The Story of the Heavens Part 10

These two laws completely prescribe the motion of a planet round the sun. The first defines the path which the planet pursues; the second describes how the velocity of the body varies at different points along its path. But Kepler added to these a third law, which enables us to compare the movements of two different planets revolving round the same sun. Before stating this law, it is necessary to explain exactly what is meant by the _mean_ distance of a planet. In its elliptic path the distance from the sun to the planet is constantly changing; but it is nevertheless easy to attach a distinct meaning to that distance which is an average of all the distances. This average is called the mean distance. The simplest way of finding the mean distance is to add the greatest of these quant.i.ties to the least, and take half the sum. We have already defined the periodic time of the planet; it is the number of days which the planet requires for the completion of a journey round its path. Kepler's third law establishes a relation between the mean distances and the periodic times of the various planets. That relation is stated in the following words:--

"_The squares of the periodic times are proportional to the cubes of the mean distances._"

Kepler knew that the different planets had different periodic times; he also saw that the greater the mean distance of the planet the greater was its periodic time, and he was determined to find out the connection between the two. It was easily found that it would not be true to say that the periodic time is merely proportional to the mean distance. Were this the case, then if one planet had a distance twice as great as another, the periodic time of the former would have been double that of the latter; observation showed, however, that the periodic time of the more distant planet exceeded twice, and was indeed nearly three times, that of the other. By repeated trials, which would have exhausted the patience of one less confident in his own sagacity, and less a.s.sured of the accuracy of the observations which he sought to interpret, Kepler at length discovered the true law, and expressed it in the form we have stated.

To ill.u.s.trate the nature of this law, we shall take for comparison the earth and the planet Venus. If we denote the mean distance of the earth from the sun by unity then the mean distance of Venus from the sun is 07233. Omitting decimals beyond the first place, we can represent the periodic time of the earth as 3653 days, and the periodic time of Venus as 2247 days. Now the law which Kepler a.s.serts is that the square of 3653 is to the square of 2247 in the same proportion as unity is to the cube of 07233. The reader can easily verify the truth of this ident.i.ty by actual multiplication. It is, however, to be remembered that, as only four figures have been retained in the expressions of the periodic times, so only four figures are to be considered significant in making the calculations.

The most striking manner of making the verification will be to regard the time of the revolution of Venus as an unknown quant.i.ty, and deduce it from the known revolution of the earth and the mean distance of Venus. In this way, by a.s.suming Kepler's law, we deduce the cube of the periodic time by a simple proportion, and the resulting value of 2247 days can then be obtained. As a matter of fact, in the calculations of astronomy, the distances of the planets are usually ascertained from Kepler's law. The periodic time of the planet is an element which can be measured with great accuracy; and once it is known, then the square of the mean distance, and consequently the mean distance itself, is determined.

Such are the three celebrated laws of Planetary Motion, which have always been a.s.sociated with the name of their discoverer. The profound skill by which these laws were elicited from the ma.s.s of observations, the intrinsic beauty of the laws themselves, their widespread generality, and the bond of union which they have established between the various members of the solar system, have given them quite an exceptional position in astronomy.

As established by Kepler, these planetary laws were merely the results of observation. It was found, as a matter of fact, that the planets did move in ellipses, but Kepler a.s.signed no reason why they should adopt this curve rather than any other. Still less was he able to offer a reason why these bodies should sweep over equal areas in equal times, or why that third law was invariably obeyed. The laws as they came from Kepler's hands stood out as three independent truths; thoroughly established, no doubt, but unsupported by any arguments as to why these movements rather than any others should be appropriate for the revolutions of the planets.

It was the crowning triumph of the great law of universal gravitation to remove this empirical character from Kepler's laws. Newton's grand discovery bound together the three isolated laws of Kepler into one beautiful doctrine. He showed not only that those laws are true, but he showed why they must be true, and why no other laws could have been true. He proved to demonstration in his immortal work, the "Principia,"

that the explanation of the famous planetary laws was to be sought in the attraction of gravitation. Newton set forth that a power of attraction resided in the sun, and as a necessary consequence of that attraction every planet must revolve in an elliptic orbit round the sun, having the sun as one focus; the radius of the planet's...o...b..t must sweep over equal areas in equal times; and in comparing the movements of two planets, it was necessary to have the squares of the periodic times proportional to the cubes of the mean distances.

