Popular Science Monthly/Volume 58/April 1901/The Planet Eros


By Professor SOLON I. BAILEY,


EROS is the name of a small planet discovered in 1898, by Witt, of Berlin. It does not appear to be altogether certain that it really belongs to the group of minor planets, usually known as planetoids or asteroids. With the exception of Eros, all known asteroids move in orbits whose mean distances are greater than that of Mars and less than that of Jupiter. The mean distance from the sun of Mars is 141 million miles, and that of Jupiter is 483 million miles, while the distances of the asteroids vary in round numbers between 200 and 400 million miles. The mean distance of Eros, however, is only 135 million miles, which is less than that of Mars. In spite of this very important difference, Eros has been placed among the great band of asteroids, among whom he numbers 433. To belong to the celestial 400 is perhaps more of misfortune than of honor, for the number of this plebeian band has already waxed so great that they have become a care which threatens in the future to balance the benefits which they bring to astronomy. Nevertheless, the history of this numerous family is sufficiently full of interest, and throws light upon the way in which we should regard them.

In 1772, Bode announced the so-called law which bears his name. The law may be stated as follows: If to a series of 4's, beginning at the second, the numbers 3, 6, 12, 24, etc., be added, the resulting numbers divided by 10 will approximately express the distance of the planets from the sun in terms of the distance of our earth taken as unity. The law gave fairly well the distances of all the planets known at that time, except that it called for a planet between Mars and Jupiter, where nothing was then known to exist. When, a few years later, in 1784, Uranus was discovered and was found to conform closely to the law, the impression was deepened that the missing member of the solar system must somehow be supplied or explained, and an association of astronomers was formed to hunt for it. At that time the discovery of a small body, such as one of the asteroids, was no easy matter, and the honor of finding the first did not fall to one of the associates, but to Piazzi, a Sicilian astronomer, who discovered it while making a star catalogue. It was perhaps fitting that a century which was to be signalized by the discovery of some 450 new but small worlds, where one had been sought, should be properly opened: Ceres, the first asteroid, was found on the first day of the nineteenth century. Bode's law, therefore, appeared to have found confirmation here, for, though there was no single great planet, as elsewhere, nevertheless the small army of fragments seemed to point to some abortive attempt of Nature to form a world in the usual order, or else to an explosion of one already formed. In either case the distance of the 'mean asteroid' might be expected to follow the law, which it was found approximately to do. It seems a pity that the law, having survived so many tests, should go to pieces at last on what was perhaps the final test which remained to be applied. When Neptune was discovered, however, in 1846, it did not conform to the law at all. The following table gives a comparison between the true distances and those which result from Bode's law, the distance of the earth being taken as unity:

Planet. Distance. Bode. Difference. Period.
Mercury 0 .39 0 .4 -0 .01 3 months.
Venus 0 .72 0 .7 +0 .02 7 .4"
Earth 1 .00 1 .0 0 .00 1 .0 years.
Mars 1 .52 1 .6 -0 .08 1 .9"
Mean Asteroid 2 .65 2 .8 -1 .15 ....
Jupiter 5 .20 5 .2 0 .00 11 .9 years.
Saturn 9 .54 10 .0 -0 .46 29 .5"
Uranus 19 .18 19 .6 -0 .42 84 .0"
Neptune 30 .05 38 .8 -8 .75 164 .8"

