The Great Size of Jupiter

The Story of the Heavens by Robert S. Ball is part of the HackerNoon Books Series. You can jump to any chapter in this book here. JUPITER

In our exploration of the beautiful series of bodies which form the solar system, we have proceeded step by step outwards from the sun. In the pursuit of this method we have now come to the splendid planet Jupiter, which wends its majestic way in a path immediately outside those orbits of the minor planets which we have just been considering. Great, indeed, is the contrast between these tiny globes and the stupendous globe of Jupiter. Had we adopted a somewhat different method of treatment—had we, for instance, discussed the various bodies of our planetary system in the order of their magnitude—then the minor planets would have been the last to be considered, while the leader of the host would be Jupiter. To this position Jupiter is entitled without an approach to rivalry. The next greatest on the list, the beautiful and interesting Saturn, comes a long distance behind. Another great descent in the scale of magnitude has to be made before we reach Uranus and Neptune, while still another step downwards must be made before we reach that lesser group of planets which includes our earth. So conspicuously does Jupiter tower over the rest, that even if Saturn were to be augmented by all the other globes of our system rolled into one, the united mass would still not equal the great globe of Jupiter.

Fig. 56.—The Relative Dimensions of Jupiter and the Earth.

The adjoining picture (Fig. 56) shows the relative dimensions of Jupiter and the earth, and it conveys to the eye a more vivid impression of the enormous bulk of Jupiter than we can readily obtain by merely considering the numerical statements by which his bulk is to be accurately estimated. As, however, it will be necessary to place the numerical facts before our readers, we do so at the outset of this chapter.

Jupiter revolves in an elliptic orbit around the sun in the focus, at a mean distance of 483,000,000 miles. The path of Jupiter is thus about 5·2 times as great in diameter as the path pursued by the earth. The shape of Jupiter's orbit departs very appreciably from a circle, the greatest distance from the sun being 5·45, while the least distance is about 4·95, the earth's distance from the sun being taken as unity.[Pg 247] In the most favourable circumstances for seeing Jupiter at opposition, it must still be about four times as far from the earth as the earth is from the sun. This great globe will also illustrate the law that the more distant a planet is, the slower is the velocity with which its orbital motion is accomplished. While the earth passes over eighteen miles each second, Jupiter only accomplishes eight miles. Thus for a twofold reason the time occupied by an exterior planet in completing a revolution is greater than the period of the earth. Not only has the outer planet to complete a longer course than the earth, but the speed is less; it thus happens that Jupiter requires 4,332·6 days, or about fifty days less than twelve years, to make a circuit of the heavens.

The mean diameter of the great planet is about 87,000 miles. We say the mean diameter, because there is a conspicuous difference in the case of Jupiter between his equatorial and his polar diameters. We have already seen that there is a similar difference in the case of the earth, where we find the polar diameter to be shorter than the equatorial; but the inequality of these two dimensions is very much larger in Jupiter than in the earth. The equatorial diameter of Jupiter is 89,600 miles, while the polar is not more than 84,400 miles. The ellipticity of Jupiter indicated by these figures is sufficiently marked to be obvious without any refined measures. Around the shortest diameter the planet spins with what must be considered an enormous velocity when we reflect on the size of the globe. Each rotation is completed in about 9 hrs. 55 mins.

We may naturally contrast the period of rotation of Jupiter with the much slower rotation of our earth in twenty-four hours. The difference becomes much more striking if we consider the relative speeds at which an object on the equator of the earth and on that of Jupiter actually moves. As the diameter of Jupiter is nearly eleven times that of the earth, it will follow that the speed of the equator on Jupiter must be about twenty-seven times as great as that on the earth. It is no doubt to this high velocity of rotation that we must ascribe the extraordinary ellipticity of Jupiter; the rapid[Pg 248] rotation causes a great centrifugal force, and this bulges out the pliant materials of which he seems to be formed.

Jupiter is not, so far as we can see, a solid body. This is an important circumstance; and therefore it will be necessary to discuss the matter at some little length, as we here perceive a wide contrast between this great planet and the other planets which have previously occupied our attention. From the measurements already given it is easy to calculate the bulk or the volume of Jupiter. It will be found that this planet is about 1,300 times as large as the earth; in other words, it would take 1,300 globes, each as large as our earth, all rolled into one, to form a single globe as large as Jupiter.