As this is not a mathematical treatise, it will be impossible for us to discuss the proofs which Newton has given, and which have commanded the immediate and universal acquiescence of all who have taken the trouble to understand them. We must here confine ourselves only to a very brief and general survey of the subject, which will indicate the character of the reasoning employed, without introducing details of a technical character.

Let us, in the first place, endeavour to think of a globe freely poised in s.p.a.ce, and completely isolated from the influence of every other body in the universe. Let us imagine that this globe is set in motion by some impulse which starts it forward on a rapid voyage through the realms of s.p.a.ce. When the impulse ceases the globe is in motion, and continues to move onwards. But what will be the path which it pursues? We are so accustomed to see a stone thrown into the air moving in a curved path, that we might naturally think a body projected into free s.p.a.ce will also move in a curve. A little consideration will, however, show that the cases are very different. In the realms of free s.p.a.ce we find no conception of upwards or downwards; all paths are alike; there is no reason why the body should swerve to the right or to the left; and hence we are led to surmise that in these circ.u.mstances a body, once started and freed from all interference, would move in a straight line. It is true that this statement is one which can never be submitted to the test of direct experiment. Circ.u.mstanced as we are on the surface of the earth, we have no means of isolating a body from external forces. The resistance of the air, as well as friction in various other forms, no less than the gravitation towards the earth itself, interfere with our experiments. A stone thrown along a sheet of ice will be exposed to but little resistance, and in this case we see that the stone will take a straight course along the frozen surface. A stone similarly cast into empty s.p.a.ce would pursue a course absolutely rectilinear. This we demonstrate, not by any attempts at an experiment which would necessarily be futile, but by indirect reasoning. The truth of this principle can never for a moment be doubted by one who has duly weighed the arguments which have been produced in its behalf.

Admitting, then, the rectilinear path of the body, the next question which arises relates to the velocity with which that movement is performed. The stone gliding over the smooth ice on a frozen lake will, as everyone has observed, travel a long distance before it comes to rest. There is but little friction between the ice and the stone, but still even on ice friction is not altogether absent; and as that friction always tends to stop the motion, the stone will at length be brought to rest. In a voyage through the solitudes of s.p.a.ce, a body experiences no friction; there is no tendency for the velocity to be reduced, and consequently we believe that the body could journey on for ever with unabated speed. No doubt such a statement seems at variance with our ordinary experience. A sailing ship makes no progress on the sea when the wind dies away. A train will gradually lose its velocity when the steam has been turned off. A humming-top will slowly expend its rotation and come to rest. From such instances it might be plausibly argued that when the force has ceased to act, the motion that the force generated gradually wanes, and ultimately vanishes. But in all these cases it will be found, on reflection, that the decline of the motion is to be attributed to the action of resisting forces. The sailing ship is r.e.t.a.r.ded by the rubbing of the water on its sides; the train is checked by the friction of the wheels, and by the fact that it has to force its way through the air; and the atmospheric resistance is mainly the cause of the stopping of the humming-top, for if the air be withdrawn, by making the experiment in a vacuum, the top will continue to spin for a greatly lengthened period. We are thus led to admit that a body, once projected freely in s.p.a.ce and acted upon by no external resistance, will continue to move on for ever in a straight line, and will preserve unabated to the end of time the velocity with which it originally started. This principle is known as the _first law of motion_.

Let us apply this principle to the important question of the movement of the planets. Take, for instance, the case of our earth, and let us discuss the consequences of the first law of motion. We know that the earth is moving each moment with a velocity of about eighteen miles a second, and the first law of motion a.s.sures us that if this globe were submitted to no external force, it would for ever pursue a straight track through the universe, nor would it depart from the precise velocity which it possesses at the present moment. But is the earth moving in this manner? Obviously not. We have already found that our globe is moving round the sun, and the comprehensive laws of Kepler have given to that motion the most perfect distinctness and precision. The consequence is irresistible. The earth cannot be free from external force. Some potent influence on our globe must be in ceaseless action.

That influence, whatever it may be, constantly deflects the earth from the rectilinear path which it tends to pursue, and constrains it to trace out an ellipse instead of a straight line.

