CELESTIAL MECHANISM
As soon as we begin to inquire closely into the actual condition of the
various members of the solar system we are struck with a certain
distinction. We find that there are two quite different points of view
from which these bodies can be regarded. For instance, we may make our
estimates of them either as regards _volume_--that is to say, the mere
room which they take up; or as regards _mass_--that is to say, the
amount of matter which they contain.
Let us imagine two globes of equal volume; in other words, which take up
an equal amount of space. One of these globes, however, may be composed
of material much more tightly put together than in the other; or of
greater _density_, as the term goes. That globe is said to be the
greater of the two in mass. Were such a pair of globes to be weighed in
scales, one globe in each pan, we should see at once, by its weighing
down the other, which of the two was composed of the more tightly packed
materials; and we should, in astronomical parlance, say of this one that
it had the greater mass.
Volume being merely another word for size, the order of the members of
the solar system, with regard to their volumes, will be as follows,
beginning with the greatest:--the Sun, Jupiter, Saturn, Uranus,
Neptune, the Earth, Venus, Mars, and Mercury.
With regard to mass the same order strangely enough holds good. The
actual densities of the bodies in question are, however, very different.
The densest or closest packed body of all is the Earth, which is about
five and a half times as dense as if it were composed entirely of water.
Venus follows next, then Mars, and then Mercury. The remaining bodies,
on the other hand, are relatively loose in structure. Saturn is the
least dense of all, less so than water. The density of the Sun is a
little greater than that of water.
This method of estimating is, however, subject to a qualification. It
must be remembered that in speaking of the Sun, for instance, as being
only a little denser than water, we are merely treating the question
from the point of view of an average. Certain parts of it in fact will
be ever so much denser than water: those are the parts in the centre.
Other portions, for instance, the outside portions, will be very much
less dense. It will easily be understood that in all such bodies the
densest or most compressed portions are to be found towards the centre;
while the portions towards the exterior being less pressed upon, will be
less dense.
We now reach a very important point, the question of Gravitation.
_Gravitation_, or _gravity_, as it is often called, is the attractive
force which, for instance, causes objects to fall to the earth. Now it
seems rather strange that one should say that it is owing to a certain
force that things fall towards the earth. All things seem to us to fall
so of their own accord, as if it were quite natural, or rather most
unnatural if they did not. Why then require a "force" to make them fall?
The story goes that the great Sir Isaac Newton was set a-thinking on
this subject by seeing an apple fall from a tree to the earth. He then
carried the train of thought further; and, by studying the movements of
the moon, he reached the conclusion that a body even so far off as our
satellite would be drawn towards the earth in the same manner. This
being the case, one will naturally ask why the moon herself does not
fall in upon the earth. The answer is indeed found to be that the moon
is travelling round and round the earth at a certain rapid pace, and it
is this very same rapid pace which keeps her from falling in upon us.
Any one can test this simple fact for himself. If we tie a stone to the
end of a string, and keep whirling it round and round fast enough, there
will be a strong pull from the stone in an outward direction, and the
string will remain tight all the time that the stone is being whirled.
If, however, we gradually slacken the speed at which we are making the
stone whirl, a moment will come at length when the string will become
limp, and the stone will fall back towards our hand.
It seems, therefore, that there are two causes which maintain the stone
at a regular distance all the time it is being steadily whirled. One of
these is the continual pull inward towards our hand by means of the
string. The other is the continual pull away from us caused by the rate
at which the stone is travelling. When the rate of whirling is so
regulated that these pulls exactly balance each other, the stone travels
comfortably round and round, and shows no tendency either to fall back
upon our hand or to break the string and fly away into the air. It is
indeed precisely similar with regard to the moon. The continual pull of
the earth's gravitation takes the place of the string. If the moon were
to go round and round slower than it does, it would tend to fall in
towards the earth; if, on the other hand, it were to go faster, it would
tend to rush away into space.
The same kind of pull which the earth exerts upon the objects at its
surface, or upon its satellite, the moon, exists through space so far as
we know. Every particle of matter in the universe is found in fact to
attract every other particle. The moon, for instance, attracts the earth
also, but the controlling force is on the side of the much greater mass
of the earth. This force of gravity or attraction of gravitation, as it
is also called, is perfectly regular in its action. Its power depends
first of all exactly upon the mass of the body which exerts it. The
gravitational pull of the sun, for instance, reaches out to an enormous
distance, controlling perhaps, in their courses, unseen planets circling
far beyond the orbit of Neptune. Again, the strength with which the
force of gravity acts depends upon distance in a regularly diminishing
proportion. Thus, the nearer an object is to the earth, for instance,
the stronger is the gravitational pull which it gets from it; the
farther off it is, the weaker is this pull. If then the moon were to be
brought nearer to the earth, the gravitational pull of the latter would
become so much stronger that the moon's rate of motion would have also
to increase in due proportion to prevent her from being drawn into the
earth. Last of all, the point in a body from which the attraction of
gravitation acts, is not necessarily the centre of the body, but rather
what is known as its _centre of gravity_, that is to say, the balancing
point of all the matter which the body contains.