If the materials of which Jupiter is composed were of a nature analogous to the materials of the earth, we might expect that the weight of the planet would exceed the weight of the earth in something like the proportion of their volumes. This is the matter now proposed to be brought to trial. Here we may at once be met with the query, as to how we are to find the weight of Jupiter. It is not even an easy matter to weigh the earth on which we stand. How, then, can we weigh a mighty planet vastly larger than the earth, and distant from us by some hundreds of millions of miles? Truly, this is a bold problem. Yet the intellectual resources of man have proved sufficient to achieve this feat of celestial engineering. They are not, it is true, actually able to make the ponderous weighing scales in which the great planet is to be cast, but they are able to divert to this purpose certain natural phenomena which yield the information that is required.

Such investigations are based on the principle of universal gravitation. The mass of Jupiter attracts other masses in the solar system. The efficiency of that attraction is more particularly shown on the bodies which are near the planet. In virtue of this attraction certain movements are performed by those bodies. We can observe their character with our telescopes, we can ascertain their amount, and from our measurements we can calculate the mass of the body by which the movements have been produced. This is the sole method which we possess for the investigation of the masses[Pg 249] of the planets; and though it may be difficult in its application—not only from the observations which are required, but also from the intricacy and the profundity of the calculations to which those observations must be submitted—yet, in the case of Jupiter at least, there is no uncertainty about the result.

The task is peculiarly simplified in the case of the greatest planet of our system by the beautiful system of moons with which he is attended. These little moons revolve under the guidance of Jupiter, and their movements are not otherwise interfered with so as to prevent their use for our present purpose. It is from the observations of the satellites of Jupiter that we are enabled to measure his attractive power, and thence to calculate the mass of the mighty planet.

To those not specially conversant with the principles of mechanics, it may seem difficult to realise the degree of accuracy of which such a method is capable. Yet there can be no doubt that his moons inform us of the mass of Jupiter, and do not leave a margin of inaccuracy so great as one hundredth part of the total amount. If other confirmation be needed, then it is forthcoming in abundance. A minor planet occasionally draws near the orbit of Jupiter and experiences his attraction; the planet is forced to swerve from its path, and the amount of the deviation can be measured. From that measurement the mass of Jupiter can be computed by a calculation, of which it would be impossible to give an account in this place. The mass of Jupiter, as determined by this method, agrees with the mass obtained in a totally different manner from the satellites.

Nor have we yet exhausted the resources of astronomy in its bearing on this question. We can discard the planetary system, and invite the assistance of a comet which, flashing through the orbits of the planets, occasionally experiences large and sometimes enormous disturbances. For the present it suffices to remark, that on one or two occasions it has happened that venturous comets have been near enough to Jupiter to be much disturbed by his attraction, and then to proclaim in their altered movements the magnitude of the[Pg 250] mass which has affected them. The satellites of Jupiter, the minor planets, and the comets, all tell the weight of the giant orb; and, as they all concur in the result (at least within extremely narrow limits), we cannot hesitate to conclude that the mass of the greatest planet of our system has been determined with accuracy.

The results of these measures must now be stated. They show, of course, that Jupiter is vastly inferior to the sun—that, in fact, it would take about 1,047 Jupiters, all rolled into one, to form a globe equal in weight to the sun. They also show us that it would take 316 globes as heavy as our Earth to counterbalance the weight of Jupiter.

No doubt this proves Jupiter to be a body of magnificent proportions; but the remarkable circumstance is not that Jupiter should be 316 times as heavy as the earth, but that he is not a great deal more. Have we not stated that Jupiter is 1,300 times as large as the earth? How then comes it that he is only 316 times as heavy? This points at once to some fundamental contrast between the constitution of Jupiter and of the earth. How are we to account for this difference? We can conceive of two explanations. In the first place, it might be supposed that Jupiter is constituted of materials partly or wholly unknown on the earth. There is, however, an alternative supposition at once more philosophical and more consistent with the evidence. It is true that we know little or nothing of what the elementary substances on Jupiter may be, but one of the great discoveries of modern astronomy has taught us something of the elementary bodies present in other bodies of the universe, and has demonstrated that to a large extent they are identical with the elementary bodies on the earth. If Jupiter be composed of bodies resembling those on the earth, there is one way, and only one, in which we can account for the disparity between his size and his mass. Perhaps the best way of stating the argument will be found in a glance at the remote history of the earth itself, for it seems not impossible that the present condition of Jupiter was itself foreshadowed by the condition of our earth countless ages ago.

