1. V. R. Eshleman et al., Space Sci. Rev. 21 207 (1977), V. R. Eshleman et al., Science 204, 976 (1979), V. R. Eshleman et al., ibid. 206, 959 (1979), G. L. Tyler et al., ibid. 212, 201 (1981); G. L. Tyler et al., ibid. 215, 553 (1982).
2. R. E. Edelson et al., Science 204, 913 (l979).
3. Signal-to-noise (SN) ratios on the order of 50,000 and 3,000 were achieved at 3.6 and 13 cm, respectively, from the Canberra DSN 64-m antenna with 1-second coherent integration intervals. Subsequent combination of data from Canberra and Parkes should improve the SN ratio at 3.6 cm by 3 dB; combination of data from the two Canberra antennas should improve the SN ratio at 13 cm by about 1 dB. Equipment at Parkes was shared [from CSIRO (Commonwealth Scientific and Industrial Research Organisation), ESA (European Space Agency), and NASA].
4. These include real-time measurements of the signal amplitude frequent and frequency dispersion at coarse time resolution.
5. Primary data for radio propagation consist of sample measurements of signals at the antenna terminals recorded on computer-compatible tape at rates between 50,000 and 80,000 samples per second.
6. From Earth-view, the virtual radio image of the spacecraft followed the dashed track along the planet's limb indicated in Fig.1. In the central portion of the occultation, the angle of refraction exceeded the width of the spacecraft antenna beam at both wavelengths; hence the experiment required a continous maneuver to point the spacecraft antenna at the Planet's limb.
7. J. B. Pollack, M. Podolak, P. Bodenheimer, B. Christofferson, in preparation.
8. G. Fjeldbo et al.,Astron. J. 76, 123 (1971).
9. Computations of the infrared brightness spectra were performed by B. Conrath and D. Gautier [R. Hanel et al. Science 233, 70 (1986)] using data from coordinated IRIS and RSS observations in the equatorial regions of the atmosphere.
10. The He fraction, 0.15 +/- 0.05, corresponds to 52 +/- 2.5 K for the temperature minimum at the tropopause.
11. G. S. Orton, Science 231, 836 (1986).
12. B. J. Conrath et al., Astrophys. J. 282, 807 (1984).
13. G. F. Lindal et al., J. Geophys. Res. 86, 8721 (1981); G. F. Lindal et al., Astron. J. 90, 1136 (1985).
14. As of this writing no moving cloud features have been reported at this latitude.
15. See, for example J. F. Appleby, Icarus, in press, particularly model "c" of Fig. 2 therein.
16. The approach used here is the same as that employed in the analysis of the Titan data; for a more detailed discussion see G. F. Lindal et al., Icarus 53, 348 (1983)
17. S. T. Massie and D. M. Hunten, ibid. 49, 213 (1982); B. J. Conrath and P. J. Gierasch, ibid. 57, 184 (1984).
18. L. Trafton, Astrophys. J. 207, 1007 (1976); L. Wallace, Icarus 43, 231 (1980), J. T. Bergstralh and K. H. Baines, in Uranus and Neptune, J. T. Bergstralh, Ed. (NASA Conf. Publ. 2330, 1984), p. 179; G. S. Orton and J. F. Appleby, ibid., p. 89.
19. See, for example, D. P. Hinson, J. Geophys. Res. 89, 65 (1984); ______ and G. L. Tyler, Icarus 54, 337 (1983).
20. R. H. Chen, J. Geophys. Res. 86, 7792 (1981).
21. For theory of radio ring occultation and analysis see E. A. Marouf et al., Icarus 49, 161 (1982), E. A. Marouf et al., in preparation; H. A. Zebker, thesis, Stanford University (1984).
22. Earth-based studies of Uranus' rings by stellar occultations provide only lower bounds on the optical depth of the six unresolved rings 6,5,4, eta, gamma, and delta [see, for example, J. L. Elliot and P. D. Nicholson, in Planetary Rings, R. Greenberg and A. Brahic, Eds. (Univ. of Arizona Press, Tucson, 1985), pp. 25-72]. The maximum optical depth observed at radio wavelengths (Table 1) often exceeds these bounds. Secondary broad components associated with the eta and delta rings [J. L. Elliot et al., Astron. J. 86, 444 (1981)] were also observed in the radio data. The prominent structure of the 3.6-cm profile of the epsilon ring, shown in Fig. 3B at 1-km resolution, corresponds to features observed from Earth [see Fig. 4 of P. D. Nicholson et al., Astron. J. 87, 433 (1982)].
