Popular Science Monthly/Volume 23/May 1883/The Boundaries of Astronomy I
IS GRAVITATION UNIVERSAL?
By ROBERT S. BALL,
ASTRONOMER-ROYAL OF IRELAND.
IT is proposed in this and the following paper to trace some parts of the boundary-line which divides the truths which have been established in astronomy from those parts of the science which must be regarded as more or less hypothetical. It will be obvious that only a small part of so wide a subject can be discussed, or even alluded to, in the limits proposed. We intend, therefore, to select certain prominent questions, and to discuss those questions with such fullness as the circumstances will admit.
It will be desirable to commence with that great doctrine in astronomy which is often regarded as almost universally established. The doctrine to which we refer is known as the law of universal gravitation. It is customary to enunciate this law in the proposition that every particle of matter attracts every other particle with a force which varies directly as the product of the masses and inversely as the square of their distance. It is no doubt convenient to enunciate the great law in this very simple manner. It might seem awkward to have to specify all the qualifications which would be necessary if that enunciation is to assert no more than what we absolutely know. Perhaps many people believe, or think they believe, the law to be true in its general form; yet the assertion that the law of gravitation is universally true is an enormous, indeed, an infinite, exaggeration of the actual extent of our information.
To make this clear, let us contrast the law of gravitation as generally stated with the proposition which asserts that the earth rotates on its axis. No one who is capable of understanding the evidence on the question can doubt that the earth really does rotate upon its axis. I purposely set aside any difficulties of a quasi-metaphysical character, and speak merely of words in their ordinary acceptation. In stating that the earth rotates upon its axis, we assert merely a definite proposition as regards one body, all the facts which the assertion involves are present to our minds, and we know that the assertion must be true. Equally conclusive is the evidence for the statement that the earth revolves around the sun. Concrete truths of this kind could be multiplied indefinitely. We can make similar assertions with regard to the planets. We can assert that the planets rotate upon their axes, and that the planets revolve around the sun. But the law of gravitation is a proposition of quite a different nature. Let us examine briefly the evidence by which this law has been established.
The science of dynamics is founded upon certain principles known as the laws of motion. The simplest of these principles asserts that a body, once set moving in a straight line, will continue to move on uniformly forever in the same straight line, unless some force be permitted to act upon that body. For nature as we know it, this law seems to be fully proved. It has been tested in every way that we have been able to devise. All these tests have tended to confirm that law. The law is therefore believed to be true, at all events throughout the regions of space accessible to us and to our telescopes. Assuming this law and the other principles analogous to it, we can apply them to the case of the revolution of the earth around the sun. As the earth is not moving in a straight line, it must be acted upon by some force. It can be shown that this force must be directed toward the sun. It will further appear that the intensity of this force will vary inversely as the square of the distance between the earth and the sun. The movements of the planets can be made to yield the same conclusions. All these movements can be accounted for on the supposition that each planet is attracted by the sun with a force which varies directly as the product of the masses, and inversely as the square of the distance between the two bodies. When more careful observations are introduced, it is seen that the planets exhibit some slight deviations from the movements which they would have were each planet only acted upon by the attraction of the sun. These deviations do not invalidate the principle of attraction. They have been shown to arise from the mutual attractions of the planets themselves. Each of the planets is thus seen to attract each of the other planets. The intensity of this attraction between any pair of the planets is proportional to the masses of these planets, and varies inversely as the square of the distance between them. "We may use similar language with regard to the satellites by which so many of the planets are attended. Each satellite revolves around its primary. The movements of each satellite are mainly due to the preponderating attraction of the primary." Irregularities in the movements of the satellites are well known to astronomers, but these irregularities can be accounted for by the attraction of other bodies of the system. The law of attraction thus seems to prevail among the small bodies of the system as well as among the large bodies. It is true that there are still a few outstanding discrepancies which can not yet be said to have been completely accounted for by the principle of gravitation. This is probably due to the difficulties of the subject. The calculations which are involved are among the most difficult on which the mind of man has ever been engaged. We may practically assume that the law of gravitation is universal between the sun, the planets, and the satellites; and we may suppose that the few difficulties still outstanding will be finally cleared away, as has been the case with so many other seeming discrepancies. But even when these admissions have been made, are we in a position to assert that the law of gravitation is universal throughout the solar system? We are here confronted with a very celebrated difficulty. Do those erratic objects known as comets acknowledge the law of gravitation? There can be no doubt that in one sense the comets do obey the law of gravitation in a most signal and emphatic manner. A comet usually moves in an orbit of very great eccentricity; and it is one of the most remarkable triumphs of Newton's discovery, that we were by its means able to render account of how the movements of a comet could be produced by the attraction of the sun. As a whole, the comet is very amenable to gravitation, but what are we to say as to the tails of comets, which certainly do not appear to follow the law of universal attraction? The tails of comets, so far from being attracted toward the sun, seem actually to be repelled from the sun. Nor is even this an adequate statement of the case. The repulsive force by which the tails of the comets are driven from the sun is sometimes a very much more intense force than the attraction of gravitation.
