Small satellites of Uranus: Disk-integrated photometry and estimated radii

iCARUS 81, 92-101 (1989)

Small Satellites of Uranus: Disk-Integrated Photometry and Estimated Radii PETER THOMAS, CATHERINE W E I T Z , AND J O S E P H VEVERKA Center for Radiophysics and Space Research, Cornell University, Ithaca. New York 14853 R e c e i v e d August 1, 1988; revised J a nua ry 23, 1989

Disk-integrated photometry from Voyager 2 clear-filter images is used to compare properties of the ten small satellites that orbit Uranus interior to Miranda. Two satellites, 1985U1 Puck and 1986U7 Cordelia, are resolved. Observations of Puck cover phase angles of 15 to 33 ° and yield a phase coefficient of 0.031 -.+ 0.003 mag/deg. The mean radius of Puck is 77 - 3 km; its geometric albedo (Voyager clear filter, A ~ 0.48/~m) is 0.074 ± 0.008. Cordelia's albedo is found to be similar to that of Puck. This result suggests that all the small satellites may be iow-aibedo objects with reflectances similar to, but slightly higher than, those of the ring material. Satellite radii calculated with the assumption that they have the same reflectance as Puck range from 13 --. 2 km (1986U7 Cordelia) to 55 ± 6 km (1986U1 Portia). The ~-ring shepherds have calculated radii of 13 ± 2 and 16 ± 2 km; these radii correspond to approximate masses of 1.4 and 2.5 × 1019 g, respectively. No useful constraints on the colors of the small satellites can be obtained given the low signal-to-noise ratio of the color data. We estimate that the opposition magnitudes range from + 20.4 for Puck to + 23.9 and 24.2 for the two ~-ring shepherds.

© 1989 AcademicPress, Inc.

tant in studying the evolution of the Uranian system. In this study we use Voyager imaging data to establish their relative diskintegrated properties and radii. First, we examine phase information and derive reflectances for the two objects in the data set that are spatially resolved by the Voyager observations. Then we estimate relative sizes on the basis of relative apparent brightness (actually disk-integrated flux) and examine available color information. Finally, we discuss our results in the context of the origin of these small bodies and their possible relationship to material forming the rings.

INTRODUCTION

Voyager 2 discovered l0 small satellites orbiting Uranus interior to Miranda (Smith et al. 1986). They are listed with their orbital radii in Table I. The largest, 1985U1 Puck, was resolved in a single image at 4.5 km/pixel, and was found to be irregularly shaped (R - 77 km) and dark (albedo 0.07-0.09) (Thomas et al. 1987). Two of these small satellites, 1986U7 and 1986U8, shepherd the e ring, and may also serve as shepherds for the outer edge of the 6 and 7 rings (Porco and Goldreich 1987, Goidreich and Porco 1987, French et al. 1988). While properties of the ring particles and large satellites have been studied intensively, the small satellites have been investigated only in dynamical contexts. Because these bodies occupy the region between the large, icy satellites, and the very dark ring particles, any information on their surface properties or sizes is impor-

TECHNIQUES

Photometrically useful images were obtained in the last 2 days before encounter with the wide-angle system, and some useful narrow-angle images were obtained 5 days prior to encounter. Inspection of the images showed that the larger satellites 92

0019-1035/89 $3.00 Copyright © 1989by Academic Press, Inc. All rights of reproduction in any form reserved.

SMALL SATELLITES OF URANUS TABLE I

I / F -- DN - Dnbg

(1)

tOo" EXP

SMALL SATELLITES OF URANUS

1986U7 1986U8 1986U9 1986U3 1986U6 1986U2 1986U 1 1986U4 1986U5 1985U 1

93

Proposed name d

Semimajor axis of orbit, a (km) b

Cordelia Ophelia Bianca Cressida Desdemona Juliet Portia Rosalind Belinda Puck

49,752 53,764 59,165 61,767 62,659 64,358 66,097 69,927 75,255 86,006

a Proposed names from I A U Circular 4609. b F r o m O w e n and Synnott (1987).