23. The quantity calculated is the sum[tau(r_i,lambda)deltar], where r is distance from Uranus across each ring, lambda is wavelength, and tau is corrected for the obliquity. The resolution deltar chosen for each particular case varied between 200 and 1000 m, depending on the width of the ring and the SN ratio. It was reported at a Voyager press briefing 27 January 1986, that the epsilon ring displayed no wavelength dependence; this statement applies to the data in Fig. 3B; those in Fig. 3A had not been examined.
24. Because the ring material is spread over a large area, by more than 3:1 between (A) and (B) of Fig. 3, independency scattering (that is, well-spaced) particles will show a decrease in the total optical depth by the same factor. This is observed in a general way between (A) and (B) but not in detail. At 3.6 cm the unchanged value of the integrated extinction indicates that the extinction per particle has been conserved, assuming that the particles themselves are unchanged; a similar, albeit weaker, result is observed at 13 cm.
25. For independent scattering, the minimum particle separation in the direction of propagation should be about ten diameters or more for each unit of tau. For tau = 2 to 8 observed here, the extension of the ring would be several tens of diameters. Strict radiative transfer-type models typically have volume fractions less than 1e-3, which would imply an even thicker extended ring.
26. The radar cross section of a rough dielectric sphere such as a planet or satellite, is of the order (radius)^2. To account for the present observation, such an object would need to be larger than Uranus itself.
27. Both Earth-based and spacecraft observations show that Saturn's A ring exhibits an azimuthally asymmetric reflectivity [see, for example, H. J. Reitsema et al., Astron. J. 81, 209 (1976); B. A. Smith et al. Science 215, 504 ( l98l)]. G. Colombo et al. [Nature (London) 264, 344 (l976)] suggest that the asymmetry is due to trailing density wakes of embedded large particles. See also W. H. Julian and A. Toomre, Astrophys. J. 146, 810 (1966); F. A. Franklin and G. Colombo, Icarus 33, 279 (1978).
28. A combination of radio and optical navigation data yields an additional factor of 2 improvement in the mass determination for the Uranian system, but we are reluctant to recommend the smaller uncertainty until the relative weighting of the two data types is better understood. System mass obtained from the radio data alone does not correlate with any other parameters and is reliable. Determining the mass of the planet alone depends on knowing the sum of the masses of the five principal satellites, which requires optical navigation data for highest accuracy. For our more accurate planet mass we used a fit to optical and radio data, but we increased the uncertainty significantly with respect to the formal uncertainty to allow for a possible incorrect relative weighting of the two data types.
29. O. Struve, Mon. Not. R. Astron. Soc. 8, 44 (1848); J. C. Adams, ibid. 9, 159 (1849).
30. S. Newcomb [U.S. Nav. Obs. App. 1, 7 (1875)] obtained a value for M_sys^(-1) of 22,600 +/- 150.
31. G. W. Hill [Astron. J. 19, 157 (1898); Astron. Pap. Am. Ephem. 7 (1898)] obtained a value for M_sys^(-1), of 23,239 +/- 132.
32. D. L. Harris, thesis, University of Chicago (1950); D. W. Dunham, thesis, Yale University (1971).
33. W. J. Klepcyznski et al., Astron. J. 75, 739 (1970).
34. The determination of M_sys^(-1) of 22,900 +/- 200 from meridian circle and radar range observations of the planets [M. E. Ash, I. I. Shapiro, W. B. Smith Science 174, 551 (1971)] probably represents the best that can be accomplished with planetary perturbations.
35. S. Newcomb, Astron. Pap. Am. Ephem. 6 (1898); ibid 7 (1898). Newcomb's value was also used recently in a study of ephemerides [X. X. Newhall et al., Astron. Astrophys. 125, 150 (1983)].
36. S. F. Dermott and P. D. Nicholson, Bull. Am. Astron. Soc. 17, 742 (1986); Nature (London), in press.
37. We have neglected the mass of the material in the rings and the Uranian satellites newly discovered by Voyager. We estimate the total mass of this material to be less than 1 km^3 sec^(-2).
