THE ROTATION OF URANUS. By J. H. Moore and D. H. Menzel

Transcription

1 330 PUBLICATIONS OF THE THE ROTATION OF URANUS By J. H. Moore and D. H. Menzel The earliest determination of the period of rotation of the planet Uranus was made by Percival Lowell and V. M. Slipher at Flagstaff. In this work, the slit of a one-prism spectrograph was set parallel to the planet s equator, the plane of which was assumed to be that of the orbits of the satellites. This assumption is justified by the absence of any satellite perturbation that could be ascribed to the action of an equatorial protuberance not in the plane of the satellites orbits. The planet s rotation would be made evident through an inclination of the spectral lines upon the plate. From the magnitude of the inclination the relative velocities of two points situated on opposite sides of the equator could be calculated. The Lowell results were based upon seven spectrograms secured in August and September, 9. The plates were measured independently by Lowell and Slipher with the following results : TABLE I Lowell Slipher Mean Equatorial Velocity Period of Rotation 3.60 ±0. km/sec..75 ± 0.35 hrs* 4.2 ± 0.6 km/sec ± 0.37 hrs ±0. km/sec ±0.28 hrs. * In computing the period the Lowell observers used the old value of 24,295 km for the radius of Uranus, and the corresponding figure for the apparent semidiameter. The period actually turns out to be independent of the values used, so long as the two are consistent. In 97 Pickering 2 announced that Leon Campbell s photo- metric observations of Uranus indicated that the planet s light was variable with a range of about 0.5 mag. in a period of 0.45 days (0.8 hours). The probable error of the result was not given. Nevertheless the close agreement of the photo- metric and the spectroscopic periods was regarded as a striking Lowell Obs. Bull., 2, 7, H.C.O. Circular 200, 97.

2 ASTRONOMICAL SOCIETY OF THE PACIFIC 33 confirmation of the latter. It is to be regretted that so few details of this very important investigation have been published, especially so, since the more recent photoelectric observations of Stebbins and Jacobsen 3 raise a doubt as to the planet s varia- bility. Perenago, 4 at Moscow, made measures of the brightness of Uranus with the aid of a wedge photometer during the year 926. In 927, Slavenas, 5 at Yale, employed a photographic method of photometry. Both of these observers find periods of variation of the same order as the spectrographic. The respec- tive ranges of light variation, 0.4 and 0.08 magnitudes, ap- pear, however, to be not much greater than the probable errors of the observations. Stebbins and Jacobsen 6 at Lick Observa- tory during July, August, and September, 927, obtained 28 observations of Uranus with the photoelectric photometer. These observations were grouped, according to phase computed by Campbell s period, into 2 normals. The mean residual of each normal with respect to the mean of all the observations in no case exceeded magnitudes and was usually much less, the probable error of a single normal being but magni- tudes. These observers conclude: on the basis of the photo- electric observations we shall have to call Uranus as nearly con- stant in light as any object in the sky. It would thus appear that the most accurate photometric observations ever made of Uranus fail to disclose any evidence whatever of light varia- tion. It may, of course, be argued that the hypothetical spots giving rise to the variation observed by Campbell may have dis- appeared in the interim, but, it is interesting to note, this ex- planation meets with difficulties in accounting for the results of Slavenas, since his observations were made in September, Oc- tober, November, and December of the same year as those of Stebbins and Jacobsen. In view of the contradictory evidence as to the short-period variation in the light of Uranus, it appeared to us that a repe- tition of the spectrographic observations of the planet was de- 3 Lick Obs. Bull., 3, 80, Publ. Astroph. Inst, of Russia, 4, 200, A.N., 233, 25, Op. cit.