(1985U1, 1986U1, 1986U3) are detectable in some earlier images, but in view of the obvious difficulties in using data of only a few pixels and a few data numbers (DN) above background, no wide-angle images prior to FDS 26792.07 were used in this study. All of the images in Table III were obtained using the clear filters of the cameras. Most exposures were 15.4 sec long; a few, with the narrow-angle camera, were only 7.7 sec. Our data are obtained from raw image files. The predicted line and sample coordinates in Voyager images of all the small satellites derived by optical navigation routines were supplied by S. Synnott. After visual location of the satellites, the DN around the satellite were extracted. The background values (dark current DN) were calculated and used to measure the sum of the satellite signal above background. Most satellite images are smeared substantially and appear as elongated streaks 10 to 25 pixels in area. We have assumed complete linearity of DN and flux, though the results below suggest that for data only slightly above dark current, strict linearity may not apply. Reflectance for a particular pixel is calculated from

where I is intensity of scattered light, and 7rF is the incident flux. DN and D N b g a r e the observed data numbers for the satellite and background (sky and dark current), respectively. The calibration factor, too, is that appropriate for the particular filter, camera, and solar distance; EXP is exposure in seconds. The calibration factors recommended at the time of encounter (Johnson 1986) and used in most early publications of Voyager Uranus results (Smith et al. 1986, Veverka et al. 1987) are listed in Table II. Although there has been some small adjustment of the recommended too values since encounter (Johnson et al. 1988), these make no practical impact on our results or conclusions. In practice the DN are summed for the area above dark current, and the total applicable dark current is subtracted. The resultant sum of DN is scaled by too and exposure time and by the square of the target range to obtain total fluxes comparable between images. The resulting value would be equivalent to I / F if the object subtended one pixel of the wide-angle camera at 106 km (4622 km2). Because nearly all the objects subtend less than 1 pixel, these numbers tend to be very much smaller than real I / F values would be. These reflectances are summarized in Table III. RESULTS: DISK-INTEGRATED PHASE CURVES

The disk-integrated brightnesses are plotted in Fig. 1 as functions of phase angle. The brightnesses are referenced to arbitrary

T A B L E II CALIBRATION FACTORS (19.1 AU) ~ Clear Wide angle Narrow angle

Violet

Blue

Orange Green

846.566 189.983 451.056 71.265 249.205 159.879 49.481 67.259 15.187 35.149

a FromJohnson(1986).

94

THOMAS,

WEITZ, AND VEVERKA T A B L E ili

IMAGES USED AND DISK-INTEGRATED BRIGHTNESS Satellite FDS

1985U1 26660.31 26793.37 26793.43 26794.19 26837.16 1986U 1 26793.07 26793.49 26793.55 26824.38 1986U2 26793.01 26.793.07 26793.49 26793.55 26794.01 26794.07 26824.32 1986U3 26793.37 26793.43 26794.19 26824.38 1986U4 26793.13 26793.19 26794.01 26794.07 26824.32 1986U5 26793.37 26793.43 26794.19 1986U6 26793.13 26793.19 26793.25 26793.31 26794.13 26824.56 1986U7 26762.25 26762.19 26762.31 26794.19 26814.10 26822.26 26824.44

Z(I/Fttl pixel"

Filter

Exp (secl

Phase angle ot (o)

Range (106 km)

Scale (km/pxl)

