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Observatoire de Paris

Direct optical measurements of asteroid diameters obtained by telescopic observations are scarce. Although several adequate instrumentations and techniques are available for the purpose, they have not been used. The importance of these determinations should be stressed for the attention of observers.

The filar micrometer was used only by one observer during the last century, and no additional measures have been made since. This was in 1894 and 1895 when E. Barnard (1902) used the 90 cm refractor of Lick Observatory, and the 100 cm refractor of Yerkes Observatory. The results are as follows:

Ceres: apparent diameter at 1 AU. 1"060, or 770 km (28 nights)
Pallas: apparent diameter at 1 AU. 0.675, or 490 km (5 nights)
Juno: apparent diameter at 1 AU: 0.266, or 195 km (5 nights)
Vesta: apparent diameter at 1 AU: 0'531, or 390 km (21 nights)

These filar micrometer measurements are difficult to make when the disks are only slightly larger than the image of the diffraction pattern blurred by atmospheric seeing; the accuracy is necessarily poor, especially for Juno; the last decimals given are not significant.

The interferometer with a double slit in the wavefront was used by M. Hamy (1899) with the 60 cm coudé refractor of the Paris Observatory, but only on Vesta: apparent diameter at 1 AU. 0'54, or 400 km (8 nights).

Once again, this technique was not used again, despite the improvements in interferometric techniques and the larger telescopes now available.

The double-image micrometer has been used more recently in France by several collaborating observers. For descriptions of the double-image micrometer, see papers by P. Muller (1949) and A. Dollfus (1954). Although the survey is not yet complete, some of the as yet unpublished preliminary results are summarized in table I.

For small apparent diameters of only two to three times the effective resolving power of the telescope, large uncertainties remain in the measurements, and systematic errors occur. Some of them were computed or simulated at the laboratory by H. Camichel (1958), A. Dollfus (1963), and M. Hugon et al. (Camichel et al., 1964).

TABLE I.—Double-Image Diameter Measurements of Asteroids (Preliminary Results)

Apparent Asteroid Diameter Average
Date Observers Telescope stellar apparent Distance, at at
diameter diameter AU 1 AU 1 AU
(measured) (measured)
June 5, 1967 A. Dollfus and 83 cm Meudon - 0'48 1.196 0'57
J. Focas 83 cm Meudon - .48 1.196 .57 0'60
July 11, 1967 P. Muller 83 cm Meudon - .42 1.454 .61 +0"10
July 21, 1967 P. Muller 83 cm Meudon - .43 1.553 .67
June 7, 1969 A. Dollfus and 107 cm Pic-du-Midi 0.29 .53 2.513 1.34
J. Lecacheux 107 cm Pic-du-Midi .23 .50 2.513 1.25 1.27
June 8, 1969 A. Dollfus and 107 cm Pic-du-Midi .31 .49 2.510 1.24 +0'35
H. Camichel 107 cm Pic-du-Midi .34 .50 2.510 1.25

The error limits given in the table, #0"10 for Vesta and +0"35 for Pallas, are only estimates based on the practice of the laboratory simulations, taking into account the seeing conditions at the telescope when measurements were made. The measurement of Vesta agrees with the values of Barnard (1902) and Hamy (1899); but the diameter of Pallas is larger than the Barnard value by a factor on the order of 2. This very large discrepancy casts a doubt on the overall accuracy of the presently available determinations of asteroid diameterS. The diskmeter, designed by H. Camichel (1953), is a device producing a small artificial bright disk in the field of the telescope, with adjustable brightness, color, blurring, and diameter. Looking first at a nearby star, the observer adapts the brightness, color, and instrumental blurring for an artificial image of negligible apparent diameter, to reproduce as closely as possible the brightness configuration of the stellar image. Then, looking at the asteroid (or a small satellite), the observer readapts brightness and color, and without changing the blurring adjustment, increases the diameter of the artificial image until reproducing the behavior of the object in the field. This kind of instrument was successfully used by H. Camichel with the French Pic-du-Midi 60 cm refractor and by G. P. Kuiper with the Palomar 500 cm reflector on Neptune, Pluto, and planetary satellites. Kuiper used a diskmeter to measure some asteroids, but the details of this work have not been published." This technique seems to be particularly well adapted for asteroid diameter determinations and should be used. The occultation of asteroids by the edge of the Moon provides curves of brightness variations with time, from which the apparent disk diameter can be derived with an excellent accuracy. For stellar objects of negligible apparent diameter, the photoelectric lightcurves recorded with a time resolution of a millisecond display a drop of brightness lasting some tenths of milliseconds, associated with at least one maximum and one minimum due to the diffraction pattern (see fig. 1); the higher order diffraction variations vanish into the noise

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Figure 1.-Lightcurve of the lunar occultation of e-Capricorni, 4.7 mag, B5p. December 9, 1964, at 19n:51m48s; green filter. (60 cm telescope of Meudon Observatory, France; photoelectric observation by G. Spaak.)

*Note added in proof, by T. Gehrels: A summary paragraph occurs on p. 352 of Surfaces and Interiors of Planets and Satellites (ed., A. Dollfus; Academic Press, Inc.; London; 1970); the wording of that paragraph was checked with G. P. Kuiper.

TABLE II.-Asteroidal Diameter Determinations Available in 1970

Number of Apparent Average Normal
Asteroid Technique independent diameter apparent Diameter, reflectivity,
measures at 1 AU diameter km hy
at 1 AU

Vesta Filar 21 0.53

Interference 8 .54 0'56 410 0.40

Double image 4 .60
Ceres Filar 28 1.06 1.06 770 0.13
Juno Filar 5 .27 .27 195 0.27
Pallas Filar 5 .68

Double image 4 1.27 (.97) (700) (0.055)

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