Robert S. Ball

The Lesser Members of our System—Bode's Law—The Vacant Region in the Planetary System—The Research—The Discovery of Piazzi—Was the small Body a Planet?—The Planet becomes Invisible—Gauss undertakes the Search by Mathematics—The Planet Recovered—Further Discoveries—Number of Minor Planets now known—The Region to be Searched—The Construction of the Chart for the Search for Small Planets—How a Minor Planet is Discovered—Physical Nature of the Minor Planets—Small Gravitation on the Minor Planets—The Berlin Computations—How the Minor Planets tell us the Distance of the Sun—Accuracy of the Observations—How they may be Multiplied—Victoria and Sappho—The most Perfect Method.

In our chapters on the Sun and Moon, on the Earth and Venus, and on Mercury and Mars, we have been discussing the features and the movements of globes of vast dimensions. The least of all these bodies is the moon, but even that globe is 2,000 miles from one side to the other. In approaching the subject of the minor planets we must be prepared to find objects of dimensions quite inconsiderable in comparison with the great spheres of our system. No doubt these minor planets are all of them some few miles, and some of them a great many miles, in diameter. Were they close to the earth they would be conspicuous, and even splendid, objects; but as they are so distant they do not, even in our greatest telescopes, become very remarkable, while to the unaided eye they are almost all invisible.

In the diagram (p. 234) of the orbits of the various planets, it is shown that a wide space exists between the orbit of Mars and that of Jupiter. It was often surmised that this ample region must be tenanted by some other planet. The presumption became much stronger when a remarkable law was discovered which exhibited, with considerable accuracy, the relative distances of the great planets of our system. Take the series of numbers, 0, 3, 6, 12, 24, 48, 96, whereof each number (except the second) is double of the number which precedes it. If we now add four to each, we have the series 4, 7, 10, 16, 28, 52, 100. With the exception of the fifth of these numbers (28), they are all sensibly proportional to the distances of the various planets from the sun. In fact, the distances are as follows:—Mercury, 3·9; Venus, 7·2; Earth, 10; Mars, 15·2; Jupiter, 52·9; Saturn, 95·4. Although we have no physical reason to offer why this law—generally known as Bode's—should be true, yet the fact that it is so nearly true in the case of all the known planets tempts us to ask whether there may not also be a planet revolving around the sun at the distance represented by 28.

So strongly was this felt at the end of the eighteenth century that some energetic astronomers decided to make a united effort to search for the unknown planet. It seemed certain that the planet could not be a large one, as otherwise it must have been found long ago. If it should exist, then means were required for discriminating between the planet and the hosts of stars strewn along its path.

The search for the small planet was soon rewarded by a success which has rendered the evening of the first day in the nineteenth century memorable in astronomy. It was in the pure skies of Palermo that the observatory was situated where the memorable discovery of the first known minor planet was made by Piazzi. This laborious and accomplished astronomer had organised an ingenious system of exploring the heavens which was eminently calculated to discriminate a planet among the starry host. On a certain night he would select a series of stars to the number of fifty, more or less, according to circumstances. With his meridian circle he determined the places of the chosen objects. The following night, or, at all events, as soon as convenient, he re-observed the whole fifty stars with the same instrument and in the same manner, and the whole operation was afterwards repeated on two, or perhaps more, nights. When the observations were compared together he was in possession of some four or more places of each one of the stars on different nights, and the whole series was complete. He was persevering enough to carry on these observations for very many groups, and at length he was rewarded by a success which amply compensated him for all his toil.

It was on the 1st of January, 1801, that Piazzi commenced for the one hundred and fifty-ninth time to observe a new series. Fifty stars this night were viewed in his telescope, and their places were carefully recorded. Of these objects the first twelve were undoubtedly stellar, and so to all appearance was the thirteenth, a star of the eighth magnitude in the constellation of Taurus. There was nothing to distinguish the telescopic appearance of this object from all the others which preceded or followed it. The following night Piazzi, according to his custom, re-observed the whole fifty stars, and he did the same again on the 3rd of January, and once again on the 4th. He then, as usual, brought together the four places he had found for each of the several bodies. When this was done it was at once seen that the thirteenth object on the list was quite a different body from the remainder and from all the other stars which he had ever observed before. The four places of this mysterious object were all different; in other words, it was in movement, and was therefore a planet.

A few days' observation sufficed to show how this little body, afterwards called Ceres, revolved around the sun, and how it circulated in that vacant path intermediate between the path of Mars and the path of Jupiter. Great, indeed, was the interest aroused by this discovery and the influence which it has exercised on the progress of astronomy. The majestic planets of our system had now to admit a much more humble object to a share of the benefits dispensed by the sun.

After Piazzi had obtained a few further observations, the season for observing this part of the heavens passed away, and the new planet of course ceased to be visible. In a few months, no doubt, the same part of the sky would again be above the horizon after dark, and the stars would of course be seen as before. The planet, however, was moving, and would continue to move, and by the time the next season had arrived it would have passed off into some distant region, and would be again confounded with the stars which it so closely resembled. How, then, was the planet to be pursued through its period of invisibility and identified when it again came within reach of observation?