I have no intention to discuss here the vexed question as to the origin of the tails of comets. I do not now inquire whether the repulsion by which the tail is produced be due to the intense radiation from the sun, or to electricity, or to some other agent. It is sufficient for our present purpose to note that, even if the tails of comets do gravitate toward the sun, the attraction is obscured by a more powerful repulsive force.
The solar system is a very small object when viewed in comparison with the dimensions of the sidereal system. The planets form a group nestled up closely around the sun. This little group is separated from its nearest visible neighbors in space by the most appalling distances. A vessel in the middle of the Atlantic Ocean is not more completely isolated from the shores of Europe and America than is our solar system from the stars and other bodies which surround it in space. Our knowledge of gravitation has been most entirely obtained from the study of the bodies in the solar system. Let us inquire what can be ascertained as to the existence of this law in other parts of the universe. Newton knew nothing of the existence of the law of gravitatation beyond the confines of the solar system. A little more is known now.
Our actual knowledge of the existence of gravitation in the celestial spaces outside the solar system depends entirely upon those very interesting objects known as binary stars. There are in the heavens many cases of two stars occurring quite close together. A well-known instance is presented in the star Epsilon Lyræ, where two stars are so close together that it is a fair test of good vision to be able to separate them. But there are many cases in which the two stars are so close together that they can not be seen separately without the aid of a telescope. We may take, for instance, the very celebrated double star Castor, well known as one of the Twins. Viewed by the unaided eye, the two stars look like a single star, but in a moderately good telescope it is seen that the object is really two separate stars quite close together. The question now comes as to whether the propinquity of the two stars is apparent or real. It might be explained by the supposition that the two stars were indeed close together compared with the distance by which they are separated; or it could be equally explained by supposing that the two stars, though really far apart, yet appeared so nearly in the same line of vision that when projected on the surface of the heavens they seemed close together. It can not be doubted that in the case of many of the double stars, especially those in which the components appear tolerably distant, the propinquity is only apparent, and arises from the two stars being near the same line of vision. But it is, also, undoubtedly true that in the case of very many of the double stars, especially among those belonging to the class which includes Castor, the two stars are really at about the same distance from us, and, therefore, as compared with that distance, they are really close together.
Among the splendid achievements of Sir William Herschel, one of the greatest was his discovery of the movements of the binary stars. It was shown by Herschel that in some of the double stars one star of the pair was moving around the other, and that their apparent distances were changing. The discoveries inaugurated by Herschel have been widely extended by other astronomers. One of the more rapidly moving of the double stars lies in the constellation of Coma Berenices. The revolution of one component around the other requires a period of 25·7 years. The two components of this star are exceedingly close together, the greatest distance being about one second of arc. There is very great difficulty in making accurate measurements of a double star of which the components are so close. More reliance may consequently be placed upon the determination of the orbits of other binary stars of which the components are farther apart. Among these we may mention the remarkable binary star ξ Ursæ Majoris. The distance between the two components of this star varies from one second of arc to three seconds. The first recorded measurement of this object was by Sir William Herschel, in 1781, and since that date it has been repeatedly observed. From a comparison of all the measurements which have been made it appears that the periodic time of the revolution of one of these components about the other is about sixty years. This star has thus been followed through more than one entire revolution. The importance of these discoveries became manifest when an attempt was made to explain the movements. It was soon shown that the movements of the stars were such as could be explained if the two stars attracted each other in conformity with the law of gravitation. It would, however, be hardly correct to assert that the discovery of the binary stars proved that the two stars attracted each other with a force which varies inversely as the square of their distance. Even under the most favorable circumstances the observations are very difficult; they can not be made with the same accuracy as is attained in observing the movements of the planets; they have not even the value which antiquity will often confer on an observation which has not much else in its favor. There are probably many different suppositions which would explain all that has yet been observed as to the motions of the binary stars. Gravitation is but one of those suppositions. Gravitation will no doubt carry with it the prestige acquired by its success in explaining phenomena in the solar system. I do not know that any one has ever seriously put forward any other explanation except gravitation to account for the movements of the binary stars, nor is any one likely to do so while gravitation can continue to render an account of the observed facts; but all this is very different from saying that the discovery of the binary stars has proved that the law of gravitation extends to the stellar regions.
