Part 16 (1/2)

The value for Juno is, however, very uncertain, and by far the greater number of the minor planets are very much smaller than the figures here given would indicate. It is possible by a certain calculation to form an estimate of the aggregate ma.s.s of all the minor planets, inasmuch as observations disclose to us the extent of their united disturbing influences on the motion of Mars. In this manner Le Verrier concluded that the collected ma.s.s of the small planets must be about equal to one-fourth of the ma.s.s of the earth. Harzer, repeating the enquiry in an improved manner, deduced a collected ma.s.s one-sixth of that of the earth. There can be no doubt that the total ma.s.s of all the minor planets at present known is not more than a very small fraction of the amount to which these calculations point. We therefore conclude that there must be a vast number of minor planets which have not yet been recognised in the observatory. These unknown planets must be extremely minute.

The orbits of this group of bodies differ in remarkable characteristics from those of the larger planets. Some of them are inclined at angles of 30 to the plane of the earth's...o...b..t, the inclinations of the great planets being not more than a few degrees. Some of the orbits of the minor planets are also greatly elongated ellipses, while, of course, the orbits of the large planets do not much depart from the circular form.

The periods of revolution of these small objects round the sun range from three years to nearly nine years.

A great increase in the number of minor planets has rewarded the zeal of those astronomers who have devoted their labours to this subject. Their success has entailed a vast amount of labour on the computers of the ”Berlin Year-Book.” That useful work occupies in this respect a position which has not been taken by our own ”Nautical Almanac,” nor by the similar publications of other countries. A skilful band of computers make it their duty to provide for the ”Berlin Year-Book” detailed information as to the movements of the minor planets. As soon as a few complete observations have been obtained, the little object pa.s.ses into the secure grasp of the mathematician; he is able to predict its career for years to come, and the announcements with respect to all the known minor planets are to be found in the annual volumes of the work referred to.

The growth of discovery has been so rapid that the necessary labour for the preparation of such predictions is now enormous. It must be confessed that many of the minor planets are very faint and otherwise devoid of interest, so that astronomers are sometimes tempted to concur with the suggestion that a portion of the astronomical labour now devoted to the computation of the paths of these bodies might be more profitably applied. For this it would be only necessary to cast adrift all the less interesting members of the host, and allow them to pursue their paths unwatched by the telescope, or by the still more ceaseless tables of the mathematical computer.

The sun, which controls the mighty orbs of our system, does not disdain to guide, with equal care, the tiny globes which form the minor planets.

At certain times some of them approach near enough to the earth to merit the attention of those astronomers who are specially interested in determining the dimensions of the solar system. The observations are of such a nature that they can be made with considerable precision; they can also be multiplied to any extent that may be desired. Some of these little bodies have consequently a great astronomical future, inasmuch as they seem destined to indicate the true distance from the earth to the sun more accurately than Venus or than Mars. The smallest of these planets will not answer for this purpose; they can only be seen in powerful telescopes, and they do not admit of being measured with the necessary accuracy. It is also obvious that the planets to be chosen for observation must come as near the earth as possible. In favourable circ.u.mstances, some of the minor planets will approach the earth to a distance which is about three-quarters of the distance of the sun. These various conditions limit the number of bodies available for this purpose to about a dozen, of which one or two will usually be suitably placed each year.

For the determination of the sun's distance this method by the minor planets offers unquestionable advantages. The orb itself is a minute star-like point in the telescope, and the measures are made from it to the stars which are seen near it. A few words will, perhaps, be necessary at this place as to the nature of the observations referred to. When we speak of the measures from the planet to the star, we do not refer to what would be perhaps the most ordinary acceptation of the expression. We do _not_ mean the actual measurement of the number of miles in a straight line between the planet and the star. This element, even if attainable, could only be the result of a protracted series of observations of a nature which will be explained later on when we come to speak of the distances of the stars. The measures now referred to are of a more simple character; they are merely to ascertain the apparent distance of the objects expressed in angular measure. This angular measurement is of a wholly different character from the linear measurement, and the two methods may, indeed, lead to results that would at first seem paradoxical.