The discovery of asteroids has been much simplified by the increase of star maps, and especially by the advances in celestial photography. One feature, which is incidental to the duration of the photographic exposure, renders the detection of such objects comparatively easy. When a photographic plate is exposed to the sky in a camera or telescope, if there is no clockwork, so that the instrument remains at rest, the images of the stars are drawn out into lines or trails. Ordinarily, however, the instrument is kept in motion by a driving clock, so that it exactly follows the stars in their apparent daily motion, and the images of the stars result as circular dots on the plate. An asteroid, however, from its nearness has so rapid an apparent motion among the stars that, if an exposure is made of an hour or more, its image is spread out in a line, while the images of stars remain circular. On some of the plates, for example, made with the great Bruce photographic telescope at Arequipa, several hundred thousand stars appear. On one of these plates, which had an exposure of four hours, seven asteroid trails were found. If these asteroids had formed circular images, similar to those of the stars, their detection among the several hundred thousand images on the plate would have been an enormous labor and would have required other photographs of the same region for comparison. To pick out the trails, however, is the work of an hour. The finding of the images on the photographs is only a small part of the work involved. First, one must know whether the object seen is new or old. This implies tables giving the positions of all known asteroids, the computation of which involves a great amount of labor, and, in most cases, the results in themselves seem to be of small value. With the greater telescopes and more sensitive plates of the future, it seems probable, unless some kind Providence prevents it, that the number will become so great that astronomers will grow weary of the enormous labor involved in making ephemerides of them all. Twenty-two of them are, as Professor Young expresses it, 'endowed.' These were discovered by Professor Watson, who, at his death, left a fund to bear the expense of taking care of them. These favored ones will evidently be followed carefully, however unobserved their less aristocratic sisters go sweeping on in their neglected orbits.

It is probable that all the larger asteroids have already been found. Professor Barnard has made many micrometric measurements of the diameters of the largest of these baby worlds, using the great telescopes of the Lick and Yerkes observatories. He has recently published in the 'Monthly Notices' of the Royal Astronomical Society the following results:

Asteroid. Diameter. Albedo.
Ceres 477 miles 0.67
Pallas 304" 0.88
Juno 120" 1.67
Vesta 239" 2.77

The albedo, or light-reflecting power, is referred to that of Mars as unity. The values in the third column are derived from the measured diameters and the known brightness of the asteroids. Vesta, though not the largest by the above measures, is the brightest of them all, and is sometimes visible to the naked eye. Probably none, except the four given above, has a diameter as great as 100 miles, and the vast majority perhaps not more than ten or twenty miles. Eros itself, at its nearest approach, will perhaps present a disc of sufficient size to permit measurements in the most powerful instruments. Its diameter is probably not more than twenty-five miles, though no precise determination has yet been made. On such a world the force of superficial gravity would be about one three-hundredth of that at the surface of the earth, and a person might almost throw a stone with sufficient velocity to make it fly off into space and become an independent planet. To make up a world even one-hundredth as large as the earth would take hundreds of thousands of such worlds.

On the night of August 13, 1898, Herr Witt made a photograph of the region near β Aquarii, with an exposure of two hours. He wished to obtain an observation of a known asteroid which had not been observed for nine years, and which his calculations assigned to that region. When developed and examined on the following day, the plate not only showed the object desired, and also a second known asteroid, but a faint and long trail of some unknown object. From its rapid motion it was at first thought to be a comet, but an examination on the following night with a visual telescope revealed its true nature. As soon as the well-known computer of minor planet orbits, Herr Berberich, had computed its approximate orbit, the astonishing nature of the new planet became apparent. Of all the previously known members of the solar system, with the obvious exception of our moon, Venus and Mars approach nearest to the earth. Venus is distant from us at the most favorable times about twenty-five million miles, and Mars thirty-five million miles. Eros, however, approaches the earth at the most favorable oppositions within less than fourteen million miles, so that he is our nearest celestial neighbor. This leads to a solution, under better conditions perhaps than ever before granted, of that fundamental problem in astronomy, the distance of the sun, or, in other words, the determination of the solar parallax. In order to determine the orbit and position of a planet, certain quantities must be found, based upon at least three observations of the planet's place in the sky. It is, however, highly desirable to have more than three observations of the planet's position and to have them widely separated in time.