This difficulty attracted the attention of astronomers, and they sought for some method by which the place of the planet could be recovered so as to prevent Piazzi's discovery from falling into oblivion. A young German mathematician, whose name was Gauss, opened his distinguished career by a successful attempt to solve this problem. A planet, as we have shown, describes an ellipse around the sun, and the sun lies at a focus of that curve. It can be demonstrated that when three positions of a planet are known, then the ellipse in which the planet moves is completely determined. Piazzi had on each occasion measured the place which it then occupied. This information was available to Gauss, and the problem which he had to solve may be thus stated. Knowing the place of the planet on three nights, it is required, without any further observations, to tell what the place of the planet will be on a special occasion some months in the future. Mathematical calculations, based on the laws of Kepler, will enable this problem to be solved, and Gauss succeeded in solving it. Gauss demonstrated that though the telescope of the astronomer was unable to detect the wanderer during its season of invisibility, yet the pen of the mathematician could follow it with unfailing certainty. When, therefore, the progress of the seasons permitted the observations to be renewed, the search was recommenced. The telescope was directed to the point which Gauss's calculations indicated, and there was the little Ceres. Ever since its re-discovery, the planet has been so completely bound in the toils of mathematical reasoning that its place every night of the year can be indicated with a fidelity approaching to that attainable in observing the moon or the great planets of our system.

The discovery of one minor planet was quickly followed by similar successes, so that within seven years Pallas, Juno, and Vesta were added to the solar system. The orbits of all these bodies lie in the region between the orbit of Mars and of Jupiter, and for many years it seems to have been thought that our planetary system was now complete. Forty years later systematic research was again commenced. Planet after planet was added to the list; gradually the discoveries became a stream of increasing volume, until in 1897 the total number reached about 430. Their distribution in the solar system is somewhat as represented in Fig. 55. By the improvement of astronomical telescopes, and by the devotion with which certain astronomers have applied themselves to this interesting research, a special method of observing has been created for the distinct purpose of searching out these little objects.

It is known that the paths in which all the great planets move through the heavens coincide very nearly with the path which the sun appears to follow among the stars, and which is known as the ecliptic. It is natural to assume that the small planets also move in the same great highway, which leads them through all the signs of the zodiac in succession. Some of the small planets, no doubt, deviate rather widely from the track of the sun, but the great majority are approximately near it. This consideration at once simplifies the search for new planets. A certain zone extending around the heavens is to be examined, but there is in general little advantage in pushing the research into other parts of the sky.

The next step is to construct a map containing all the stars in this region. This is a task of very great labour; the stars visible in the large telescopes are so numerous that many tens of thousands, perhaps we should say hundreds of thousands, are included in the region so narrowly limited. The fact is that many of the minor planets now known are objects of extreme minuteness; they can only be seen with very powerful telescopes, and for their detection it is necessary to use charts on which even the faintest stars have been depicted. Many astronomers have concurred in the labour of producing these charts; among them may be mentioned Palisa, of Vienna, who by means of his charts has found eighty-three minor planets, and the late Professor Peters, of Clinton, New York, who in a similar way found forty-nine of these bodies.

The astronomer about to seek for a new planet directs his telescope towards that part of the sun's path which is on the meridian at midnight; there, if anywhere, lies the chance of success, because that is the region in which such a body is nearer to the earth than at any other part of its course. He steadfastly compares his chart with the heavens, and usually finds the stars in the heavens and the stars in the chart to correspond; but sometimes it will happen that a point in the heavens is missing from the chart. His attention is at once arrested; he follows the object with care, and if it moves it is a planet. Still he cannot be sure that he has really made a discovery; he has found a planet, no doubt, but it may be one of the large number already known. To clear up this point he must undertake a further, and sometimes a very laborious, enquiry; he must search the Berlin Year-Book and other ephemerides of such planets and see whether it is possible for one of them to have been in the position on the night in question. If he can ascertain that no previously discovered body could have been there, he is then entitled to announce to his brother astronomers the discovery of a new member of the solar system. It seems certain that all the more important of the minor planets have been long since discovered. The recent additions to the list are generally extremely minute objects, beyond the powers of small telescopes.

Since 1891 the method of searching for minor planets which we have just described has been almost abandoned in favour of a process greatly superior. It has been found feasible to employ photography for making charts of the heavens. A photographic plate is exposed in the telescope to a certain region of the sky sufficiently long to enable very faint telescopic stars to imprint their images. Care has to be taken that the clock which moves the camera shall keep pace most accurately with the rotation of the earth, so that fixed stars appear on the plate as sharp points. If, on developing the plate, a star is found to have left a trail, it is evident that this star must during the time of exposure (generally some hours) have had an independent motion of its own; in other words, it must be a planet. For greater security a second picture is generally taken of the same region after a short interval. If the place occupied by the trail on the first plate is now vacant, while on the second plate a new trail appears in a line with the first one, there remains no possible doubt that we have genuine indications of a planet, and that we have not been led astray by some impurity on the plate or by a few minute stars which happened to lie very closely together. Wolf, of Heidelberg, and following in his footsteps Charlois, of Nice, have in this manner discovered a great number of new minor planets, while they have also recovered a good many of those which had been lost sight of owing to an insufficiency of observations.