NACL ' WACL WACL WACL NACL

15.4 15.4 15.4 15.4 1.4

14.7 19.2 19.2 19.4 33.0

8.05 2.37 2.37 2.34 0.49

73.4 161.0 161.0 159.0 4.5

0.186 0.170 0.179 0.173 0.114

-+ 0.018 _+ 0.016 _+ 0.017 +_ 0.016 _+ 0.001

WACL WACL WACL WACL

15.4 15.4 15.4 15.4

17.4 17.4 17.5 22.1

2.39 2.36 2.36 1.04

163.0 161.0 161.0 71.0

0.0917 0.0924 0.0882 0.0843

+ 0.0070 _+ 0.0075 -+ 0.0060 + 0.0027

WACL WACL WACL WACL WACL WACL WACL

15.4 15.4 15.4 15.4 15.4 15.4 15.4

16.6 16.6 16.3 16.3 16.1 16.1 18.5

2.40 2.39 2.36 2.36 2.36 2.35 1.04

163.0 163.0 161.0 161.0 161.0 160.0 71.0

0.0528 0.0556 0.0571 0.0509 0.0581 0.0591 0.0578

-+ 0.0051 -+ 0.0061 -+ 0.0062 -+ 0.0065 ± 0.0016 _+ 0.0028 _+ 0.0016

WACL WACL WACL WACL

15.4 15.4 15.4 15.4

17.3 17.3 17.6 22.5

2.37 2.37 2.34 1.04

161.0 161.0 159.0 71.0

0.0344 0.0300 0.0289 0.0276

-+ 0.0022 ± 0.0025 -+ 0.0025 -+ 0.0023

WACL WACL WACL WACL WACL

15.4 15.4 15.4 15.4 15.4

15.4 15.4 17.4 17.4 21.8

2.39 2.39 2.36 2.35 1.04

163.0 162.0 160.0 160.0 71.0

0.0211 0.0198 0.0221 0.0217 0.0256

-+ 0.0028 -+ 0.0026 -+ 0.0030 ± 0.0025 _+ 0.0013

WACL WACL WACL

15.4 15.4 15.4

16.9 16.9 17.3

2.37 2.37 2.34

161.0 161.0 159.0

0.0317 _+ 0.0045 0.0370 -+ 0.0040 0.0358 -+ 0.0035

WACL WACL WACL WACL WACL WACL

15.4 15.4 15.4 15.4 15.4 15.4

15.7 15.7 15.7 15.7 15.0 21.3

2.39 2.38 2.38 2.38 2.35 1.03

163.0 162.0 162.0 162.0 160.0 70.0

0.0232 0.0219 0.0224 0.0222 0.0234 0.0227

-+ 0.0019 _+ 0.0018 _+ 0.0025 -+ 0.0027 _+ 0.0031 +_ 0.0015

NACL NACL NACL WACL NACL NACL WACL

15.4 15.4 15.4 15.4 7.7 7.7 15.4

15.5 15.5 15.5 17.4 19.7 20.7 20.1

3.71 3.71 3.70 2.34 1.49 1.14 1.04

33.7 33.7 33.7 159.0 13.6 10.3 71.0

0.00426 0.00515 0.00515 0.00530 0.00463 0.00464 0.00434

_+ 0.0010 -+ 0.0011 ± 0.0011 -+- 0.00080 -+ 0.00041 _+ 0.00023 -+ 0.00051

Average 1/F;'

0.0462 0.0423 0.0445 0.0430 0.0282

_+ 0.0045 + 0.0040 _+ 0.0042 -+- 0.0040 _+ 0.0002

SMALL SATELLITES OF URANUS

95

TABLE lii--Continued Satellite FDS

Filter

Exp (sec)

Phase angle a

Range (10 6 km)

Scale (km/pxl)

E ( I / F ) / ! pixeP

Average I / F b

t°) 1986U8 26752.44 26752.50 26752.56 26753.02 26753.08 26764.39 26792.07 26794.07 26824.38 1986U9 26793.49 26824.32