In a previous chapter we had occasion to point out how the earth seemed to be cooling from an earlier and highly heated condition. The further we look back, the hotter our globe seems to have been; and if we project our glance back to an epoch sufficiently remote, we see that it must once have been so hot that life on its surface would have been impossible. Back still earlier, we find the heat to have been such that water could not rest on the earth; and hence it seems likely that at some incredibly remote epoch all the oceans now reposing in the deeps on the surface, and perhaps a considerable portion of its now solid crust, must have been in a state of vapour. Such a transformation of the globe would not alter its mass, for the materials weigh the same whatever be their condition as to temperature, but it would alter the size of our globe to a very considerable extent. If these oceans were transformed into vapour, then the atmosphere, charged with mighty clouds, would have a bulk some hundreds of times greater than that which it has at present. Viewed from a distant planet, the cloud-laden atmosphere would indicate the visible size of our globe, and its average density would accordingly appear to be very much less than it is at present.

From these considerations it will be manifest that the discrepancy between the size and the weight of Jupiter, as contrasted with our earth, would be completely removed if we supposed that Jupiter was at the present day a highly heated body in the condition of our earth countless ages ago. Every circumstance of the case tends to justify this argument. We have assigned the smallness of the moon as a reason why the moon has cooled sufficiently to make its volcanoes silent and still. In the same way the smallness of the earth, as compared with Jupiter, accounts for the fact that Jupiter still retains a large part of its original heat, while the smaller earth has dissipated most of its store. This argument is illustrated and strengthened when we introduce other planets into the comparison. As a general rule we find that the smaller bodies, like the earth and Mars, have a high density, indicative of a low temperature,[Pg 252] while the giant planets, like Jupiter and Saturn, have a low density, suggesting that they still retain a large part of their original heat. We say "original heat" for the want, perhaps, of a more correct expression; it will, however, indicate that we do not in the least refer to the solar heat, of which, indeed, the great outer planets receive much less than those nearer the sun. Where the original heat may have come from is a matter still confined to the province of speculation.

A complete justification of these views with regard to Jupiter is to be found when we make a minute telescopic scrutiny of its surface; and it fortunately happens that the size of the planet is so great that, even at a distance of more millions of miles than there are days in the year, we can still trace on its surface some significant features.

Plate XI. gives a series of four different views of Jupiter. They have been taken from a series of admirable drawings of the great planet made by Mr. Griffiths in 1897. The first picture shows the appearance of the globe at 10h. 20m. Greenwich time on February 17th, 1897, through a powerful refracting telescope. We at once notice in this drawing that the outline of Jupiter is distinctly elliptical. The surface of the planet usually shows the remarkable series of belts here represented. They are nearly parallel to each other and to the planet's equator.

When Jupiter is observed for some hours, the appearance of the belts undergoes certain changes. These are partly due to the regular rotation of the planet on its axis, which, in a period of less than five hours, will completely carry away the hemisphere we first saw, and replace it by the hemisphere originally at the other side. But besides the changes thus arising, the belts and other features on the planet are also very variable. Sometimes new stripes or marks appear, and old ones disappear; in fact, a thorough examination of Jupiter will demonstrate the remarkable fact that there are no permanent features whatever to be discerned. We are here immediately struck by the contrast between Jupiter and Mars; on the smaller planet the main[Pg 253] topographical outlines are almost invariable, and it has been feasible to construct maps of the surface with tolerably accurate detail; a map of Jupiter is, however, an impossibility—the drawing of the planet which we make to-night will be different from the drawing of the same hemisphere made a few weeks hence.

It should, however, be noticed that objects occasionally appear on the planet which seem of a rather more persistent character than the belts. We may especially mention the object known as the great oblong Red Spot, which has been a very remarkable feature upon the southern hemisphere of Jupiter since 1878. This object, which has attracted a great deal of attention from observers, is about 30,000 miles long by about 7,000 in breadth. Professor Barnard remarks that the older the spots on Jupiter are, the more ruddy do they tend to become.