On the 13th of August, 1898, Herr G. Witt, of the observatory of Urania in Berlin, discovered a new asteroid by the photographic method. This object was at first regarded merely as forming an addition of no special importance to the 432 asteroids whose discovery had preceded it. It received, as usual, a provisional designation in accordance with a simple alphabetical device. This temporary label affixed to Witt's asteroid was "D Q." But the formal naming of the asteroid has now superseded this label. Herr Witt has given to his asteroid the name of "Eros." This has been duly accepted by astronomers, and thus for all time the planet is to be known.

The feature which makes the discovery of Eros one of the most remarkable incidents in recent astronomy is that on those rare occasions when this asteroid comes nearest to the earth it is closer to the earth than the planet Mars can ever be. Closer than the planet Venus can ever be. Closer than any other known asteroid can ever be. Thus we assign to Eros the exceptional position of being our nearest planetary neighbour in the whole host of heaven. Under certain circumstances it will have a distance from the earth not exceeding one-seventh of the mean distance of the sun.

Of the physical composition of the asteroids and of the character of their surfaces we are entirely ignorant. It may be, for anything we can tell, that these planets are globes like our earth in miniature, diversified by continents and by oceans. If there be life on such bodies, which are often only a few miles in diameter, that life must be something totally different from anything with which we are familiar. Setting aside every other difficulty arising from the possible absence of water and from the great improbability of finding there an atmosphere of a density and a composition suitable for respiration, gravitation itself would prohibit organic beings adapted for this earth from residing on a minor planet.

Let us attempt to illustrate this point, and suppose that we take the case of a minor planet eight miles in diameter, or, in round numbers, one-thousandth part of the diameter of the earth. If we further suppose that the materials of the planet are of the same nature as the substances in the earth, it is easy to prove that the gravity on the surface of the planet will be only one-thousandth part of the gravity of the earth. It follows that the weight of an object on the earth would be reduced to the thousandth part if that object were transferred to the planet. This would not be disclosed by an ordinary weighing scales, where the weights are to be placed in one pan and the body to be weighed in the other. Tested in this way, a body would, of course, weigh precisely the same anywhere; for if the gravitation of the body is altered, so is also in equal proportion the gravitation of the counterpoising weights. But, weighed with a spring balance, the change would be at once evident, and the effort with which a weight could be raised would be reduced to one-thousandth part. A load of one thousand pounds could be lifted from the surface of the planet by the same effort which would lift one pound on the earth; the effects which this would produce are very remarkable.

In our description of the moon it was mentioned (p. 103) that we can calculate the velocity with which it would be necessary to discharge a projectile so that it would never again fall back on the globe from which it was expelled. We applied this reasoning to explain why the moon has apparently altogether lost any atmosphere it might have once possessed.

If we assume for the sake of illustration that the densities of all planets are identical, then the law which expresses the critical velocity for each planet can be readily stated. It is, in fact, simply proportional to the diameter of the globe in question. Thus, for a minor planet whose diameter was one-thousandth part of that of the earth, or about eight miles, the critical velocity would be the thousandth part of six miles a second—that is, about thirty feet per second. This is a low velocity compared with ordinary standards. A child easily tosses a ball up fifteen or sixteen feet high, yet to carry it up this height it must be projected with a velocity of thirty feet per second. A child, standing upon a planet eight miles in diameter, throws his ball vertically upwards; up and up the ball will soar to an amazing elevation. If the original velocity were less than thirty feet per second, the ball would at length cease to move, would begin to turn, and fall with a gradually accelerating pace, until at length it regained the surface with a speed equal to that with which it had been projected. If the original velocity had been as much as, or more than, thirty feet per second, then the ball would soar up and up never to return. In a future chapter it will be necessary to refer again to this subject.

A few of the minor planets appear in powerful telescopes as discs with appreciable dimensions, and they have even been measured with the micrometer. In this way Professor Barnard, late of the Lick Observatory, determined the following values for the diameters of the four first discovered minor planets:—

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 mass 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 mass of the small planets must be about equal to one-fourth of the mass of the earth. Harzer, repeating the enquiry in an improved manner, deduced a collected mass one-sixth of that of the earth. There can be no doubt that the total mass 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 orbit, 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 passes 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 circumstances, 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 illustration, 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 repetitions 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 quantity 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 circumstances 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 participated 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 quantity.

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 circumstanced.

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 passes.

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.