3 332 PUBLICATIONS OF THE sirable. Moreover, it was noticed that the present time offered a more favorable condition for the spectrographic determination of the planet s rotational speed than existed at the date of Lowell and Slipher s observations, since during the past few years the plane of Uranus equator has made a small angle with the line of sight, while in 9 this angle was 49?3. The first of our plates was secured in October, 927, with the new Mills 3-prism spectrograph, which gives a linear dispersion at X4500 of 0.9 A per mm. This instrument was attached to the 36-inch refractor, provided with the usual photographic correcting lens. With this equipment, an exposure time of even six hours with Eastman 40 plates was found insufficient to give a well-exposed spectrogram of Uranus. Although six spectrograms were secured in this manner, with the slit placed parallel to the equator in position angles 65 and 345, it has been possible to utilize only three of these, the quality of the others having been impaired by underexposure, by temperature changes that occurred in the spectrograph during the extremely long exposures, by poor seeing, or by drifting of the image upon the slit. Measurement of these plates convinced us that the advantages of the higher dispersion were largely offset by the unavoidable irregularities in the lines produced by graininess of the plate, intensified by underexposure. Furthermore, with exposures of this length, the effects of poor seeing, the unavoidable drifting of the image along the slit, and instrumental changes would operate, of course, to cut down the inclination of the spectral lines. For this reason, in our later work, we turned to instruments of lower dispersion, for which the exposure times on fine-grained Eastman 33 plates were from one to two hours only. In 928, 929, and 930 eleven satisfactory spectrograms were obtained with the light one-prism spectrograph (dispersion at Hy, 57 A per mm) and in 930 two spectrograms with the dense one-prism instrument (dispersion at Hy, 37.7 A per mm). Here, as in the case of the three-prism spectrographs, in order to eliminate errors that might enter through possible instrumental asymmetry, plates were secured with the slit in both position-angles. In every instance, both for the

4 ASTRONOMICAL SOCIETY OF THE PACIFIC 333 three- and one-prism spectrographs, the slit was carefully placed in the focus of the 36-inch objective for the particular region of the spectrum to be studied. All of the spectrograms have been measured independently by each of us. The inclinations of the lines of the planetary spectrum with reference to those of the comparison spectrum were measured upon a special Gaertner engine provided with a rotating table whose index could bo read, if desired, to hundredths of a degree. Two methods were employed : in one, the average inclinations of neighboring lines in some ten sections of the plate were determined ; in the other, individual measures of about 5 selected lines, the strongest and best-defined on the plate, gave the desired inclinations. The results, for the respective plates and observers, are given in Table II, columns 4 and 5. TABLE II Three-Prism Spectrograms Plate No. Date P.A. of Inclination Slit Moore Menzel Equational Velocity Moore Menzel Wt Oct. Oct. Oct ? A km/sec km/sec Light One-Prism Spectrograms Oct Oct Nov Nov Nov Nov Sept Sept Sept Sept Sept Dense One-Prism Spectrograms Sept Sept

5 334 PUBLICATIONS OF THE The equatorial velocity of Uranus, v e, is given by the follow- ing simple formula: a tan i rv 8 v e = 4 cos u where a is the width of the spectrum computed from the known constants of the instrument and the apparent diameter of Uranus (in every case this agreed very closely with the actual measured width), % the measured inclination, rv 8 a factor which reduces displacements (in millimeters) upon the plate to radial velocity (in kilometers per second) for the particular spectral region involved, and & the angle between the equatorial plane of Uranus and the line of sight. For the three-prism, light one- prism, and dense one-prism spectrographs the values of a are, respectively, 0.23, 0.8, and 0.8 mm, and of rv 8 (mean for the spectral region employed) 760, 3500, and The re- spective values of for 927, 928, 929, and 930 are 4?9, 8?5, 22?4, and 26?4. With the aid of these figures, the re- sultant equatorial velocities quoted in columns 6 and 7 were computed. In combining the observations, we have assigned weight 2 to the three-prism plates, with the exception of the one for October 2, which was somewhat underexposed, and unit weight to all others. The period is computed from the observed equatorial velocity on the basis of 24,850 km, for the semidiam- eter of Uranus. The final results are summarized in Table III, the construction of which is similar to that of Table I. TABLE III Moore Menzel Mean Equatorial Velocity Period of Rotation 3.84 ± 0.07 km/sec..30 ± 0.2 hrs. 4.5 ± 0.09 km/sec ± 0.24 hrs. 0 ± 0.06 km/sec ± 0.6 hrs. Several plates were secured with the slit of the spectrograph parallel to the assumed axis of the planet. On these, the spectral lines showed no inclination, which is in harmony with the hypothesis that the satellites orbits and the Uranian equator are co-planar.

6 ASTRONOMICAL SOCIETY OF THE PACIFIC 335 The direction of rotation, deduced from the sense of the inclination of the spectral lines, is the same as that of the revolution of the satellites in their orbits, i.e., retrograde. This investigation, therefore, very definitely confirms the results obtained by the Lowell observers, both as to the direction of rotation and as to the order of its period. The very close agreement in the period, however, is probably fortuitous and it is our opinion that its value, as derived by spectroscopic observations of a planet with so small a disk, may be in error by as much as half an hour.