The great problem to be solved is now easily stated. There must be some external agent constantly influencing the earth. What is that agent, whence does it proceed, and to what laws is it submitted? Nor is the question confined to the earth. Mercury and Venus, Mars, Jupiter, and Saturn, unmistakably show that, as they are not moving in rectilinear paths, they must be exposed to some force. What is this force which guides the planets in their paths? Before the time of Newton this question might have been asked in vain. It was the splendid genius of Newton which supplied the answer, and thus revolutionised the whole of modern science.

The data from which the question is to be answered must be obtained from observation. We have here no problem which can be solved by mere mathematical meditation. Mathematics is no doubt a useful, indeed, an indispensable, instrument in the enquiry; but we must not attribute to mathematics a potency which it does not possess. In a case of this kind, all that mathematics can do is to interpret the results obtained by observation. The data from which Newton proceeded were the observed phenomena in the movement of the earth and the other planets. Those facts had found a succinct expression by the aid of Kepler's laws. It was, accordingly, the laws of Kepler which Newton took as the basis of his labours, and it was for the interpretation of Kepler's laws that Newton invoked the aid of that celebrated mathematical reasoning which he created.

The question is then to be approached in this way: A planet being subject to _some_ external influence, we have to determine what that influence is, from our knowledge that the path of each planet is an ellipse, and that each planet sweeps round the sun over equal areas in equal times. The influence on each planet is what a mathematician would call a force, and a force must have a line of direction. The most simple conception of a force is that of a pull communicated along a rope, and the direction of the rope is in this case the direction of the force.

Let us imagine that the force exerted on each planet is imparted by an invisible rope. Kepler's laws will inform us with regard to the direction of this rope and the intensity of the strain transmitted through it.

The mathematical a.n.a.lysis of Kepler's laws would be beyond the scope of this volume. We must, therefore, confine ourselves to the results to which they lead, and omit the details of the reasoning. Newton first took the law which a.s.serted that the planet moved over equal areas in equal times, and he showed by unimpeachable logic that this at once gave the direction in which the force acted on the planet. He showed that the imaginary rope by which the planet is controlled must be invariably directed towards the sun. In other words, the force exerted on each planet was at all times pointed from the planet towards the sun.

It still remained to explain the intensity of the force, and to show how the intensity of that force varied when the planet was at different points of its path. Kepler's first law enables this question to be answered. If the planet's path be elliptic, and if the force be always directed towards the sun at one focus of that ellipse, then mathematical a.n.a.lysis obliges us to say that the intensity of the force must vary inversely as the square of the distance from the planet to the sun.

The movements of the planets, in conformity with Kepler's laws, would thus be accounted for even in their minutest details, if we admit that an attractive power draws the planet towards the sun, and that the intensity of this attraction varies inversely as the square of the distance. Can we hesitate to say that such an attraction does exist? We have seen how the earth attracts a falling body; we have seen how the earth's attraction extends to the moon, and explains the revolution of the moon around the earth. We have now learned that the movement of the planets round the sun can also be explained as a consequence of this law of attraction. But the evidence in support of the law of universal gravitation is, in truth, much stronger than any we have yet presented.

We shall have occasion to dwell on this matter further on. We shall show not only how the sun attracts the planets, but how the planets attract each other; and we shall find how this mutual attraction of the planets has led to remarkable discoveries, which have elevated the law of gravitation beyond the possibility of doubt.

Admitting the existence of this law, we can show that the planets must revolve around the sun in elliptic paths with the sun in the common focus. We can show that they must sweep over equal areas in equal times.

We can prove that the squares of the periodic times must be proportional to the cubes of their mean distances. Still further, we can show how the mysterious movements of comets can be accounted for. By the same great law we can explain the revolutions of the satellites. We can account for the tides, and for other phenomena throughout the Solar System. Finally, we shall show that when we extend our view beyond the limits of our Solar System to the beautiful starry systems scattered through s.p.a.ce, we find even there evidence of the great law of universal gravitation.

CHAPTER VI.

THE PLANET OF ROMANCE.

Outline of the Subject--Is Mercury the Planet nearest the Sun?--Transit of an Interior Planet across the Sun--Has a Transit of Vulcan ever been seen?--Visibility of Planets during a Total Eclipse of the Sun--Professor Watson's Researches in 1878.

