistent with the indications of the nebular
theory. The evolution in each case has been a reproduction in miniature
of the evolution of the solar system.
But the satellites of Uranus and Neptune present, it must be admitted,
the greatest stumbling block to the acceptance of the nebular theory.
Both as to the directions in which they move and as to the planes in
which their orbits lie, it must be admitted that the satellites of
Uranus are distinctly at variance with what the nebular theory would
suggest. The consideration of this subject will be found in the next
chapter.
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