Orbits of Saturn's F ring and its shepherding satellites

ICARUS 53, 156-158 (1983)

NOTE Orbits of Saturn's F Ring and Its Shepherding Satellites S. P. S Y N N O T T , 1 R. J. T E R R I L E , R. A. J A C O B S O N , AND B. A. SMITH* Jet Propulsion Laboratory, Pasadena, California 91109, and *University o f Arizona, Tucson, Arizona 85721 Received August 9, 1982; revised November 3, 1982 The shape and orientation of Saturn's F ring and the orbits of its two shepherding satellites have been determined from Voyager images. The data and processing are described, and orbital parameter estimates and associated uncertainties are presented. In addition, evidence that suggests that the F-ring braids are formed very near the conjunctions of the shepherding satellites is presented. Unexpected clumping and braiding were observed (Smith et al., 1981) in high-resolution Voyager images of Saturn's F ring and the most likely cause is the disturbing effect of the shepherding satellites on the orbits of the F-ring particles. The detailed calculation of the perturbations will depend on accurate models for the relative positions of the satellites and the F-ring particles, and in this note we describe the analysis of Voyager images to determine the F-ring "orbit" and to improve on the previously reported shepherding satelrite orbits (Synnott et al., 1981). Data description and processing. Approximately 25 Voyager 2 images for each of the F-ring shepherding satellites 1980S26 and 1980S27 have been analyzed to determine the shape and orientation of the orbits of these satellites. The images were recorded over the last 30 days of the approach to Saturn, with the camera resolution in this period ranging from 300 km down to about 50 km for the last frames taken a few days before encounter. Approximately 300° of each satellite's orbital motion was observed, with about 30° gaps existing at the spacecraft relative transit and occultation regions of each orbit. The root-mean-square fits to the satellite observations were less than 0.5 pixel (a pixel is a single camera resolution element). The resulting accuracy of the orbit determinations is discussed below. In addition, two different types of imaging observations of the F ring were analyzed. Fifteen Voyager 2 frames which captured a particular condensation of Fring material or "clump," and a reference star or one of Saturn's classical satellites, were processed, primarily to determine the mean motion of particles in the F ring and hence its mean radial distance from the planet center. The frames were shuttered about 11 days from planet encounter when 1 pixel was equivalent to about 110 km in position at Saturn. The observations spanned 31 hr, or slightly more than two ort To whom correspondence should be addressed.

bital periods of particles in the F ring. The clump was not a point source, and depending on the projection angle, its size ranged from - 2 pixels up to ~7 pixels. This required that a "center" be chosen from the linearly extended image, and this process introduced errors of the order of - l pixel. The rms fit to the data was in fact - 1 pixel, and this implies that the uncertainty in the mean orbital distance of the F ring from this determination is less than 30 km, with 95% confidence. This uncertainty is of the-order of the radial width of the ring. Other data were acquired to accurately determine the F-ring eccentricity and inclination. Specifically at about 2.5 days from Saturn closest approach, when the pixel resolution was 25 to 30 km, five frames were taken to capture approximately uniformly spaced parts of the F ring against a suitable star background. Each frame captured a small strip of the ring and at least one star, which was used as a pointing reference. Points were selected along the ring images at approximately 0.5 deg longitudinal steps, and a single elliptical orbit was fit through the data from all five frames. Because we did not follow one point source image in its motion around the ring, there is no along-orbit eccentricity information in these data and the eccentricity is measured by determining the shape of the ring. The difficulty of picking points in the actual data at exact longitudinal spacings was avoided by solving for a different orbital angular position for each data point. Therefore only shape information normal to the line of sight and normal to the ring image was used. The accuracy achieved by this procedure is discussed below. Parameter estimation results. The values and associated uncertainties of the orbital parameters of the F ring and its shepherding satellites derived from the Voyager 2 data described above are presented in Table I. For comparison the estimates derived from Voyager 1 data for the parameters e and to of the two satellites are also shown. As a check that these estimates from observations of the objects individually are meaning156

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NOTE

157

TABLE I ORBITAL ELEMENTS

FOR THE F RING AND ITS SHEPHERDING SATELLITES (Epoch JD = 2,444,839.6682)

198OS26

Parameter’ ab e i WC n

141,700 x 10-3) + 0.6 x 1O-3 0.0 * 0.1 22(31) 2 30 572.7891 2 O.OC!M

4.2 x W’(4.4

198OS27 139,353 2.4 x W1(3.0 x lo-‘) ? 0.6 x lo-’ 0.0 2 0.1 173(178) 2 20 587.2890 2 0.0005

