Too Many Planets
For over forty years only the orginal four asteroids were known: Ceres, Pallas, Juno, and Vesta. Searches for more were made, but did not go faint enough. The fifth asteroid, Astraea, was finally found on December 8, 1845, by the amateur Hencke of Dresden after fifteen years of searching. 1 On July 1, 1847 Hencke found number 6, Hebe. About the same time a steady and increasing stream of asteroid discoveries started, due largely to new star charts constructed under the organization of the Berlin Academy and going as faint as ninth magnitude. By 1852 the number of known asteroids had reached 20; by 1870 it was 110. These were increasingly smaller and fainter objects, their discovery brightnesses decreased to ninth magnitude, then lower and lower, to tenth, eleventh, and twelfth. The Berlin maps were no longer useful for new asteroids; the chief discoverers constructed and published new maps with fainter stars. Finally photography came into use to simplify the work and became the major source of new discoveries. 2
Increasing numbers
The two plots below show the rapid increase in the number of known asteroids starting in the late 1840s. The first plot shows how many new asteroids were discovered each year. It looks like World War II reduced asteroid discoveries in the 1940s. The second plot shows the overall total known (the integral of the first plot). The second plot is also available in a log version which shows a 41 year plateau after the first four. The data for these plots was obtained from the Minor Planet Center, under Discovery Circumstances: Numbered Minor Planets (an excellent source of asteroid names).
Increasing work
Kepler's Laws of orbital motion state that objects move in elliptical orbits, and the line connecting the sun and the object sweeps out an area per unit time at a constant rate. Once the elements of such an orbit are known and the period of revolution about the sun, the object's position may be computed for any time, past or future. However, Kepler's Laws apply only to a two body system, the sun and object alone, with no other influences. Real solar system objects are only approximated by these laws. For asteroids the case is complicated by the proximity of the most massive planet in the solar system, Jupiter. Determining a good orbit is tedious even for the simple elliptical orbit case. A long quote from Pannekoek throws some interesting light on this:
Drawing an ellipseFrom the very first, the computation of orbits meant a lot of work. The computation of an elliptical orbit from three observations -- roughly some days after the discovery, but more precisely from observations a month later -- could be performed rapidly enough by Gauss's method. But in order to predict the positions in later years with sufficient certainty, a large number of observations, extending over the entire period of visibility, was first needed, and then the computations of the most probable elements from all these observations had to follow. Moreover, the work was never finished, because every succeeding year brought a new opposition, with new observations. If however this work were neglected, the predicted result would be more and more in error, so that the planets could not be found again among all the little stars, and if seen by chance later could not be identified; general confusion would result. Now and again it was said that we should disregard all the small fry and drop them; but where is the limit? It was the same here as with the entire technical development of the nineteenth century; people were dragged along in endless labour which allowed no slackening. In the early years, about the middle of the century, the enthusiasm and perseverance of young scientists and the charm of astronomical computing sufficed to satisfy the needs. When the numbers increased alarmingly, when, moreover, the ever smaller bodies lost their salient individuality although names were assigned to them, this supply of work began to fall short. Now the work was concentrated more and more in computing offices, where official duty and routine, organization and mechanized computing methods, combined to cope with the ever increasing flood, though with a decimal less in accuracy. The Berlin Computing Office afterwards transferred to Dahlem, and christened 'Copernicus Institute', among other duties took over the major part of this crowd of celestial Lilliputians. 3Another early view from Burritt's 1850 book:The calculation of the latitude and longitude of the asteroids is a labor of extreme difficulty, requiring more than 400 equations to reduce their anomalous perturbations to the true place. This arises from the want of auxiliary tables, and from the fact that the elements of the star-form planets are very imperfectly determined. Whether any of the asteroids has a rotation on its axis, remains to be ascertained. 4Perturbations by the major planets made things even harder. Another quote from Pannekoek gives the picture for the late 1800s:If only the regular orbit computation had been the only task! All these little bodies, however, were subjected to the attraction not only of the sun but also of the major planets. So their orbits were continually changed through perturbations. These perturbations are even larger than those of the older planets, first because the minor planets come nearer than any other to Jupiter, the great perturber of the solar system, and also because their orbits often have great eccentricities and inclinations. Yet the perturbations must be computed. If we should neglect them, the computed orbits within a few years would be far too incorrect; the errors of the computed positions would be so large as to render the entire computation useless. Nor could we think of developing the perturbations, once and for all, in a general algebraic way, as Laplace had done for the seven major planets. Whereas in the latter case, where the high order terms rapidly decrease, the theory of one planet may already demand extertion over dozens of years, the number of terms for a minor planet would be endless. Hansen in later years, in 1865, indicated an approximate method, and applied it to some of the first discovered asteroids. However, all the astronomers who first encountered the problem -- Gauss, Encke, Olbers, Bessel -- agreed that there was only one practical way to take account of the perturbations. This was the same method used since Clairaut for the comets: to follow the planet in its course continually, from place to place, from week to week or month to month, computing for every moment the perturbing forces, motions and displacements, and to see where they next brought it. It is a never-ending work, each year requiring as much time as did the preceding one. Since, however, there was no other way, this method of 'special perturbations' has been built up, mainly by Encke, into a handy, fixed and simple routine scheme that has been used by all good computers [human computers that is] of the first dozens of planetoids, to give a solid basis to the derivation of orbits. Finally, however, when the number grew into hundreds, even the greatest ardour and patience could not master the work. The computing offices had now to devise gross methods for rapid and approximate computation of peturbation terms for a number of similar orbits. In the judicious balancing of the opposing demands of feasible work and attainable accuracy, no less ingenuity was needed here than formerly for the mathematical problems themselves. Yet astronomers always have to face the question of whether it pays to derive orbits for all those small and smaller lumps of rock of some tens of kilometres straying thorugh space. 5Asteroid discoverers could become attached to their discoveries:Watson, one of the chief American discoverers of asteroids in the last century [1800s], realized that the 22 bodies discovered by him might be lost [In fact, of of the 22, Aethra (132), was lost within a few weeks after discovery in 1873 and not recovered until found by chance in 1922] on account of the changes in the orbits and at his death left a sum of money to the National Academy of Sciences, Washington, D. C., in order to have tables of the perturbations calculated so that it would be a simple matter to determine and apply the corrections to the ever-changing orbits. This work was put into the hands of Prof. A. O. Leuschner of the University of California and is now practically completed. 6
Back: A Planet is Found Table of Contents Next: The Quest for the Solar Parallax
References
1 Henry Norris Russell, Raymond Smith Dugan, and John Quincy Stewart, Astronomy (Boston: Ginn and Company, 1945), p. 348.
2 A. Pannekoek, A History of Astronomy (New York: Interscience Publishers, 1961), p. 353.
3 Ibid., p. 355.
4 Elijah H. Burritt, The Geography of the Heavens (New York: Huntington and Savage, 1850), p. 237.
5 Pannekoek, p. 355,356.
6 Edward A. Fath, The Elements of Astronomy (New York: McGraw-Hill, 1928), p. 169.
Illustrations:
"Drawing an Ellipse" scanned from Fourteen Weeks in Descriptive Astronomy, J. Dorman Steele, A. S. Barnes & Co., New York, 1871