Provided with a general survey of the Solar System, and with such an outline of the law of universal gravitation as the last chapter has afforded us, we commence the more detailed examination of the planets and their satellites. We shall begin with the planets nearest to the sun, and then we shall gradually proceed outwards to one planet after another, until we reach the confines of the system. We shall find much to occupy our attention. Each planet is itself a globe, and it will be for us to describe as much as is known of it. The satellites by which so many of the planets are accompanied possess many points of interest. The circ.u.mstances of their discovery, their sizes, their movements, and their distances must be duly considered. It will also be found that the movements of the planets present much matter for reflection and examination. We shall have occasion to show how the planets mutually disturb each other, and what remarkable consequences have arisen from these influences. We must also occasionally refer to the important problems of celestial measuring and celestial weighing. We must show how the sizes, the weights, and the distances of the various members of our system are to be discovered. The greater part of our task will fortunately lead us over ground which is thoroughly certain, and where the results have been confirmed by frequent observation. It happens, however, that at the very outset of our course we are obliged to deal with observations which are far from certain. The existence of a planet much closer to the sun than those hitherto known has been a.s.serted by competent authority. The question is still unsettled, but the planet cannot at present be found. Hence it is that we have called the subject of this chapter, The Planet of Romance.

It had often been thought that Mercury, long supposed to be the nearest planet to the sun, was perhaps not really the body ent.i.tled to that distinction. Mercury revolves round the sun at an average distance of about 36,000,000 miles. In the interval between it and the sun there might have been one or many other planets. There might have been one revolving at ten million miles, another at fifteen, and so on. But did such planets exist? Did even one planet revolve inside the orbit of Mercury? There were certain reasons for believing in such a planet. In the movements of Mercury indications were perceptible of an influence that it was at one time thought might have been accounted for by the supposition of an interior planet.[13] But there was necessarily a great difficulty about seeing this object. It must always be close to the sun, and even in the best telescope it is generally impossible to see a star-like point in that position. Nor could such a planet be seen after sunset, for under the most favourable conditions it would set almost immediately after the sun, and a like difficulty would make it invisible at sunrise.

Our ordinary means of observing a planet have therefore completely failed. We are compelled to resort to extraordinary methods if we would seek to settle the great question as to the existence of the intra-Mercurial planets. There are at least two lines of observation which might be expected to answer our purpose.

An opportunity for the first would arise when it happened that the unknown planet came directly between the earth and the sun. In the diagram (Fig. 40) we show the sun at the centre; the internal dotted circle denotes the orbit of the unknown planet, which has received the name of Vulcan before even its very existence has been at all satisfactorily established. The outer circle denotes the orbit of the earth. As Vulcan moves more rapidly than the earth, it will frequently happen that the planet will overtake the earth, so that the three bodies will have the positions represented in the diagram. It would not, however, necessarily follow that Vulcan was exactly between the earth and the luminary. The path of the planet may be tilted, so that, as seen from the earth, Vulcan would be over or under the sun, according to circ.u.mstances.

If, however, Vulcan really does exist, we might expect that sometimes the three bodies will be directly in line, and this would then give the desired opportunity of making the telescopic discovery of the planet. We should expect on such an occasion to observe the planet as a dark spot, moving slowly across the face of the sun. The two other planets interior to the earth, namely, Mercury and Venus, are occasionally seen in the act of transit; and there cannot be a doubt that if Vulcan exists, its transits across the sun must be more numerous than those of Mercury, and far more numerous than those of Venus. On the other hand, it may reasonably be antic.i.p.ated that Vulcan is a small globe, and as it will be much more distant from us than Mercury at the time of its transit, we could not expect that the transit of the planet of romance would be at all comparable as a spectacle with those of either of the two other bodies we have named.