NACL NACL NACL NACL NACL NACL WACL WACL WACL

15.4 15.4 15.4 15.4 15,4 15.4 15.4 15.4 15.4

15.4 15.3 15.3 15.3 15.3 15.6 16.1 15.1 19.3

4.12 4.12 4.12 4.11 4.10 3.61 2.44 2.35 1.04

37.5 37.4 37.4 37.3 37.3 32.8 166.0 160.0 71.0

WACL WACL

15.4 15.4

17.5 18.2

2.36 1.04

160.0 71.0

0.00755 0.00825 0.00865 0.00706 0.00826 0.00807 0.00797 0.00790 0.00573

± ± ± ± ± ± -+ ±

0.00054 0.00057 0.00056 0.00050 0.00086 0.00085 0.00020 0.00021 0.00080

0.0104 ± 0.0021 0.0151 ± 0.0018

S u m of I / F is equivalent to the reflectance o f one wide-angle pixel at 106 km, an area of 4622 km 2. h For Puck the size is k n o w n (gm = 77 km), so the average I / F for a full disk (~-R2m)can be calculated. ' N A C L , narrow angle clear; W A C L , wide angle clear.

values and expressed as changes in magnitude. The " e r r o r " bars are calculated solely from the uncertainties due to variations in dark current (standard deviation of DN in 4 × 4-pixel boxes bracketing the satellite image) and do not include any estimates of systematic errors. Some suspected systematic effects are discussed below. Virtually all the data were obtained between phase angles of 15 and 22°; the major exception is Puck, for which there are data at 14.7, 19.2, 19.4, and 33° phase. Only for Puck, 1986U!, 1986U3, and 1986U7 are the phase data good enough to warrant fits for phase coefficients. The resulting phase coefficients, given in Table IV with their formal uncertainties, range from 0.017 to 0.031 mag/deg. The coefficient for Puck is the best determined (Fig. 2), and even including the lower value for 1986U1, the values are consistent with those of other dark objects. For example, Phoebe, a small, spectrally bland object with a geometric albedo of about 0.05, has a disk-integrated phase coefficient of about 0.033 to 0.036 mag/deg (Thomas et al. 1983). Mariner 9 data for

Phobos and Deimos, which are also dark objects, yield phase coefficients of 0.032 and 0.030 over phase angles of 20-80 ° (Noland and Veverka 1976). Disk-resolved Viking photometry suggests similar, but slightly higher, disk-integrated phase coefficients for these satellites (Klaasen et al. 1979). The phase data for Puck allow a refinement of the estimate of its albedo made by Thomas et al. (1987). Extrapolation to 0° gives a disk-averaged I / F of 0.074 +- 0.008; this value is equivalent to geometric albedo if there is no limb darkening. T A B L E IV DISK-INTEGRATED PHASE COEFFICIENTS, CLEAR FILTER Satellite

P h a s e angle range (°)

1985U1 P u c k 1986U1 1986U3 1986U7

14.7-33 17.4-22.1 17.3-22.5 15.5-20.7

/3 (mag/deg) 0.031 0.017 0.026 0.031

± ± ± ±

0.003 0.007 0.004 0.010

Note. Formal errors. It is noted in the text that systematic errors m a y be significant for 1986UI and 1986U3.

96

THOMAS, WEITZ, AND VEVERKA

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SMALL SATELLITES OF URANUS -0.2

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Possible sources of systematic error include the effects of viewing at different aspects and problems in measuring the small differences in DN between object and dark current. Objects of elongate shape and/or nonuniform albedo can introduce substantial differences in disk-integrated reflectances with changes in rotational phase; this effect is probably not significant here because all the images were taken from high latitudes (65-73°). There is evidence of systematic errors in the conversion of DN to flux in the very small and faint images. Only Puck and Cordelia are ever resolved; most satellite images are 5-20 pixels wide and 5-30 DN above background (Fig. 3). The data for 1986U4 and 1986U9 provide the best evidence of possible linearity failure. 1986U4 appears to brighten with increasing phase angle; the higher-phase-angle images are those taken close to encounter and at the highest spatial resolution. The low-phase image of 1986U4, 26793.13, has only 6 pixels above background, and only two that are more than 10 DN above background. This satellite is estimated to have a radius of about 28 km (see below); thus, in image 26793.13 (scale = 163 km/pixel), it covers only about a 0. l-pixel area. The situation is very similar for 1986U9 (Fig. 1, Table III), and probably for several other satellites. In the cases of 1986U7 and 1986U8, the early

