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   Chapter 4 CELESTIAL MECHANISM

Astronomy of To-day By Cecil G. Dolmage Characters: 11483

Updated: 2017-12-06 00:02


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.

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