The conclusion is irresistibly forced upon us that when we view the surface of Jupiter we are not looking at any solid body. The want of permanence in the features of the planet would be intelligible if what we see be merely an atmosphere laden with clouds of impenetrable density. The belts especially support this view; we are at once reminded of the equatorial zones on our own earth, and it is not at all unlikely that an observer sufficiently remote from the earth to obtain a just view of its appearance would detect upon its surface more or less perfect cloud-belts suggestive of those on Jupiter. A view of our earth would be, as it were, intermediate between a view of Jupiter and of Mars. In the latter case the appearance of the permanent features of the planet is only to a trifling extent obscured by clouds floating over the surface. Our earth would always be partly, and often perhaps very largely, covered with cloud, while Jupiter seems at all times completely enveloped.

From another class of observations we are also taught the important truth that Jupiter is not, superficially at least, a solid body. The period of rotation of the planet around its axis is derived from the observation of certain marks, which present sufficient definiteness and sufficient[Pg 254] permanence to be suitable for the purpose. Suppose one of these objects to lie at the centre of the planet's disc; its position is carefully measured, and the time is noted. As the hours pass on, the mark moves to the edge of the disc, then round the other side of the planet, and back again to the visible disc. When it has returned to the position originally occupied the time is again taken, and the interval which has elapsed is called the period of rotation of the spot.

If Jupiter were a solid, and if these features were engraved upon its surface, then it is perfectly clear that the time of rotation as found by any one spot must coincide precisely with the time yielded by any other spot; but this is not observed to be the case. In fact, it would be nearer the truth to say that each spot gives a special period of its own. Nor are the differences very minute. It has been found that the time in which the red spot (the latitude of which is about 25° south) is carried round is five minutes longer than that required by some peculiar white marks near the equator. The red spot has now been watched for about twenty years, and during most of that time has had a tendency to rotate more and more slowly, as may be seen from the following values of its rotation period:—

Since 1891 this tendency seems to have ceased, while the spot has been gradually fading away. Generally speaking, we may say that the equatorial regions rotate in about 9h. 50m. 20s., and the temperate zones in about 9h. 55m. 40s. Remarkable exceptions are occasionally met with. Some small black spots in north latitude 22°, which broke out in 1880 and again in 1891, rotated in 9h. 48m. to 9h. 49-1⁄2m. It may, therefore, be regarded as certain that the globe of Jupiter, so far as we can see it, is not a solid body. It consists, on the exterior at all events, of clouds and vaporous masses, which seem to be agitated by storms of the utmost intensity, if we are to judge from the ceaseless changes of the planet's surface.

PLATE XI.
Feb. 2nd.  Feb. 4th.
Feb. 12th.  Feb. 28th.
THE PLANET JUPITER.
1897.

Fig. 57.—The Occultation of Jupiter (1).

Fig. 58.—The Occultation of Jupiter (2).

Fig. 59.—The Occultation of Jupiter (3).

Fig. 60.—The Occultation of Jupiter (4).

Various photographs of Jupiter have been obtained; those which have been taken at the Lick Observatory being specially interesting and instructive. Pictures of the planet obtained with the camera in remarkable circumstances are represented in Figs. 57–60, which were taken by Professor Wm. H. Pickering at Arequipa, Peru, on the 12th of August, 1892.[21] The small object with the belts is the planet Jupiter. The[Pg 256] large advancing disc (of which only a small part can be shown) is the moon. The phenomenon illustrated is called the "occultation" of the planet. The planet is half-way behind the moon in Fig. 59, while in Fig. 60 half of the planet is still hidden by the dark limb of the moon.

It is well known that the tempests by which the atmosphere surrounding the earth is convulsed are to be ultimately attributed to the heat of the sun. It is the rays from the great luminary which, striking on the vast continents, warm the air in contact therewith. This heated air becomes lighter, and rises, while air to supply its place must flow in along the surface. The currents so produced form a breeze or a wind; while, under exceptional circumstances, we have the phenomena of cyclones and hurricanes, all originated by the sun's heat. Need we add that the rains, which so often accompany the storms, have also arisen from the solar beams, which have distilled from the wide expanse of ocean the moisture by which the earth is refreshed?