It should here be noted that the moon does not actually revolve around
the centre of gravity of the earth. What really happens is that both
orbs revolve around their _common_ centre of gravity, which is a point
within the body of the earth, and situated about three thousand miles
from its centre. In the same manner the planets and the sun revolve
around the centre of gravity of the solar system, which is a point
within the body of the sun.
The neatly poised movements of the planets around the sun, and of the
satellites around their respective planets, will therefore be readily
understood to result from a nice balance between gravitation and speed
of motion.
The mass of the earth is ascertained to be about eighty times that of
the moon. Our knowledge of the mass of a planet is learned from
comparing the revolutions of its satellite or satellites around it, with
those of the moon around the earth. We are thus enabled to deduce what
the mass of such a planet would be compared to the earth's mass; that is
to say, a study, for instance, of Jupiter's satellite system shows that
Jupiter must have a mass nearly three hundred and eighteen times that of
our earth. In the same manner we can argue out the mass of the sun from
the movements of the planets and other bodies of the system around it.
With regard, however, to Venus and Mercury, the problem is by no means
such an easy one, as these bodies have no satellites. For information in
this latter case we have to rely upon such uncertain evidence as, for
instance, the slight disturbances caused in the motion of the earth by
the attraction of these planets when they pass closest to us, or their
observed effect upon the motions of such comets as may happen to pass
near to them.
Mass and weight, though often spoken of as one and the same thing, are
by no means so. Mass, as we have seen, merely means the amount of matter
which a body contains. The weight of a body, on the other hand, depends
entirely upon the gravitational pull which it receives. The force of
gravity at the surface of the earth is, for instance, about six times as
great as that at the surface of the moon. All bodies, therefore, weigh
about six times as much on the earth as they would upon the moon; or,
rather, a body transferred to the moon's surface would weigh only about
one-sixth of what it did on the terrestrial surface. It will therefore
be seen that if a body of given _mass_ were to be placed upon planet
after planet in turn, its _weight_ would regularly alter according to
the force of gravity at each planet's surface.
Gravitation is indeed one of the greatest mysteries of nature. What it
is, the means by which it acts, or why such a force should exist at all,
are questions to which so far we have not had even the merest hint of an
answer. Its action across space appears to be instantaneous.
The intensity of gravitation is said in mathematical parlance "to vary
inversely with the square of the distance." This means that at _twice_
the distance the pull will become only _one-quarter_ as strong, and not
one-half as otherwise might be expected. At _four_ times the distance,
therefore, it will be _one-sixteenth_ as strong. At the earth's surface
a body is pulled by the earth's gravitation, or "falls," as we
ordinarily term it, through 16 feet in one _second_ of time; whereas at
the distance of the moon the attraction of the earth is so very much
weakened that a body would take as long as one _minute_ to fall through
the same space.
Newton's investigations showed that if a body were to be placed _at
rest_ in space entirely away from the attraction of any other body it
would remain always in a motionless condition, because there would
plainly be no reason why it should move in any one direction rather than
in another. And, similarly, if a body were to be projected in a certain
direction and at a certain speed, it would move always in the same
direction and at the same speed so long as it did not come within the
gravitational attraction of any other body.
The possibility of an interaction between the celestial orbs had
occurred to astronomers before the time of Newton; for instance, in the
ninth century to the Arabian Musa-ben-Shakir, to Camillus Agrippa in
1553, and to Kepler, who suspected its existence from observation of the
tides. Horrox also, writing in 1635, spoke of the moon as moved by an
_emanation_ from the earth. But no one prior to Newton attempted to
examine the question from a mathematical standpoint.
Notwithstanding the acknowledged truth and far-reaching scope of the law
of gravitation--for we find its effects exemplified in every portion of
the universe--there are yet some minor movements which it does not
account for. For instance, there are small irregularities in the
movement of Mercury which cannot be explained by the influence of
possible intra-Mercurial planets, and similarly there are slight
unaccountable deviations in the motions of our neighbour the Moon.