narrow-angle views alleviate this problem. These data suggest that the very faintest detections are undermeasured due to a lack of perfect reciprocity at low DN. There is a hint of this condition in the calibration measurements of Benesh and Jepsen (1978), but it is not quantifiable at the DN levels involved here. In-flight calibration images of the plaque during cruise do not cover very low DN, but may show some departures from reciprocity at midrange DN (R. Thompson, personal communication). Thus, we are somewhat suspicious of those phase coefficients in Table IV based on data in which low phase angles correlate with low spatial resolution: 1986U1 and 1986U3. RADII AND OPPOSITION MAGNITUDES

The size of 1985U1 Puck has been directly measured at 77 -+ 3 km (Thomas et al. 1987). This value applies to the cross section nearly in the orbital plane. Because all the measurements of these satellites are from high latitudes, we are basically comparing equatorial cross sections. Of the other small satellites, only 1986U7 Cordelia is even marginally resolved. In image 26822.26 at 10.3 km/pixel, its diameter (perpendicular to smear) is 3.0 _+ 0.6 pixels or 31 -+ 6.2 km. The calculated area yields an average I / F of 0.029 +- 0.012 at a = 20.7 °. This satellite appears to have a phase coeffi-

98

THOMAS, WEITZ, AND VEVERKA

cient the same as that o f Puck (Table IV), so we can c o m p a r e calculated reflectances of the two objects. The disk-averaged reflectance for Puck at 20.7 ° phase is 0.041 ± 0.01 I. The reflectances of the two satellites are marginally consistent. In what follows, we a s s u m e that all the small satellites are as dark as Puck, but this must be recognized as only a plausible assumption. V o y a g e r data do not exist to d e m o n s t r a t e that all the small satellites are dark. We h a v e estimated the radii of the satellites if they h a v e the s a m e reflectances as Puck; the results are s h o w n in Table V. The disk-integrated fluxes are c o m p a r e d at a -15 °, using either the phase coefficients listed in Table IV or 0.3 m a g / d e g as an app r o x i m a t e m e a n value. F o r two satellites, three data that w e r e a n o m a l o u s l y low were excluded (26762.25, 26793.01, 26793.55), but these would m a k e v e r y little difference in the calculated radii. The uncertainties listed for the radii include allowance for a m i s m a t c h in albedo (by an arbitrary 25%) of the satellite and Puck (corresponding to a ± 1 2 % e r r o r in radius) as well as for the uncertainty in the relative disk-integrated flux (Table V, column 3).

TABLE

V

D I S K - I N T E G R A T E D R E F L E C T A N C E S , R A D I I , AND OPPOSITION M A G N I T U D E S Satellite

1986U7 1986U8 1986U9 1986U3 1986U6 1986U2 1986U1 1986U4 1986U5 1985U1

Cordelia Ophelia Bianca Cressida Desdemona Juliet Portia Rosalind Belinda Puck

Disk-integrated flux relative to Puck"

Radius h (kin)

0.0275 0.0407 0.0849 0.179 0.140 0.298 0.503 0.146 0.200

13 16 22 33 29 42 55 29 34 77

-+ 0.010 -+ 0.0036 -+ 0.0155 -+ 0.015 -+ 0.009 +- 0.016 -+ 0.012 -+ 0.025 -+ 0.019

++ -+ -+ -+ -+ -+ -+ -+ +

2 2 3 4 3 5 6 4 4 3 '1

Opposition Magnitude"

24.2 23.9 23.1 22.3 22.5 21.7 21.1 22.5 22.1 20.4

A t ct = 15°; calculated with the m e a s u r e d phase coefficients (Table IV) or mean v a l u e o f 0.03 mag/deg. b C a l c u l a t e d with a s s u m p t i o n o f albedo e q u i v a l e n t to that o f 1985U1 Puck. See text for d i s c u s s i o n o f uncertainties o f radii. c Mean o p p o s i t i o n magnitude. U n c e r t a i n t i e s are approximately 0 . 2 - 0 . 3 mag. See text. a Measured.