The storms on Jupiter seem to be vastly greater than those on the earth. Yet the intensity of the sun's heat on Jupiter is only a mere fraction—less, indeed, than the twenty-fifth part—of that received by the earth. It is incredible that the motive power of the appalling tempests on the great planet can be entirely, or even largely, due to the feeble influence of solar heat. We are, therefore, led to seek for some other source of such disturbances. What that source is to be will appear obvious when we admit that Jupiter still retains a large proportion of primitive internal heat. Just as the sun itself is distracted by violent tempests as an accompaniment of its intense internal fervour, so, in a lesser degree, do we observe the same phenomena in Jupiter. It may also be noticed that the spots on the sun usually lie in more or less regular zones, parallel to its equator, the arrangement being in this respect not dissimilar to that of the belts on Jupiter.

It being admitted that the mighty planet still retains some of its internal heat, the question remains as to how much. It is, of course, obvious that the heat of the planet is [Pg 257]inconsiderable when compared with the heat of the sun. The brilliance of Jupiter, which makes it an object of such splendour in our midnight sky, is derived from the same great source which illuminates the earth, the moon, or the other planets. Jupiter, in fact, shines by reflected sunlight, and not in virtue of any intrinsic light in his globe. A beautiful proof of this truth is familiar to every user of a telescope. The little satellites of the planet sometimes intrude between him and the sun, and cast a shadow on Jupiter. The shadow is black, or, at all events, it seems black, relatively to the brilliant surrounding surface of the planet. It must, therefore, be obvious that Jupiter is indebted to the sun for its brilliancy. The satellites supply another interesting proof of this truth. One of these bodies sometimes enters the shadow of Jupiter and lo! the little body vanishes. It does so because Jupiter has cut off the supply of sunlight which previously rendered the satellite visible. But the planet is not himself able to offer the satellite any light in compensation for the sunlight which he has intercepted.[22]

Enough, however, has been demonstrated to enable us to pronounce on the question as to whether the globe of Jupiter can be inhabited by living creatures resembling those on this earth. Obviously this cannot be so. The internal heat and the fearful tempests seem to preclude the possibility of organic life on the great planet, even were there not other arguments tending to the same conclusion. It may, however, be contended, with perhaps some plausibility, that Jupiter has in the distant future the prospect of a glorious career as the residence of organic life. The time will assuredly come when the internal heat must decline, when the clouds will gradually condense into oceans. On the surface dry land may then appear, and Jupiter be rendered habitable.

From this sketch of the planet itself we now turn to the interesting and beautiful system of five satellites by which Jupiter is attended. We have, indeed, already found it necessary to allude more than once to these little bodies, but not[Pg 258] to such an extent as to interfere with the more formal treatment which they are now to receive.

The discovery of the four chief satellites may be regarded as an important epoch in the history of astronomy. They are objects situated in a remarkable manner on the border-line which divides the objects visible to the unaided eye from those which require telescopic aid. It has been frequently asserted that these objects have been seen with the unaided eye; but without entering into any controversy on the matter, it is sufficient to recite the well-known fact that, although Jupiter had been a familiar object for countless centuries, yet the sharpest eyes under the clearest skies never discovered the satellites until Galileo turned the newly invented telescope upon them. This tube was no doubt a very feeble instrument, but very little power suffices to show objects so dose to the limit of visibility.

Fig. 61.—Jupiter and his Four Satellites as seen in a Telescope of Low Power.

The view of the planet and its elaborate system of satellites as shown in a telescope of moderate power, is represented in Fig. 61. We here see the great globe, and nearly in a line parsing through its centre lie four small objects, three on one side and one on the other. These little bodies resemble stars, but they can be distinguished therefrom by their ceaseless movements around the planet, which they never fail to accompany during his entire circuit of the heavens. There is no more pleasing spectacle for the student than to follow with his telescope the movements of this beautiful system.

Fig. 62.—Disappearances of Jupiter's Satellites.

In Fig. 62 we have represented some of the various phenomena which the satellites present. The long black shadow is that produced by the interposition of Jupiter in the path of the sun's rays. In consequence of the great distance of the sun this shadow will extend, in the form of a very elongated cone, to a distance far beyond the orbit of the outer satellite. The second satellite is immersed in this shadow, and consequently eclipsed. The eclipse of a satellite must not be attributed to the intervention of the body of Jupiter between the satellite and the earth. Such an occurrence is called an occultation, and the third satellite is shown in this condition. The second and the third satellites are thus alike invisible, but the cause of the invisibility is quite different in the two cases. The eclipse is much the more striking phenomenon of the two, because the satellite, at the moment it plunges into the darkness, may be still at some apparent distance from the edge of the planet, and is thus seen up to the moment of the eclipse. In an occultation the satellite in passing behind the planet is, at the time of disappearance,[Pg 260] close to the planet's bright edge, and the extinction of the light from the small body cannot be observed with the same impressiveness as the occurrence of an eclipse.