The following elements for Eros were computed by Dr. S. C. Chandler, and were based on the observations of 1898, combined with those of the Harvard photographs made in the years 1893, 1894 and 1896:


Mean Anomaly 221° 35' 45. "6
Perihelion Distance of Ascending Node 177 37 56. 0 1898.0
Longitude of Ascending Node 303 31 57. 1
Inclination of Orbit to Ecliptic 10 50 11. 8
Angle whose Sin is the Eccentricity 12 52 9. 8
Mean Daily Motion 2015. "2326
Logarithm of Semi-major Axis 0.1637876
Period of Revolution around Sun 643d .10

Later observations will doubtless slightly modify these results, but they are sufficiently precise for our purpose. These elements were published in December, 1898, and well illustrate the enormous photographic resources which at the present time are in the possession of the Harvard Observatory. Twenty years ago, the present Director, Prof. Edward C. Pickering, began photographing the heavens, and at the present time there are in the Observatory more than 100,000 photographs of the sky made during those years. Some of these are on a large scale, and are of special objects, but many thousands of them are charts on so small a scale that the entire sky has been photographed many times. On nearly all these plates stars are shown to the tenth magnitude, and in many cases stars as faint as the fifteenth or sixteenth magnitude appear. The early elements of Eros showed that the planet made a close approach to the earth in 1894, and a search was promptly instituted on the Harvard photographs. At first the available observations were insufficient to give the elements with the accuracy which was necessary in order to determine the planet's

PSM V58 D653 Path of eros in 1893 and 1894 mapped from photographs.png
Fig. 1. Path of Eros in 1893 and 1894. The Circular Dots represent the Positions which were determined from the Harvard Photographs.

position in 1894. An error of 1″ in the mean daily motion would change the right ascension in 1894 by about half an hour. On this account no image of the planet was found on the photographs first examined. By an examination, however, of plates made in 1896 Mrs. Fleming found several images of Eros, and Mr. Chandler then provided a corrected ephemeris, by means of which the planet was readily found on plates made in 1893 and 1894. Thus several years' history of this remarkable object was at once presented to the astronomical world.

While the mean distance of Eros is 135 million miles, its aphelion distance is 166 millions and its perihelion distance 105 millions. Since this planet is sometimes within and sometimes without the orbit of Mars, it might be expected that at favorable times it would approach nearer to Mars than to the earth. Owing to the large inclination of the planes of the two planets, and the unfavorable position of the line in which the planes intersect, this is not the case, as was pointed out by Mr. Crommelin. Eros does not approach Mars nearer than twenty million miles, so that the Martians, if such exist, have no advantage in this line of research.

At his approach in 1894, the brightness of Eros was computed by Professor Pickering to have been about the seventh magnitude. This places it just beyond the reach of the naked eye, even at the most favorable oppositions. During the recent opposition Eros was thirty million miles distant, and fainter than the ninth magnitude.

E. von Oppolzer has recently announced that Eros undergoes, within a few hours, variations in light amounting to a whole magnitude.

PSM V58 D654 Orbits of eros earth and mars.png
Fig. 2. Orbits of Eros, Earth and Mars. Relative Positions of Eros and Earth.

This variation has been confirmed at the Harvard Observatory, where there are observations, visual and photographic, extending back over eight years, sufficient to establish the period with precision. The variability of Eros is doubtless due to its axial revolution, and may be caused by the unequal light-reflecting power of different parts of its surface.

From the elements and diagram, it may be seen that the distance from perihelion, or the point nearest the sun, to the descending node, or the point where the planet passes through the plane of the earth's orbit, is less than three degrees. This is fortunate, for otherwise the planet's distance would be increased. The longitude of the planet's perihelion is 121°. The earth's longitude—or the sun's longitude, as seen from the earth, plus 180°—is 121° on January 21. In 1894, the planet was in perihelion on January 22, only a few hours later than the earth arrived at the same longitude; so that the opposition at that time was nearly as favorable as can ever occur. Since the period of Eros is 643d.10, it will be easy to compute when the planet will again come to perihelion near the date January 21. The relation between the periods of Eros and the earth is such that a close approach will always be followed in seven years by one not so good, but yet favorable. This is illustrated by the near approach of 1894 and the less favorable opposition of 1901. Seven revolutions of the earth take 2556d.8, and four revolutions of Eros, 2572d.4. Hence every seventh year the position of Eros will be repeated, with respect to the earth, within 156d. So that if Eros arrived at perihelion one day later than the earth reached the same longitude in 1894, it would arrive there about seventeen days later in 1901, thirty-two days later in 1908, etc. It is evident that by following this series no close approach would come again till far into the next century. This series includes one-fourth of the perihelion returns of Eros. Three other series will include the remainder. They may be reckoned from that of 1895, when it occurred eighty-seven days earlier than the earth reached the same longitude, that of 1897, 175 days earlier, and that of 1899, 262 days earlier. Beginning with the difference of eighty-seven days in 1895, the number decreases by 15d.6 every seven years, so that in 1931 Eros will arrive at perihelion about ten days ahead of the earth, and in 1938 about six days later. This pair of oppositions appear to be the best which will occur during the next half century. The series which begins in 1897 with a difference of 175 days would apparently give a close approach after about three quarters of a century, and the remaining series much later still. It seems, therefore, that not till the latter part of the present century can so favorable an opposition recur, as that of 1894, which was lost except for the Harvard photographs. These conclusions may, however, be modified by a study of the perturbations of Eros by the other planets, which have not been considered in the above computations.