The question arises as to whether telescopic research has ever disclosed anything which can be regarded as a transit of Vulcan. On this point it is not possible to speak with any certainty. It has, on more than one occasion, been a.s.serted by observers that a spot has been seen traversing the sun, and from its shape and general appearance they have presumed it to have been an intra-Mercurial planet. But a close examination of the circ.u.mstances in which such observations have been made has not tended to increase confidence in this presumption. Such discoveries have usually been made by persons little familiar with telescopic observations. It is certainly a significant fact that, notwithstanding the diligent scrutiny to which the sun has been subjected during the past century by astronomers who have specially devoted themselves to this branch of research, no telescopic discovery of Vulcan on the sun has been announced by any really experienced astronomer. The last announcement of a planet having crossed the sun dates from 1876, and was made by a German amateur, but what he thought to have been a planet was promptly shown to have been a small sun-spot, which had been photographed at Greenwich in the course of the daily routine work, and had also been observed at Madrid. From an examination of the whole subject, we are inclined to believe that there is not at this moment any reliable telescopic evidence of the transit of an intra-Mercurial planet over the face of the central luminary.

[Ill.u.s.tration: Fig. 40.--The Transit of the Planet of Romance.]

But there is still another method by which we might reasonably hope to detect new planets in the vicinity of the sun. This method is, however, but seldom available. It is only possible when the sun is totally eclipsed.

When the moon is interposed directly between the earth and the sun, the brightness of day is temporarily exchanged for the gloom of night. If the sky be free from clouds the stars spring forth, and can be seen around the obscured sun. Even if a planet were quite close to the luminary it would be visible on such an occasion if its magnitude were comparable with that of Mercury. Careful preparation is necessary when it is proposed to make a trial of this kind. The danger to be specially avoided is that of confounding the planet with the ordinary stars, which it will probably resemble. The late distinguished American astronomer, Professor Watson, specially prepared to devote himself to this research during the notable total eclipse in 1878. When the eclipse occurred the light of the sun vanished and the stars burst forth. Among them Professor Watson saw an object which to him seemed to be the long-sought intra-Mercurial planet. We should add that this zealous observer saw another object which he at first took to be the star known as Zeta in the constellation Cancer. When he afterwards found that the recorded place of this object did not agree so well as he expected with the known position of this star, he came to the conclusion that it could not be Zeta but must be some other unknown planet. The relative positions of the two objects which he took to be planets agree, however, sufficiently well, considering the difficulties of the observation, with the relative positions of the stars Theta and Zeta Cancri, and it can now hardly be doubted that Watson merely saw these two stars. He maintained, however, that he had noticed Theta Cancri as well as the two planets, but without recording its position. There is, however, a third star, known as 20 Cancri, near the same place, and this Watson probably mistook for Theta.

It is necessary to record that Vulcan has not been observed, though specially looked for, during the eclipses which have occurred since 1878, and it is accordingly the general belief among astronomers that no planet has yet been detected within the orbit of Mercury.

CHAPTER VII.

MERCURY.

The Ancient Astronomical Discoveries--How Mercury was first found--Not easily seen--Mercury was known from the earliest ages--Skill necessary in the Discovery--The Distinction of Mercury from a Star--Mercury in the East and in the West--The Prediction--How to Observe Mercury--Its Telescopic Appearance--Difficulty of Observing its Appearance--Orbit of Mercury--Velocity of the Planet--Can there be Life on the Planet?--Changes in its Temperature--Transit of Mercury over the Sun--Ga.s.sendi's Observations--Rotation of Mercury--The Weight of Mercury.

Long and glorious is the record of astronomical discovery. The discoveries of modern days have succeeded each other with such rapidity, they have so often dazzled our imaginations with their brilliancy, that we are sometimes apt to think that astronomical discovery is a purely modern product. But no idea could be more fundamentally wrong. While we appreciate to the utmost the achievements of modern times, let us endeavour to do justice to the labours of the astronomers of antiquity.

And when we speak of the astronomers of antiquity, let us understand clearly what is meant. The science is now growing so rapidly that each century witnesses a surprising advance; each generation, each decade, each year, has its own rewards for those diligent astronomers by whom the heavens are so carefully scanned. We must, however, project our glance to a remote epoch in time past, if we would view the memorable discovery of Mercury. Compared with it, the discoveries of Newton are to be regarded as very modern achievements; even the announcement of the Copernican system of the heavens is itself a recent event in comparison with the detection of this planet now to be discussed.