A satellite also assumes another remarkable situation when in the course of transit over the face of the planet. The satellite itself is not always very easy to see in such circumstances, but the beautiful shadow which it casts forms a sharp black spot on the brilliant orb: the satellite will, indeed, frequently cast a visible shadow when it passes between the planet and the sun, even though it be not actually at the moment in front of the planet, as it is seen from the earth.

The periods in which the four principal moons of Jupiter revolve around their primary are respectively, 1 day 18 hrs. 27 min. 34 secs. for the first; 3 days 13 hrs. 13 min. 42 secs., for the second; 7 days 3 hrs. 42 min. 33 secs, for the third; and 16 days 16 hrs. 32 min. 11 secs. for the fourth. We thus observe that the periods of Jupiter's satellites are decidedly briefer than that of our moon. Even the satellite most distant from the great planet requires for each revolution less than two-thirds of an ordinary lunar month. The innermost of these bodies, revolving as it does in less than two days, presents a striking series of ceaseless and rapid changes, and it becomes eclipsed during every revolution. The distance from the centre of Jupiter to the orbit of the innermost of these four attendants is a quarter of a million miles, while the radius of the outermost is a little more than a million miles. The second of the satellites proceeding outwards from the planet is almost the same size as our moon; the other three bodies are larger; the third being the greatest of all (about 3,560 miles in diameter). Owing to the minuteness of the satellites as seen from the earth, it is extremely difficult to perceive any markings on their surfaces, but the few observations made seem to indicate that the satellites (like our moon) always turn the same face towards their primary. Professor Barnard has, with the great Lick refractor, seen a white equatorial belt on the first satellite, while its poles were very dark. Mr. Douglass, observing with Mr. Lowell's great refractor, has also reported certain streaky markings on the third satellite.

A very interesting astronomical discovery was that made by Professor E.E. Barnard in 1892. He detected with the 36-inch Lick refractor an extremely minute fifth satellite to Jupiter at a distance of 112,400 miles, and revolving in a period of 11 hrs. 57 min. 22·6 secs. It can only be seen with the most powerful telescopes.

The eclipses of Jupiter's satellites had been observed for many years, and the times of their occurrence had been recorded. At length it was perceived that a certain order reigned among the eclipses of these bodies, as among all other astronomical phenomena. When once the laws according to which the eclipses recurred had been perceived, the usual consequence followed. It became possible to foretell the time at which the eclipses would occur in future. Predictions were accordingly made, and it was found that they were approximately verified. Further improvements in the calculations were then perfected, and it was sought to predict the times with still greater accuracy. But when it came to naming the actual minute at which the eclipse should occur, expectations were not always realised. Sometimes the eclipse was five or ten minutes too soon. Sometimes it was five or ten minutes too late. Discrepancies of this kind always demand attention. It is, indeed, by the right use of them that discoveries are often made, and one of the most interesting examples is that now before us.

The irregularity in the occurrence of the eclipses was at length perceived to observe certain rules. It was noticed that when the earth was near to Jupiter the eclipse generally occurred before the predicted time; while when the earth happened to be at the side of its orbit away from Jupiter, the eclipse occurred after the predicted time. Once this was proved, the great discovery was quickly made by Roemer, a Danish astronomer, in 1675. When the satellite enters the shadow, its light gradually decreases until it disappears. It is the last ray of light from the eclipsed satellite that gives the time of the eclipse; but that ray of light has to travel from the satellite to the earth, and enter our telescope, before we can note the occurrence. It used to be thought that[Pg 262] light travelled instantaneously, so that the moment the eclipse occurred was assumed to be the moment when the eclipse was seen in the telescope. This was now perceived to be incorrect. It was found that light took time to travel. When the earth was comparatively near Jupiter the light had only a short journey, the intelligence of the eclipse arrived quickly, and the eclipse was seen sooner than the calculations indicated. When the earth occupied a position far from Jupiter, the light had a longer journey, and took more than the average time, so that the eclipse was later than the prediction. This simple explanation removed the difficulty attending the predictions of the eclipses of the satellites. But the discovery had a significance far more momentous. We learned from it that light had a measurable velocity, which, according to recent researches, amounts to 186,300 miles per second.