Except for what the binary stars tell us, we would know nothing as to the existence or the non-existence of the law of gravitation beyond the confines of the solar system. Does Sirius, for instance, attract the pole-star? We really do not know. Nor can we ever expect to know. If Sirius and the pole-star do attract each other, and if the law of their attraction be the same as the law of attraction in the solar system, it will then be easy to show that the effect of this attraction is so minute that it would he entirely outside the range of our instruments even to detect it. Observation is hopeless on such a matter. If we can not detect any attraction between a star in one constellation and a star in another, no more can we detect any attraction between our sun and the stars. Such attractions may exist, or they may not exist: we have no means of knowing. Should any one assert that there is absolutely no gravitation between two bodies more than a billion miles apart, we know no facts by which he can be contradicted.
If we know so little about the existence of gravitation in the space accessible to our telescopes, what are we to say of those distant regions of space to which our view can never penetrate? Let a vast sphere be described of such mighty dimensions that it embraces not only all the objects visible to the unaided eye, not only all the objects visible in our most powerful telescopes, but even every object that the most fertile imagination can conceive, what relation must this stupendous sphere bear to the whole of space? The mighty sphere can only be an infinitely small part of space. It must bear to the whole of space a ratio infinitely less than the water in a single dew-drop bears to the water in the Atlantic Ocean. Are we then entitled to assert that every particle in the universe attracts every other particle with a force which is proportional to the product of their masses, and which varies inversely as the square of their distance? We have, indeed, but a slender basis of fact on which to rest a proposition so universal. Let us attempt to enunciate the law of gravitation so as to commit ourselves to no assertion not absolutely proved. The statement would then run somewhat as follows:
Of the whole contents of space we know nothing except within that infinitely small region which contains the bodies visible in our telescopes. Nor can we assert that gravitation pervades the entire of even this infinitely small region. It is true that in one very minute part of this infinitely small region the law of gravitation appears to reign supreme. This minute part is of course the solar system. There are also a few binary stars in this infinitely small region whose movements would admit of being explained by gravitation, though as yet they can hardly be held to absolutely prove its existence.
It must then be admitted that, when the law of gravitation is spoken of as being universal, we are using language infinitely more general than the facts absolutely warrant. At the present moment we only know that gravitation exists to a very small extent in a certain indefinitely small portion of space. Our knowledge would have to be enormously extended before we can assert that gravitation extended entirely through this very limited region; and, even when we have proved this, we should have only made an infinitesimal advance to a proof that gravitation is absolutely universal.
I do not for a moment assert that our ordinary statement of the law of gravitation is untrue. I merely say that it has not been proved, and we may also add that it does not seem as if it ever could be proved. Most people who have considered the matter will probably believe that gravitation is universal. Nor is this belief unnatural. If we set aside comets' tails, and perhaps one or two other slightly doubtful matters, we may assert that we always find the law of gravitation to be true whenever we have an opportunity of testing it. These opportunities are very limited, so that we have but very slender supports for the induction that gravitation is universal. But it must be admitted that an hypothesis which has practically borne every test which can be applied has very strong grounds for our acceptance: such, then, are the claims of the law of gravitation to be admitted to a place among the laws of Nature.