During the last few months great attention has been given to Eros at fifty of the leading observatories of the world. Professor Campbell, Director of the Lick Observatory, says that for two or three months fully half the resources of that institution have been devoted to this object. The positions of 700 fundamental stars have been determined by the meridian circle, and photographs made, which will be measured at the Observatory of Columbia University under the direction of Dr. Rees. At the Harvard Observatory several hundred photographs have been taken, and very extended photometric observations made. Owing to the exceptional conditions which prevail at the Arequipa branch of the observatory and the power of the Bruce photographic telescope, it is probable that Eros can be photographed there after it has been lost sight of at other observatories. At least, the first determination of its position at the recent opposition was made from a photograph obtained there by Dr. Stewart. The interest shown by these two institutions is equaled by that of many other observatories in Europe and the United States. The chief object of these labors is the determination of the solar parallax, which is the angle subtended at the sun by the earth's radius, and which is a measure of his distance. The methods which are in use for the solution of this problem may be divided into three groups, geometrical, gravitational and physical. The present investigation belongs to the first of these. The natural and direct method for measuring the sun's distance would be to select two stations on the earth, whose distance apart must be known, and from them measure the angle which that distance subtends at the sun itself. If the distance is the earth's radius the measured angle is the solar parallax. In fact, however, this apparently easy and direct method has now no value whatever, since the angle concerned is too small to give the best results, and also the sun is a very difficult object on which to make measurements of precision. Some other, nearer and more suitable object must be sought, and, in quest of the most exact results possible, astronomers have observed Venus, when in transit across the sun's face, Mars near opposition and various asteroids. Of these different geometrical methods, observations of the asteroids appear to have furnished the best results, so that the discovery of Eros comes at a most fortunate time to give astronomers an opportunity of testing this method under the most favorable conditions. It must be remembered, however, that the recent opposition of Eros was not an especially favorable one, and it is not certain that better results will be obtained at this time than have been secured in recent years by Dr. Gill at the Cape of Good Hope, in cooperation with Dr. Elkins, of Yale, and others. That work depended upon heliometric observations of the asteroids Iris, Victoria and Sappho, whose least distances from the earth are 0.84, 0.82 and 0.84 astronomical units. At the recent opposition the distance of Eros was little more than a third as great, and this in itself gives Eros an enormous advantage. It has been feared, however, that the faintness and rapid motion of Eros would prevent observations of the highest precision, which might be sufficient to balance the advantage which its nearness gave. Probably the difficulties on these accounts have not proved so great as was at first feared. Even if the present determination yields no better results than have been obtained before, it will make a very valuable check on previous determinations, and bring out the best methods to be pursued at some later and more favorable opposition. In this connection it may be of interest to recall that Halley, who first pointed out the possibility of determining the solar parallax by observations of the transits of Venus, well knew when he developed the methods that he himself could not live to see the experiment tried, since he was then sixty-three years of age, and the next transit of Venus did not come for forty-two years. Perhaps few of the observers who are so enthusiastically at work on Eros at this opposition will be alive to make observations at a really close approach of that interesting body.