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The estimated radii range from 13 to 55 km. Thus, the volume of Puck is slightly greater than the total of the other small satellites. The radii listed here are actually mean values of the intermediate and long axes b e c a u s e of the high latitude of viewing. To the extent that small satellites are elongate, the listed m e a n radii are too large. The possible error can be estimated by the average shapes of m a n y other small satellites where m e a n a / b is 1.4 and m e a n a / c is 1.7 ( T h o m a s 1988). Use of only the a and b axes would give radii about 12% larger than the " r e a l " m e a n radii. Thus, the values in Table V m a y be about 10% too large, due to the effect of high-latitude viewing, a negligible a m o u n t in view of other uncertainties involved. The two shepherding satellites, Cordelia and Ophelia, have calculated diameters of about 26 -+ 4 and 32 -+ 4 km. If we assume a m e a n density of 1.5 g / c m 3 (the m e a n for the larger satellites of Uranus), the corresponding masses are 1.4 and 2.5 x 1019 g. The uncertainty in the m a s s e s from the size estimates alone is a b o u t 50%. The m e a n opposition magnitudes listed in Table V are a p p r o x i m a t e and are based on the following assumptions: (a) all satellites have the same albedo as Puck, and (b) all small satellites have similar neutral colors

SMALL SATELLITES OF URANUS

99

35

URANUS SMALl_SATELLITES Best VoycRer Resolution 33 o-

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FIG. 3. Best resolution available from Voyager. Shown are points for the clear filter sequences summarized in Table III; the data are also representative of the color sequences available for some of the satellites. The radii listed in Table V are assumed.

green reflectance which implies a green/ clear ratio of 2.0. F o r 1986U9 Bianca in the same series o f images, orange, blue, and violet images all have values so much larger than in the clear (15 : 1, 3 : 1, 7 : 1) that we conclude their identifications are erroneous. In images 26795.37 and 26798.21, 1986U1 Portia has reflectances that give a green/orange ratio of 3.2. 1986U3 Cressida has a calculated green/blue ratio of 4.4 from images 26795.37 and 26796.01. This wild scatter of ratios suggests spurious data. The difficulty is easily understood if one considers the question from the opposite direction. F o r example, an object of reflecCOLORS tance 0.05 at a = 15° (a value slightly higher Color information on the small satellites than the observed values for Puck) would of Uranus is unreliable due to extreme sig- give about 21 DN for a 1-pixel area with a nal/noise problems. While several color se- 5.8-sec exposure through the orange filter quences were obtained, the results are too of the wide-angle camera. But a small satelnoisy to provide useful data. For example, lite such as 1986U9 Bianca has a radius of in the sequence 26753.02 to 26753.26, only 0.14 pixel in the 26799 image series, so 1986U8 Ophelia gives a green/clear ratio of the signal above background would be only 0.55 __- 0.2 and a violet/clear ratio o f 0.4 +_- 1.4 DN. We do not expect to detect this 0.2. In the sequence 26799, an uncertain difference reliably; in fact, we have probidentification o f I986U8 Ophelia gives a lems with DN differences 10 times this such that the factor that converts magnitudes in the V o y a g e r clear filter to V magnitudes of the U B V system is the same as that for Titania. Given a diameter of 1580 km, a geometric albedo of 0.28, and an opposition magnitude V0 = 13.9 for Titania, 1985U1 Puck (d = 154 km, albedo = 0.074 --- 0.008) is fainter by a factor of 413.6 or 6.5 mag. Thus, the estimated V0 for Puck is +20.4 0.2. Opposition magnitudes for the other satellites are scaled from the Puck value, according to their disk-integrated fluxes relative to Puck; uncertainties in these values are probably 0.2-0.3 mag.