We may take, as an ill.u.s.tration, the case of the group of stars forming the Pleiades, and those which form the Great Bear. The latter is a large group, the former is a small one. But why do we think the words large and small rightly applied here? Each pair of stars of the Great Bear makes a large angle with the eye. Each pair of stars in the Pleiades makes a small angle, and it is these angles which are the direct object of astronomical measurement. We speak of the distance of two stars, meaning thereby the angle which is bounded by the two lines from the eye to the two stars. This is what our instruments are able to measure, and it is to be observed that no reference to linear magnitude is implied.

Indeed, if we are to mention actual dimensions, it is quite possible, for anything we can tell, that the Pleiades may form a much larger group than the Great Bear, and that the apparent superiority of the latter is merely due to its being closer to us. The most accurate of these angular measures are obtained when two stars, or two star-like points, are so close together as to enable them to be included in one field of view of the telescope. There are special forms of apparatus which enable the astronomer in this case to give to his observations a precision unattainable in the measurement of objects less definitely marked, or at a greater apparent distance. The determination of the distance of the small star-like planet from a star is therefore characterised by great accuracy.

But there is another and, perhaps, a weightier argument in favour of the determination of the scale of the solar system by this process. The real strength of the minor planet method rests hardly so much on the individual accuracy of the observations, as on the fact that from the nature of the method a considerable number of repet.i.tions can be concentrated on the result. It will, of course, be understood that when we speak of the accuracy of an observation, it is not to be presumed that it can ever be entirely free from error. Errors always exist, and though they may be small, yet if the quant.i.ty to be measured is minute, an error of intrinsic insignificance may amount to an appreciable fraction of the whole. The one way by which their effect can be subdued is by taking the mean of a large number of observations. This is the real source of the value of the minor planet method. We have not to wait for the occurrence of rare events like the transit of Venus. Each year will witness the approach of some one or more minor planets sufficiently close to the earth to render the method applicable. The varied circ.u.mstances attending each planet, and the great variety of the observations which may be made upon it, will further conduce to eliminate error.

As the planet pursues its course through the sky, which is everywhere studded over with countless myriads of minute stars, it is evident that this body, itself so like a star, will always have some stars in its immediate neighbourhood. As the movements of the planet are well known, we can foretell where it will be on each night that it is to be observed. It is thus possible to prearrange with observers in widely-different parts of the earth as to the observations to be made on each particular night.

An attempt has been made, on the suggestion of Dr. Gill, to carry out this method on a scale commensurate with its importance. The planets Iris, Victoria, and Sappho happened, in the years 1888 and 1889, to approach so close to the earth that arrangements were made for simultaneous measurements in both the northern and the southern hemispheres. A scheme was completely drawn up many months before the observations were to commence. Each observer who partic.i.p.ated in the work was thus advised beforehand of the stars which were to be employed each night. Viewed from any part of the earth, from the Cape of Good Hope or from Great Britain, the positions of the stars remain absolutely unchanged. Their distance is so stupendous that a change of place on the earth displaces them to no appreciable extent. But the case is different with a minor planet. It is hardly one-millionth part of the distance of the stars, and the displacement of the planet when viewed from the Cape and when viewed from Europe is a measurable quant.i.ty.

The magnitude we are seeking is to be elicited by comparison between the measurements made in the northern hemisphere with those made in the southern. The observations in the two localities must be as nearly simultaneous as possible, due allowance being made for the motion of the planet in whatever interval may have elapsed. Although every precaution is taken to eliminate the errors of each observation, yet the fact remains that we compare the measures made by observers in the northern hemisphere with those made by different observers, using of course different instruments, thousands of miles away. But in this respect we are at no greater disadvantage than in observing the transit of Venus.