By whom was this great discovery made? Let us see if the question can be answered by the examination of astronomical records. At the close of his memorable life Copernicus was heard to express his sincere regret that he never enjoyed an opportunity of beholding the planet Mercury. He had specially longed to see this body, the movements of which were to such a marked extent ill.u.s.trative of the theory of the celestial motions which it was his immortal glory to have established, but he had never been successful. Mercury is not generally to be seen so easily as are some of the other planets, and it may well have been that the vapours from the immense lagoon at the mouth of the Vistula obscured the horizon at Frauenburg, where Copernicus dwelt, and thus his opportunities of viewing Mercury were probably even rarer than they are at other places.

The existence of Mercury was certainly quite a familiar fact in the time of Copernicus, and therefore we must look to some earlier epoch for its discovery. In the scanty astronomical literature of the Middle Ages we find occasional references to the existence of this object. We can trace observations of Mercury through remote centuries to the commencement of our era. Records from dates still earlier are not wanting, until at length we come on an observation which has descended to us for more than 2,000 years, having been made in the year 265 before the Christian era.

It is not pretended, however, that this observation records the _discovery_ of the planet. Earlier still we find the chief of the astronomers at Nineveh alluding to Mercury in a report which he made to a.s.surbanipal, the King of a.s.syria. It does not appear in the least degree likely that the discovery was even then a recent one. It may have been that the planet was independently discovered in two or more localities, but all records of such discoveries are totally wanting; and we are ignorant alike of the names of the discoverers, of the nations to which they belonged, and of the epochs at which they lived.

Although this discovery is of such vast antiquity, although it was made before correct notions were entertained as to the true system of the universe, and, it is needless to add, long before the invention of the telescope, yet it must not be a.s.sumed that the detection of Mercury was by any means a simple or obvious matter. This will be manifest when we try to conceive the manner in which the discovery must probably have been made.

Some primaeval astronomer, long familiar with the heavens, had learned to recognise the various stars and constellations. Experience had impressed upon him the permanence of these objects; he had seen that Sirius invariably appeared at the same seasons of the year, and he had noticed how it was placed with regard to Orion and the other neighbouring constellations. In the same manner each of the other bright stars was to him a familiar object always to be found in a particular region of the heavens. He saw how the stars rose and set in such a way, that though each star appeared to move, yet the relative positions of the stars were incapable of alteration. No doubt this ancient astronomer was acquainted with Venus; he knew the evening star; he knew the morning star; and he may have concluded that Venus was a body which oscillated from one side of the sun to the other.

We can easily imagine how the discovery of Mercury was made in the clear skies over an Eastern desert. The sun has set, the brief twilight has almost ceased, when lo, near that part of the horizon where the glow of the setting sun still illuminates the sky, a bright star is seen. The primaeval astronomer knows that there is no bright star at this place in the heavens. If the object of his attention be not a star, what, then, can it be? Eager to examine this question, the heavens are watched next night, and there again, higher above the horizon, and more brilliant still, is the object seen the night before. Each successive night the body gains more and more l.u.s.tre, until at length it becomes a conspicuous gem. Perhaps it will rise still higher and higher; perhaps it will increase till it attains the brilliancy of Venus itself. Such were the surmises not improbably made by those who first watched this object; but they were not realised. After a few nights of exceptional splendour the l.u.s.tre of this mysterious...o...b..declines. The planet again draws near the horizon at sunset, until at length it sets so soon after the sun that it has become invisible. Is it lost for ever? Years may elapse before another opportunity of observing the object after sunset may be available; but then again it will be seen to run through the same series of changes, though, perhaps, under very different circ.u.mstances.

The greatest height above the horizon and the greatest brightness both vary considerably.

Long and careful observations must have been made before the primaeval astronomer could a.s.sure himself that the various appearances might all be attributed to a single body. In the Eastern deserts the phenomena of sunrise must have been nearly as familiar as those of sunset, and in the clear skies, at the point where the sunbeams were commencing to dawn above the horizon, a bright star-like point might sometimes be perceived. Each successive day this object rose higher and higher above the horizon before the moment of sunrise, and its l.u.s.tre increased with the distance; then again it would draw in towards the sun, and return for many months to invisibility. Such were the data which were presented to the mind of the primitive astronomer. One body was seen after sunset, another body was seen before sunrise. To us it may seem an obvious inference from the observed facts that the two bodies were identical.

The inference is a correct one, but it is in no sense an obvious one.