100

THOMAS, WEITZ, AND VEVERKA

amount in some clear filter data. We conclude that no useful color data for these satellites can be derived from Voyager images. DICUSSION

We stress that only for two of the ten satellites (Puck and Cordelia) do we have direct estimates of the albedo, and that only in the case of Puck can the value be considered definitive. Our geometric albedo for Puck (0.074 + 0.008) is lower than that for any area on any of the five larger satellites (Miranda through Oberon) detectable at Voyager resolutions (0.6 to 12 km/lp). The value is higher, however, than commonly quoted values for Uranus ring particles. From a review of pre-Voyager data, Cuzzi (1985) arrived at a value for the equivalent of the geomeric albedo of a ring particle of 0.04-0.05 (+0.015). A slightly lower value is quoted by Ockert et al. (1987) from an analysis of Voyager 2 imaging data: their average value for the o~, /3, and e rings is 0.032 + 0.003. From a complementary study of the Voyager data, Svitek and Danielson (1987) arrive at a value higher by a factor of about 1.5 for the e ring. We conclude that the best data suggest that at least for the particles in the most conspicuous ring (the e ring), geometric albedos of macroscopic particles are in the range 0.03-0.05, lower by a factor of 1.5 to 2 than our albedo for Puck. Given the many assumptions (cf. Cuzzi 1985) that go into a determination of ring particle albedos, we are not convinced that the difference is significant. One might expect a close connection between the albedo of the e-ring particles and those of the shepherding satellites Ophelia and Cordelia. We recall that our data show that the ratio of reflectances of Puck/Cordelia is 0.041 + 0.011/0.029 -+ 0.012 - 1.4 + 0.9. Given the uncertainty associated with this estimate, we consider it more likely to assume (as done above) that Puck and Cordelia have the same albedo, rather than to suppose that Cordelia is significantly darker than Puck, and therefore

closer in geometric albedo to the values quoted for e-ring particles in the literature. We also stress that no reliable color data exist for any of the ten satellites, not even for 1985U1 Puck. Porco et al. (1987) have determined that six of the rings have gray colors (over the Voyager camera wavelength range 0.35-0.60/~m) similar to those of the larger Uranus satellites (Smith e t al., 1986). There are no data to support or contradict the popular presumption that the small satellites have similarly gray spectra. SUMMARY

The marginal spatial resolution of the small inner satellites of Uranus requires the use of 1985U1 Puck as a benchmark. The only other small satellite for which a radius is even crudely determined from an image is 1986U7; its radius is marginally consistent with the value obtained assuming reflectance properties similar to those of Puck. Using the assumption of similar reflectances which is modestly supported by this measurement, the sizes of the satellites can be calculated to - 1 0 % R. The particular values are generally only slightly different from those reported in Smith e t al. (1986). The radii of the shepherds of the e ring, 1986U7 and 1986U8, are significantly smaller than reported in Smith e t al. (1986) and as adopted by Porco and Goldreich (1987) and Goldreich and Porco (1987): 13 + 2 versus 20 + 6 for 1986U7 and 16 -+ 2 versus 25 -+ 8 for 1986U8. The few reliable data on phase coefficients are very similar to those on disk-integrated coefficients of other dark objects, - 0 . 0 3 mag/deg. ACKNOWLEDGMENTS B. Boettcher, M. Roth, S. Synnott, and R. Thompson provided technical assistance. Research was supported by NASA Grants NAGW-1221 and NSG-7156. B. Buratti and C. Porco provided helpful reviews. REFERENCES BENESH, M., AND P. JEPSEN 1978. Voyager Imaging Science Subsystem Calibration Report, pp. 618802. Jet Propulsion Laboratory, Pasadena, CA. Cuzzl, J. N. 1985. Rings of Uranus: Not so thick, not so black. Icarus 63, 312-316.

