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ASTRONOMICAL SOCIETY of the PACIFIC 233 V. COMET OTERMA 1943 A: a MINOR PLANET?

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ASTRONOMICAL SOCIETY of the PACIFIC 233 V. COMET OTERMA 1943 A: a MINOR PLANET? ASTRONOMICAL SOCIETY OF THE PACIFIC 233 V. COMET OTERMA 1943 a: A MINOR PLANET? George H. Herbig and Delia F. McMullin The orbit of Comet Oterma 1943 a closely resembles those of the Hilda group of minor planets, although the comet probably cannot be identified with any of the known members of that group. When discovered photographically on April 8 by Miss L. Oterma of Turku, Finland, the object was faint, of the fif- teenth magnitude, and moving slowly. The slow motion intro- duced considerable uncertainty in the preliminary solution, so that the derivation of a reliable orbit was delayed until the ob- served arc had lengthened. Two general solutions have been published : one by L. E. Cunningham and R. N. Thomas1 with a 37-day arc, the other by the writers2 with a 56-day arc. The two solutions are in substantial agreement. iñie object moves with a period of about , eight years in a nearly circular orbit of low inclination, which lies between the orbits of Mars and Jupiter (see Fig. 1). At aphelion, it may come very near to Jupiter; such a close approach occurred in 1938. Although it reached a minimum distance of 52,000,000 miles from Jupiter early in November 1938, the two objects had such similar motions that for about nineteen months their separation was less than 60,000,000 miles.. Perturbations during that time, therefore, were undoubtedly large. The semi-major axis, small eccentricity, and low inclination of the orbit of Comet Oterma place it in the zone of the minor planets and associate it with the Hilda group. The known mem- bers of this group move in orbits with moderate eccentricities, low inclinations, and semi-major axes between 3.88 and 3.99. The remarkable similarity of the orbit of Comet Oterma to those of the Hilda group seems more than fortuitous, in view of the compact and isolated nature of the group.8 Although the actual 1 Nos. 660-61, 1943. 2 Ibid., No. 662, 1943. 3 This feature of the Hilda group is best seen in a frequency diagram of the semi-major axes of the known minor-planet orbits. For such a dia- gram, see Marshall, Pop. Astr., 46, 17, 1938. © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 234 PUBLICATIONS OF THE identity of Comet Oterma with one of these minor planets is unlikely, the possibility should not be overlooked. An orbit of such low eccentricity is quite unlike that of any known cornet^ with the exception of Comet Schwassmann-Wachmann (1) 1925 II, which revolves between Jupiter and Saturn in a pe- riod of 16 years. Fig. 1.—The orbit of Comet Oterma 1943 a. The positions marked are for the beginning of the year. The projection makes it appear as though the closest approach to Jupiter occurred in the middle of 1938; actually, it took place in November. Table I lists the orbital elements of the 19 known members of the Hilda group and of Comet Oterma 1943 a. The data for the planets were taken from Kleine Planeten for 1943. The sec- © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System ASTRONOMICAL SOCIETY OF THE PACIFIC 235 ond column, "Mean Longitude," gives the sum of the longitude of the node, the argument of perihelion, and the mean anomaly for the date 1943 June 9.0 U.T., and serves to compare the positions of the various objects at that date. TABLE I Orbital Elements of, the Hilda Group Tisse- Mean 1950.0 rand's Minor Planet Longitude ^ Q i e a Crite- non 153 Hilda 235?7 49?5 228M 7?85 0.1520 3.968 0.5807 190 Ismene 131.6 283.5 177.1 6.15 .1679 3.944 .5816 334 Chicago 184.6 163.3 131.5 4.61 .0553 3.882 .5881 361 Bononia 294.2 73.1 19.4 12.67 .2138 3.941 .5726 499 Venusia 159.1 182.8 256.4 2.06 .2224 3.960 .5793 748 Simeisa 105.0 186.8 266.6 2.25 .1730 3.949 .5828 958 Asplinda ....317.0 100.0 344.6 5.68 .1943 3.940 .5804 1038 Tuckia 171.9 308.6, 58.8 9.26 .2474 3.928 .5740 1162 Larissa 28.4 229.1 40.8 1.93 .1086 3.967 .5856 1180 Rita 52.4 217.9 88.6 7.21 .1808 3.960 .5798 1202 Marina 188.8 315.3 51.4 3.42 .2046 3.925 .5810 1212 Francette .... 265.2 353.5 149.6 7.58 .1791 3.966 .5794 1256 Normannia .. 123.3 136.0 241.9 4.10 .0478 3.943 .5870 1268 Libya 103.6 143.6 353.5 4.42 .1044 3.928 .5858 1269 Rollandia ... 218.5 31.7 135.7 2.74 .0694 3.959 .5867 1345 Potomac ....301.8 338.9 137.5 11.36 .1770 3.974 .5758 1439 Vogtia 297.0 118.3 36.7 4.21 .1167 3.955 .5848 1512 1939 EE .... 