The wondrous series of spectroscopic researches by which Mr. Huggins has so vastly extended our knowledge should also be here referred to. Mr. Huggins has shown that many of the substances most abundant on the earth are widely spread through the universe. Take, for instance, the metal iron and the gas hydrogen. We can detect the existence of these elements in objects enormously distant. Both iron and hydrogen exist in many stars, and hydrogen has been shown, in all probability, to be an important constituent of the nebulæ. That the rest of the sidereal system should thus be composed of materials known to be to a large extent identical with the materials in the solar system is a presumption in favor of the universality of gravitation.
In what has hitherto been said, we have attempted to give an outline of the facts so far as they are certainly known to us. Into mere speculations we have no desire to enter. We may, however, sketch out a brief chapter in modern sidereal astronomy, which seems to throw a ray of light into the constituents of the vast abyss of space which lies beyond the scope of our telescopes. The ray of light is no doubt but a feeble one, but we must take whatever information we can obtain, even though it may fall far short of that which an intellectual curiosity will desire. The question now before us may be simply stated: Are we entitled to suppose that the part of the universe accessible to our telescopes is fairly typical of the other parts of the universe; or are we to believe that the system we know is altogether exceptional; that there are stars in other parts quite unlike our stars, composed of different materials, acted upon by different laws, of which we have no conception? The presumption is, that the materials of which our system is composed are representative of the materials elsewhere. This presumption is strengthened by the very important considerations now to be adduced.
In the first place, let us distinctly understand what is meant by our sidereal system. We have already dwelt on the isolated position of the sun and the attendant planets. The grandest truth in the whole of astronomy is that which asserts that our sun is only a star separated by the most gigantic distances from the other stars around. Our sun, indeed, appears to be but one of the vast host of stars which form the milky way. We need not here enter into the often-discussed question as to whether the nebulæ are, generally speaking, at distances of the same order as the stars. There seems to be no doubt that some of the nebulæ are quite as near to us as some of the stars. At all events, for our present purpose, we may group the milky way, the nebulæ, the stars, and the clusters, all into one whole which we call our sidereal system. Is this sidereal system as thus defined an isolated object in space? are its members all so bound together by the law of universal gravitation that each body, whatever be its movements, can only describe a certain path such that it can never depart finally from the system? This is a question of no small importance. It presents features analogous to certain very interesting problems in biology which the labors of Mr. Wallace have done so much to elucidate. We are told that the fauna and flora of an oceanic island, cut off from the perpetual immigration of new forms, often assumes a very remarkable type. The evolution of life under such circumstances proceeds in a very different manner to the corresponding evolution in an equal area of land which is connected with the great continental masses. Is our sidereal system to be regarded as an oceanic island in space, or is it in such connection with the systems in other parts of space as might lead us to infer that the various systems had a common character?
The evidence seems to show that the stars in our system are probably not permanently associated together, but that in the course of time some stars enter our system and other stars leave it, in such a manner as to suggest that the bodies visible to us are fairly typical of the general contents of the universe. The strongest evidence that can be presented on this subject is met with in the peculiar circumstances of one particular star. The star in question is known as No. 1830 of Groombridge's catalogue. It is a small star, not to be seen without the aid of a telescope. This star is endowed with a very large proper motion. It would not be correct to say that its proper motion exceeds that of any other known star, but it certainly has the largest visible proper motion of any star of which the distance is known. The proper motion of 1830 Groombridge amounts to over seven seconds annually. It would take between two and three centuries to move over a distance in the heavens equal to the apparent diameter of the moon. The distance of this star is much greater than might have been anticipated from its very large proper motion. The estimates of the distance present some irregularities, but we shall probably be quite correct in assuming that the distance is not less than two hundred billions of miles. This star is, indeed, ten times as far from us as α Centauri, which is generally considered to he the sun's nearest neighbor in our sidereal system. The proper motion and the distance of 1830 Groombridge being both assumed, it is easy to calculate the velocity with which that star must be moving. The velocity is indeed stupendous and worthy of a majestic sun; it is no less than 200 miles a second. It would seem that the velocity may even be much larger than this. The proper motion of the star which we see is merely the true proper motion of the star foreshortened by projection on the surface of the heavens. In adopting 200 miles a second as the velocity of 1830 Groombridge, we therefore make a most moderate assumption, which may and probably does fall considerably short of the truth. But, even with this very moderate assumption, it will be easy to show that 1830 Groombridge seems in all probability to be merely traveling through our system, and not permanently attached thereto.