SMALL SATELLITES FRENCH, R. G., J. L. ELLIOT, L. M. FRENCH, J. A. KANGAS, K. J. MEECH, M. E. RESSLER, M. W. BUIE, J. A. FROGEL, J. B. HOLBERG, J. J. FUENSALIDA, AND M. JoY 1988. Uranian ring orbits from Earth-based and Voyager occultation observations. Icarus 73, 349-378. GOLDREICH, P., AND C. C. PORCO 1987. Shepherding of the Uranian rings. II. Dynamics. Astron. J. 93, 730-737. JOHNSON, T. V. 1986. Corrections to Danielson et al. calibration, JPL memo. Jet Propulsion Laboratory, Pasadena, CA JOHNSON, T. V., J. VEVERKA, B. BURATTI, J. POLLACK, R. THOMPSON, AND P. THOMAS 1989. Voyager imaging system color correction update. In preparation. KLAASEN, K. P., T. C, DUXBURY, AND J. VEVERKA 1979. Photometry of Phobos and Deimos from Viking Orbiter images. J. Geophys. Res. $4, 84788486. NOLAND, M., AND J. VEVERKA 1976. The photometric functions of Phobos and Deimos. I. Disk-integrated photometry. Icarus 28, 405-414. OCKERT, M. E., J. N. CUZZl, C. C. PORCO, AND T. V. JOHNSON 1987. Uranian ring photometry: Results from Voyager 2. J. Geophys. Res. 92, 14,96914,978. OWEN, W. M., JR., AND S. P. SYNNOTT 1987. Orbits of the ten small satellites of Uranus. Astron. J. 93, 1268-1270. PORCO, C. C., J. N. CUZZl, M. E. OCKERT, AND R. J. TERRILE 1987. The color of the Uranian rings. Icarus 72, 69-78. PORCO, C. C., AND P. GOLDREICH 1987. Shepherding

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of the Uranian rings. I. Kinematics. Astron. J. 93, 724-729. SMITH, B. A., L. SODERBLOM, R. BEEBE, J. M. BOYCE, A. BRAHIC, G. A. BRIGGS, R. H. BROWN, S. A. COLLINS, A. F. COOK II, S. K. CROFT, J. N. Cuzzl, G. E. DANIELSON, M. E. DAVIES, T. E. DOWLING, D. GODFREY, C. J. HANSEN, C. HARRIS, G. E. HUNT, A. P. INGERSOLL, T. V. JOHNSON, R. J. KRAUSS, H. MASURSKY, D. MORRISON, T. OWEN, J. PLESC1A, J. B. POLLACK, C. C. PORCO, K. RAGES, C. SAGAN, E. M. SHOEMAKER, L. A. SROMOVSKY, C. STOKER, R. STRUM, V. E. SUOMI, S. P. SYNNOTT, R. J. TERRILE, P. THOMAS, W. R. THOMPSON, AND J. VEVERKA 1986. Voyager 2 in the Uranian system: Imaging science results. Science 233, 43 -64. SVITEK, T., AND G. E. DANIELSON 1987. Azimuthal brightness variation and albedo measurements of the Uranian rings. J. Geophys. Res. 92, 14,97914,986. THOMAS, P. C, 1988. Shapes of small satellites. Icarus 77, 248-274, THOMAS, P. C., J. VEVERKA, T. V. JOHNSON, AND R. H. BROWN 1987. Voyager observations of 1985U1. Icarus 72, 79-83. THOMAS, P., J. VEVERKA, D. MORRISON, M. DAVIES, AND T. V. JOHNSON 1983. Phoebe Voyager 2 observations. J. Geophys. Res. 85, 8736-8742. VEVERKA, J., P. THOMAS, P. HELFENSTEIN, R. H. BROWN, AND T. V. JOHNSON 1987. Satellites of Uranus: Disk-integrated photometry from Voyager imaging observations. J. Geophys. Res. 92, 14,89514,904.