One of the most celebrated attempts to ascertain the distance of the sun is derived from a combination of experiments on the velocity of light with astronomical measurements. This is a method of considerable refinement and interest, and although it does not so fulfil all the necessary conditions as to make it perfectly satisfactory, yet it is impossible to avoid some reference to it here. Notwithstanding that the velocity of light is so stupendous, it has been found possible to measure that velocity by actual trial. This is one of the most delicate experimental researches that have ever been undertaken. If it be difficult to measure the speed of a rifle bullet, what shall we say of the speed of a ray of light, which is nearly a million times as great? How shall we devise an apparatus subtle enough to determine the velocity which would girdle the earth at the equator no less than seven times in a single second of time? Ordinary contrivances for measurement are here futile; we have to devise an instrument of a wholly different character.

In the attempt to discover the speed of a moving body we first mark out a certain distance, and then measure the time which the body requires to traverse that distance. We determine the velocity of a railway train by the time it takes to pass from one mile-post to the next. We learn the speed[Pg 263] of a rifle bullet by an ingenious contrivance really founded on the same principle. The greater the velocity, the more desirable is it that the distance traversed during the experiment shall be as large as possible. In dealing with the measurement of the velocity of light, we therefore choose for our measured distance the greatest length that may be convenient. It is, however, necessary that the two ends of the line shall be visible from each other. A hill a mile or two away will form a suitable site for the distant station, and the distance of the selected point on the hill from the observer must be carefully measured.

The problem is now easily stated. A ray of light is to be sent from the observer to the distant station, and the time occupied by that ray in the journey is to be measured. We may suppose that the observer, by a suitable contrivance, has arranged a lantern from which a thin ray of light issues. Let us assume that this travels all the way to the distant station, and there falls upon the surface of a reflecting mirror. Instantly it will be diverted by reflection into a new direction depending upon the inclination of the mirror. By suitable adjustment the latter can be so placed that the light shall fall perpendicularly upon it, in which case the ray will of course return along the direction in which it came. Let the mirror be fixed in this position throughout the course of the experiments. It follows that a ray of light starting from the lantern will be returned to the lantern after it has made the journey to the distant station and back again. Imagine, then, a little shutter placed in front of the lantern. We open the shutter, the ray streams forth to the remote reflector, and back again through the opening. But now, after having allowed the ray to pass through the shutter, suppose we try and close it before the ray has had time to get back again. What fingers could be nimble enough to do this? Even if the distant station were ten miles away, so that the light had a journey of ten miles in going to the mirror and ten miles in coming back, yet the whole course would be accomplished in about the nine-thousandth part of a second—a[Pg 264] period so short that even were it a thousand times as long it would hardly enable manual dexterity to close the aperture. Yet a shutter can be constructed which shall be sufficiently delicate for the purpose.

Fig. 63.—Mode of Measuring the Velocity of Light.

The principle of this beautiful method will be sufficiently obvious from the diagram on this page (Fig. 63), which has been taken from Newcomb's "Popular Astronomy." The figure exhibits the lantern and the observer, and a large wheel with projecting teeth. Each tooth as it passes round eclipses the beam of light emerging from the lantern, and also the eye, which is of course directed to the mirror at the distant station. In the position of the wheel here shown the ray from the lantern will pass to the mirror and back so as to be visible to the eye; but if the wheel be rotating, it may so happen that the beam after leaving the lantern will not have time to return before the next tooth of the wheel comes in front of the eye and screens it. If the wheel be urged still faster, the next tooth may have passed the eye, so that the ray again becomes visible. The speed at which the wheel is rotating can be measured. We can thus determine the time taken by one of the teeth to pass in front of the eye; we have accordingly a measure of the time occupied by the ray of light in the double journey, and hence we have a measurement of the velocity of light.