43.8 248.3 10.7 6.51 \1713 3.954 .5810 1529 1938 BC .... 351.2 303.5 101.5 8.99 .1927 3.996 .5768 Comet Oterma ... 187.3 359.0 155.0 3.98 0.1427 3.984 0.5831 There are three principal criteria for establishing an identifi- cation of the comet with a known minor planet :(1) their mean longitudes should be in acceptable agreement, (2) the elements of their orbits should not differ by unreasonable amounts, and (3) their magnitudes should be in approximate agreement. 1. An examination of the table reveals that the mean longi- tude of the comet lies nearest those of (334) Chicago, (1038) Tuckia, and (1202) Marina. The actual positions in the sky of the various objects, however, are somewhat different. If the predicted positions of these three planets are compared with that © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 236 PUBLICATIONS OF THE of the comet, the differences (minor planet minus comet) for the date 1943 March 17.0 are as follows : Minor Planet Δα Αδ 334 Chicago -lh 18™7 + 9° 30' 1038 Tuckia -0 52.2 +14 25 1202 Marina —0 19 .0 + 2 43 2. It is difficult to generalize about the changes in the ele- ments after a close approach to Jupiter, but from an inspection of the orbits of members of the Hilda group in the Berkeley Research Surveys* it seems unlikely that changes of the size required to establish identification could have taken place. The problem may be approached more satisfactorily from a study of Tisserand's Criterion, a function of the geometrical elements which should remain nearly constant despite perturbations :5 1 , 2 λ/ a (1— e2) a — — Η — cos ι a ^ ajK a is the semi-major axis of the orbit of the perturbed body, ex- pressed in astronomical units; aj is the same quantity for the principal perturbing body (here, Jupiter) in the same units, and e and i are the eccentricity and inclination, respectively, of the perturbed body. It is apparent from Table I that the values of Tisserand's Criterion are not greatly different for orbits whose semi-major axes are nearly alike and whose inclinations and eccentricities are moderate. The variation in a for a minor planet of this group after a close approach to Jupiter, whether due to the approach or simply to uncertainties in the elements, is apparently smaller than the difference between the value for * Pub. Lick Obs., 19, 1935. 5 Tisserand, Mécanique Celeste (Paris, Gauthier-Villars, 1896), Vol. 4, p. 205. The form of this equation given in Moulton, Introduction to Celestial Mechanics (New York, Macmillan, 2d rev. ed., 1914), p. 298, differs from that given by Tisserand because the unit of distance (intro- duced on p. 278) is the mean distance of the disturbing body, not the astronomical unit. Moulton's qualifying clause, "where the elements are those in actual use by astronomers," tends to obscure this point, especially since his form of the equation, used with the wrong unit, gives consistent results unless the mean distance changes considerably. © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System ASTRONOMICAL SOCIETY OF THE PACIFIC 237 Comet Oterma and that for any of the planets in Table I. The change was about 0.0002 or less for the planets studied. It seems, accordingly, that the value of a for the comet is far enough from those of the three possible planets to make identi- fication unlikely. 3. The observed photographic magnitude of the comet at the beginning of July 1943 was about sixteen; visually, it was prob- ably at least a magnitude fainter.6 At the same date the visual magnitudes of the three minor planets in question, as calculated from the data of Kleine Planeten were: (334) Chicago, 12.3 mag.; (1038) Tuckia, 14.7 mag.; (1202) Marina, 15.1 mag. Correction for phase angle would probably increase these by an additional magnitude. It seems inevitable to conclude from these considerations that Chicago and Tuckia cannot possibly be identical with Comet Oterma but that there is a remote possibility that Marina might be. The question could be settled by securing a position of Marina, or by carrying its position forward from 1938 (the date of the last observation) with ^ special perturbations. Since the predicted position of Marina was only 5?5 from that of the comet on March 17.0, there was a possibility that it might be located on plates of the comet made with telescopes of fairly large field.
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