The star sweeps along through our system with this stupendous velocity. Now, there can be no doubt that if the star were permanently to retain this velocity, it would in the course of time travel right across our system, and, after leaving our system, would retreat into the depths of infinite space. Is there any power adequate to recall this star from the voyage to infinity? We know of none, unless it be the attraction of the stars or other bodies of our sidereal system. It therefore becomes a matter of calculation to determine whether the attraction of all the material bodies of our sidereal system could be adequate, even with universal gravitation, to recall a body which seems bent on leaving that system with a velocity of 200 miles per second. This interesting problem has been discussed by Professor Newcomb, whose calculations we shall here follow. In the first place, we require to make some estimate of the dimensions of the sidereal system, in order to see whether it seems likely that this star can ever be recalled. The number of stars may be taken at one hundred million, which is probably double as many as the number we can see with our best telescopes. The masses of the stars may be taken as on the average five times as great as the mass of the sun. The distribution of the stars is suggested by the constitution of the milky way. One hundred million stars are presumed to be disposed in a flat, circular layer of such dimensions that a ray of light would require thirty thousand years to traverse one diameter. Assuming the ordinary law of gravitation, it is now easy to compute the efficiency of such an arrangement in attempting to recall a moving star. The whole question turns on a certain critical velocity of twenty-five miles a second. If a star darted through the system we have just been considering with a velocity less than twenty-five miles a second, then, after that star had moved for a certain distance, the attractive power of the system would gradually bend the path of the star round, and force the star to return to the system. If therefore, the velocities of the stars were under no circumstances more than twenty-five miles a second, then, supposing the system to have the character we have described, that system might be always the same. The stars might be in incessant motion, but they must always remain in the vicinity of our present system, and our whole sidereal system might be an isolated object in space, just as our solar system is an isolated object in the extent of the sidereal system. We have, however, seen that for one star at all events the velocity is no less than 200 miles a second. If this star dash through the system, then the attractions of all the bodies in the system will unite in one grand effort to recall the wanderer. This attraction must, to some extent, be acknowledged; the speed of the wanderer must gradually diminish as he recedes into space; but that speed will never be lessened sufficiently to bring the star back again. As the star retreats farther and farther, the potency of the attraction will decrease; but, owing to the velocity of the star being over twenty-five miles a second, the attraction can never overcome the velocity; so that the star seems destined to escape. This calculation is of course founded on our assumption as to the total mass of the stars and other bodies which form our sidereal system. That estimate was founded on a liberal, indeed, a very liberal interpretation of the evidence which our telescopes have afforded. But it may still fall short of the truth. There may be more than a hundred million stars in our system: their average weight may be more than five times the weight of our sun. But, unless the assumption we have made is enormously short of the truth, our inference can not be challenged. If the stars are sixty-four times as numerous, or if the whole mass of the system be sixty-four times as great as we have supposed, then the critical velocity would be 200 miles a second instead of twenty-five miles a second. Our estimate of the system would therefore have to be enlarged sixty-four-fold, if the attraction of that system is to be adequate to recall 1830 Groombridge. It should also be recollected that our assumption of the velocity of the star is very moderate, so that it is not at all unlikely that a system at least one hundred times as massive as the system we have supposed would be required if this star was to be recalled. The result of this inquiry is really only to be stated as an alternative: either our sidereal system is not an entirely isolated object, or its bodies must be vastly more numerous or more massive than even our most liberal interpretation of observations would seem to warrant. It seems more reasonable to adopt the first branch of the alternative. If this be so, then we see that 1830 Groombridge, having traveled from an indefinitely great distance on one side of the heavens, is now passing through our system for the first and the only time. After leaving our system this star will retreat again into the depths of space, to a distance which, for anything we can tell, may be practically regarded as infinite. Although we have only used this one star as an illustration, yet it is not to be supposed that the peculiarities which it presents are absolutely unique. It seems more likely that there may be many other stars which are at present passing through our system. In fact, considering that most or all of the stars are actually in motion, it can be shown that, in the course of ages, the whole face of the heavens is gradually changing. We are thus led to the conclusion that our system is not an absolutely isolated group of bodies in the abyss of space, but that we are visited by other bodies coming from the remotest regions of space.—Contemporary Review.