At the Paris meeting of the International Astrophotographic Congress, in August, 1900, a committee was appointed to suggest the most favorable course to be pursued. The committee later advised that work be done by the micrometer, the heliometer and by photographs. The observations in each case give the distance of Eros in seconds of arc from adjacent stars. The simplest case is where simultaneous observations are made by observers at widely separated stations. Let A and B (Fig. 3) be two stations on the earth. The observer at A will see Eros projected on the celestial sphere at E1, and the observer at B, at

PSM V58 D657 Parallax of eros.png
Fig. 3. Parallax of Eros.

E2. It is only necessary for each observer to measure the distance in seconds of arc between Eros and some adjacent stars, as 1, 2, 3 and 4. The positions of the stars must be known with the greatest precision, so that the observations give the value of the arc E1E2, which equals the angle AEB. We have then the necessary material for computing the distance of Eros from the earth in miles. Given this and the orbit of Eros, the distances of the earth and all the other planets from the sun in miles follow from the known laws of gravitation. The distance AB may lie in a north and south direction, or in an east and west direction, or more probably in a combination of the two. In the first case there must be two observers, widely separated, as, for example, at Arequipa, Peru, latitude south 16°, and Helsingfors, Finland, north 50°. In the second case there may be two stations, as, one in Europe and the other in the United States, or the whole work may be done at one station by allowing the earth's diurnal motion to carry the observer to a new position. Suppose, for example, that one observation is made when the planet is rising in the east, and another twelve hours later, when it is about to set in the west. In the meantime, the observer will have been carried to a position 8,000 miles removed from that which he occupied in the morning. Each of the three methods has certain objections and difficulties. Simultaneous observations are difficult or impossible to obtain. Between the different observations both earth and Eros are sweeping along in their orbits, and this introduces complications which must be allowed for with great care. Also the size of the earth is not perfectly known, nor the distance apart of any two stations upon its surface, though the error introduced from this cause is very small.

For the determination of the position of Eros on each day during opposition, as recommended by the Paris committee, the precise positions of very many stars must be known. A few of these have already been determined, but most of them must be measured at the present time. For this purpose the positions of several hundred stars will be determined and the highest precision at different observatories with the meridian circle, and, from these as standards, many hundreds more, by photographs. For the positions of Eros itself with relation to these stars, no doubt the micrometer, the heliometer and the photograph will be used, and a comparison of the results by these three instruments will be of the greatest interest.

Observations of Eros, made during the recent opposition, or in the future, will doubtless give the most exact determination of the solar parallax possible by the geometrical method, applied to any known member of the solar system. Indeed, Eros, at the most favorable times, is perhaps as good an object as can be desired. If it came still nearer to the earth, its motion would doubtless be more rapid, so that little would be gained. According to Professor Newcomb, Eros comes 'about as near to us as observations can advantageously be made.' Nevertheless, it is doubtful whether any geometrical determination of the solar parallax will ever be accepted as final. When the astronomical world was preparing to observe the transit of Venus in 1874, Leverrier refused to take any part in it, declaring that the determination by gravitational means would make all geometrical methods of no further value. This may be true for the future, but it will not lessen, for the present, at least, the high value of the determinations now going on.

The solar parallax is about 8".80, correct within approximately 0".01. That is, the distance of the sun is about 92,897,000 miles, correct within 100,000 or 150,000 miles. It is difficult to appreciate an angle of 0".01, within which limit the determination must come to be of value. A foot rule forms an angle of 0".01, when placed at a distance of 20,626,481 feet, or over 3,900 miles. If the present work shall reduce the margin of doubt, astronomers will be well paid for their efforts.

Aside from the determination of the solar parallax, Professor Pickering has pointed out that Eros furnishes an opportunity for the investigation of several interesting photometric problems. These are: the determination of the planet's diameter; a test of the law that the light varies inversely as the square of the distance; a test of the existence of an absorbing medium within the solar system, and a test of the law connecting the phase angle of a planet with the variation in brightness.

Thus Eros, the tiny asteroid, whose total area is little larger than the State of Rhode Island, is for the moment of more importance in the eyes of the astronomical world than the greatest planet which moves about the sun.