It thus appears that we can tell the velocity of light either[Pg 265] by the observations of Jupiter's satellites or by experimental enquiry. If we take the latter method, then we are entitled to deduce remarkable astronomical consequences. We can, in fact, employ this method for solving that great problem so often referred to—the distance from the earth to the sun—though it cannot compete in accuracy with some of the other methods.

The dimensions of the solar system are so considerable that a sunbeam requires an appreciable interval of time to span the abyss which separates the earth from the sun. Eight minutes is approximately the duration of the journey, so that at any moment we see the sun as it appeared eight minutes earlier to an observer in its immediate neighbourhood. In fact, if the sun were to be suddenly blotted out it would still be seen shining brilliantly for eight minutes after it had really disappeared. We can determine this period from the eclipses of Jupiter's satellites.

So long as the satellite is shining it radiates a stream of light across the vast space between Jupiter and the earth. When the eclipse has commenced, the little orb is no longer luminous, but there is, nevertheless, a long stream of light on its way, and until all this has poured into our telescopes we still see the satellite shining as before. If we could calculate the moment when the eclipse really took place, and if we could observe the moment at which the eclipse is seen, the difference between the two gives the time which the light occupies on the journey. This can be found with some accuracy; and, as we already know the velocity of light, we can ascertain the distance of Jupiter from the earth; and hence deduce the scale of the solar system. It must, however, be remarked that at both extremities of the process there are characteristic sources of uncertainty. The occurrence of the eclipse is not an instantaneous phenomenon. The satellite is large enough to require an appreciable time in crossing the boundary which defines the shadow, so that the observation of an eclipse cannot be sufficiently precise to form the basis of an important and accurate measurement.[23] Still[Pg 266] greater difficulties accompany the attempt to define the true moment of the occurrence of the eclipse as it would be seen by an observer in the vicinity of the satellite. For this we should require a far more perfect theory of the movements of Jupiter's satellites than is at present attainable. This method of finding the sun's distance holds out no prospect of a result accurate to the one-thousandth part of its amount, and we may discard it, inasmuch as the other methods available seem to admit of much higher accuracy.

The four chief satellites of Jupiter have special interest for the mathematician, who finds in them a most striking instance of the universality of the law of gravitation. These bodies are, of course, mainly controlled in their movements by the attraction of the great planet; but they also attract each other, and certain curious consequences are the result.

The mean motion of the first satellite in each day about the centre of Jupiter is 203°·4890. That of the second is 101°·3748, and that of the third is 50°·3177. These quantities are so related that the following law will be found to be observed:

The mean motion of the first satellite added to twice the mean motion of the third is exactly equal to three times the mean motion of the second.

There is another law of an analogous character, which is thus expressed (the mean longitude being the angle between a fixed line and the radius to the mean place of the satellite): If to the mean longitude of the first satellite we add twice the mean longitude of the third, and subtract three times the mean longitude of the second, the difference is always 180°.

It was from observation that these principles were first discovered. Laplace, however, showed that if the satellites revolved nearly in this way, then their mutual perturbations, in accordance with the law of gravitation, would preserve them in this relative position for ever.

We shall conclude with the remark, that the discovery of Jupiter's satellites afforded the great confirmation of the[Pg 267] Copernican theory. Copernicus had asked the world to believe that our sun was a great globe, and that the earth and all the other planets were small bodies revolving round the great one. This doctrine, so repugnant to the theories previously held, and to the immediate evidence of our senses, could only be established by a refined course of reasoning. The discovery of Jupiter's satellites was very opportune. Here we had an exquisite ocular demonstration of a system, though, of course, on a much smaller scale, precisely identical with that which Copernicus had proposed. The astronomer who had watched Jupiter's moons circling around their primary, who had noticed their eclipses and all the interesting phenomena attendant on them, saw before his eyes, in a manner wholly unmistakable, that the great planet controlled these small bodies, and forced them to revolve around him, and thus exhibited a miniature of the great solar system itself. "As in the case of the spots on the sun, Galileo's announcement of this discovery was received with incredulity by those philosophers of the day who believed that everything in nature was described in the writings of Aristotle. One eminent astronomer, Clavius, said that to see the satellites one must have a telescope which would produce them; but he changed his mind as soon as he saw them himself. Another philosopher, more prudent, refused to put his eye to the telescope lest he should see them and be convinced. He died shortly afterwards. 'I hope,' said the caustic Galileo, 'that he saw them while on his way to heaven'"