It is, however, possible to obviate even this objection, and thus to give the minor planet method a supremacy over its rival which cannot be disputed. The difficulty would be overcome if we could arrange that an astronomer, after making a set of observations on a fine night in the northern hemisphere, should be instantly transferred, instruments and all, to the southern station, and there repeat the observations. An equivalent transformation can be effected without any miraculous agency, and in it we have undoubtedly the most perfect mode of measuring the sun's distance with which we are acquainted. This method has already been applied with success by Dr. Gill in the case of Juno, and there are other members of the host of minor planets still more favourably circ.u.mstanced.

Consider, for instance, a minor planet, which sometimes approaches to within 70,000,000 miles of the earth. When the opposition is drawing near, a skilled observer is to be placed at some suitable station near the equator. The instrument he is to use should be that marvellous piece of mechanical and optical skill known as the heliometer.[20] It can be used to measure the angular distance between objects too far apart for the filar micrometer. The measurements are to be made in the evening as soon as the planet has risen high enough to enable it to be seen distinctly. The observer and the observatory are then to be transferred to the other side of the earth. How is this to be done? Say, rather, how we could prevent it from being done. Is not the earth rotating on its axis, so that in the course of a few hours the observatory on the equator is carried bodily round for thousands of miles? As the morning approaches the observations are to be repeated. The planet is found to have changed its place very considerably with regard to the stars. This is partly due to its own motion, but it is also largely due to the parallactic displacement arising from the rotation of the earth, which may amount to so much as twenty seconds. The measures on a single night with the heliometer should not have a mean error greater than one-fifth of a second, and we might reasonably expect that observations could be secured on about twenty-five nights during the opposition. Four such groups might be expected to give the sun's distance without any uncertainty greater than the thousandth part of the total amount. The chief difficulty of the process arises from the movement of the planet during the interval which divides the evening from the morning observations. This drawback can be avoided by diligent and repeated measurements of the place of the planet with respect to the stars among which it pa.s.ses.

In the monumental piece of work which issued in 1897 from the Cape Observatory, under the direction of Dr. Gill, the final results from the observations of Iris, Victoria, and Sappho have been obtained. From this it appears that the angle which the earth's equatorial radius subtends at the centre of the sun when at its mean distance has the value 8”802. If we employ the best value of the earth's equatorial radius we obtain 92,870,000 miles as the mean distance of the centre of the sun from the centre of the earth. This is probably the most accurate determination of the scale of the solar system which has yet been made.

CHAPTER XII.

JUPITER.

The Great Size of Jupiter--Comparison of his Diameter with that of the Earth--Dimensions of the Planet and his...o...b..t--His Rotation--Comparison of his Weight and Bulk with that of the Earth--Relative Lightness of Jupiter--How Explained--Jupiter still probably in a Heated Condition--The Belts on Jupiter--Spots on his Surface--Time of Rotation of different Spots various--Storms on Jupiter--Jupiter not Incandescent--The Satellites--Their Discovery--Telescopic Appearance--Their Orbits--The Eclipses and Occultations--A Satellite in Transit--The Velocity of Light Discovered--How is this Velocity to be Measured Experimentally?--Determination of the Sun's Distance by the Eclipses of Jupiter's Satellites--Jupiter's Satellites demonstrating the Copernican System.

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 ent.i.tled 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 Ura.n.u.s 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 ma.s.s would still not equal the great globe of Jupiter.

[Ill.u.s.tration: 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 52 times as great in diameter as the path pursued by the earth. The shape of Jupiter's...o...b..t departs very appreciably from a circle, the greatest distance from the sun being 545, while the least distance is about 495, the earth's distance from the sun being taken as unity. In the most favourable circ.u.mstances 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 ill.u.s.trate the law that the more distant a planet is, the slower is the velocity with which its...o...b..tal motion is accomplished. While the earth pa.s.ses 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 4,3326 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 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 circ.u.mstance; 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.