38. The strong constraint placed on the mass of the total system, GM_sys and on the five satellite masses by the radio data is 0.2966(GM_sys - 5,794,523.4) + 0.1241(GM_1 - 81.3) - 0.5090(GM_2 - 74.2) - 0.1110(GM_3 - 249.6) - 0.5012(GM_4 - 153.2) - 0.0220(GM_5 - 4.0) = 0.0 +/- 7.3 km^3 sec^(-2), where the subscripts refer to Ariel, Umbriel, Titania, Oberon, and Miranda, respectively, and G is the universal gravitational constant. This constraint is satisfied by solutions given here.
39. B. A. Smith et al., Science 233, 43 (1986).
40. The sum of the masses of the three outer satellites as determined from radio data alone is recommended over a similar sum obtained from a combination of radio and optical data. The reason is the same as that given in (28).
41. We used the most recent numerically integrated satellite ephemerides for this work (from R. A. Jacobson, personal communication).
42. Uncompressed densities are based on the solar mix given in the text, a uniform satellite temperature of 60 K at the current epoch (corresponding to an albedo of 0.25), and homogeneous density. The rocky component is assumed to have an uncompressed density of 3.361 g cm^(-3) [M. J. Lupo, Icarus 52, 40 (1982)]. The value for compressed water ice is from M. J. Lupo and J. S. Lewis [ibid. 40, 157 (1979)]. Determinations of density eliminate compositional classes that fall outside the range of the uncertainties in the densities. In this sense, the suggestion of CH4-dominance over CO in the protoplantetary phase [J. S. Lewis and R. G. Prinn, Astrophys. J. 238, 357 (1980), R. G. Prinn and B. Fegley, ibid. 249, 308 (l98l)] represents a viable model. J. B. Pollack [in Protostars and Planets, D. C. Black and M. S. Matthews, Eds. (Univ. of Arizona Press, Tucson, 1985), pp. 791-831] considers compositional classes consistent with solar composition but differentiated by temperature and pressure conditions of formation.
43. J. S. Lewis, Earth Planet. Sci. Lett. 15, 286 (1974).
44. A. J. R. Prentice, Phys. Lett. A 114, 211 (1986).
45. D. J. Stevenson [NASA Conf. Publ. 2330, 1984, p. 409] considers a number of generic satellite compositions, including a possible Uranian class of rock plus (CO,N_2) dot (7H_2O)=ice clathrate with an un compressed density of about 1.8 g cm^(-3). A cometary composition has been suggested by R. Greenberg et al. [Icarus 59, 87 (1984)]. If we assume that the satellites of Uranus form a single compositional class, our results rule out both of these high-density models. Self-compression in the two outer satellites would result in densities well in excess of 2.0 g cm^(-3), contrary to our measurements.
46. J. L. Elliot, in Uranus and the Outer Planets, G. Hunt, Ed. (Cambridge Univ. Press, Cambridge, England, 1982), pp. 237-256; P. D. Nicholson et al.,Astron. J. 87, 433 (1982).
47. P. D. Nicholson, personal communication.
48. This experiment required extensive support from the Voyager Project and the NASA DSN, both at the Jet Propulsion Laboratory, and at the Deep Space Communication Complexes, especially in Australia, where the normal tracking facilities were augmented for Voyager by the inclusion of the Parkes Radio Astronomy Observatory. We thank these groups for their efforts in obtaining the data discussed here. Design, implementation, and execution of these experiments required the skills, creativity, and dedicated efforts of a number of individuals. The RSS support team; R. Kursinski, S. Borutzki, M. Connally, P. Eshe, H. Hotz, S. Kinslow, and K. Moyd - was responsible for coordination of activities between the Voyager project and the DSN, implementation of the observational strategy, and monitoring of the execution. F. Donivan managed this activity within the DSN. D. L. Gresh and P. A. Rosen designed and implemented much of the software necessary for planning and for data reduction. J. Lyons provided computational support in obtaining the atmospheric profiles. Essential computing equipment at Stanford was a gift of Data General Corporation. Supported by funding from NASA.
27 March 1986; accepted 5 May 1986
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