Fring 140,185 + 30 2.6 x IO-’ + 0.6 x 10-l 0.0 f 0.1 230(-) k 15 582.27 ? 0.2

a Distance in kilometers; mean motion n in degrees/day; angles in degrees. Voyager 1 result for eccentricity in parentheses. Mean motions of the satellites are derived using both Voyager 1 and Voyager 2 data. Solutions for the other parameters from the combined data are consistent with the individual estimates shown here. b Mean distance derived from mean motion n and Jz of Saturn; errors in “a” are essentially represented by errors in n. These errors are negligible for the satellites. c Voyager I p&apse angles are mapped to the Voyager 2 epoch with precession rates calculated using Saturn’s Jz and Jq. (Null et al., 1981). o is measured from Saturn’s autumnal equinox of 1950.0.

ful, we observed the relative positions of 1980827 and suitable points on the F ring in frames in which both objects appeared together. These observations which covered 180” in orbital longitude showed that the parameters contained in Table I predicted the actual relative positions to better than about 80 km in three positions around the ring and to -130 km in a fourth, which was at a point in the F ring not observed in the original data. These position errors are approximately consistent with the parameter errors quoted in the table. The errors in the table actually are somewhat conservative relative to those that would result from a typical least-squares analysis assuming that the measurement noise is 1 pixel and that there are no systematic distortions in the F-ring shape due to the shepherding satellites. Distortions are known to occur at least locally (in the braided region, for an obvious example), and such systematic shape effects can influence the results of Table I. However, the magnitude of the relative position errors is still likely to be - lo2 km, and not much larger. The current arrangement of periapses will change extremely slowly because the apsidal precession rates for 1980327 and the F ring differ by only O.OS”/day, if the planet harmonics are the only influence, and for 1980826 and the F ring by O.l”/day. Eventually these rates will produce an alignment of 198OS27’s apoapse with the F ring’s periapse with the result that the Fring particles would pass only 60 km from the surface of the satellite, if we use 70 km for the satellite radius (Smith et al., 1982) and if the current values of eccentricity remain. This may be an unstable situation, however, and a long-period variation in F-ring eccentricity (P - 20 years) possibly averts this difficulty. The corresponding minimum 1980S26-F ring distance is about 500 km. Location of the braided regions. The orbital locations of the braids B at the times they were captured in Voyager 1 and Voyager 2 frames with respect to the shepherding satellites are shown in Fig. 1. The point B represents the best estimate we could make by eyeball

of the midpoint of the braided region. For Voyager 1 this midpoint was estimated from a single high-resolution frame. No high-resolution frames of immediately adjacent parts of the ring exist and so therefore we cannot conclusively state that the braided region boundaries were accurately determined, although the braided region did seem to be wholly contained in the single frame. The relative motion between 1980827 and 198OS26is 14S”/day and so the satellites arrive at conjunction every 24.83 days, and are 3.17 days from their next close approach at the time specified in the figure. The position of the braids B is found to be very near the location of the last conjunction point 21.66 days earlier. The satellite 198OS27leads the braided region by 118”and the satellite 1980326 trails the braided region by 196”. The corresponding angles should be -108” and 206” if we project the relative mean motion in Table I over 21.67 days. Therefore the braided region seems to be behind the theoretical conjunction point by about 10”. This 10” mismatch may in part be due to the above-mentioned difticulty in establishing the beginning and end of the braided region which extends over at least 15 or 20” in longitude. But it may also indicate either that the ring particles are in higher and therefore slower orbits (by -O.Y/day which is due to an 80-km orbital radius change) possibly due to the action which formed the braids, or that the most severely affected ring particles are those that trail the satellite conjunction point by several degrees. We do not have a high-resolution history of the position of the braid region which would allow us to track the region’s motion. A somewhat different situation exists for the only braided region observed in Voyager 2 data. A single frame captured a strip of the ring spanning only about 6” in longitude within which there was a two-strand region -3” long. We chose B to represent the midpoint of this two-strand region, and its position relative to the satellites is shown in Fig. lb. In this case the conjunction occurred -10 days before the time the picture

158

NOTE

b

198OS26 74O

FIG. I. The relative positions of the shepherding satellites and the estimated midpoint B of the

observed braided region are shown, with the indicated angles measured from the autumnal equinox of Saturn. (a) Positions at the time of the Voyager 1 frame which first captured an image of braids, that is, at 13hllm4Ss UT on 12 November 1980. (b) Positions at 17h51m57sUT on 25 August 1981.

was taken, and so the mismatch between B and the conjunction point is significantly larger than in the Voyager 1 case. Again, high-resolution data of the adjacent parts of the ring do not exist, and B may not represent the true center of the braided region. Finally we make the comment that with further processing, particularly with the inclusion of some as yet unused data which directly measure the relative

positions of the satellites and parts of the ring, we should be able to reduce the uncertainties for the orbital parameters below those presented in the table, by a factor of -2 or possibly more. ACKNOWLEDGMENT We thank A. J. Donegan and L. A. Morabito for computing assistance. This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS 7-100, sponsored by the National

Aeronautics and Space Administration.

11 tracking data and Earth based Saturn satellite data. Asiron. .I. 86, 456-468. SMITH, B. A., L. SODERFILOM,R. BEEBE, J. BOYCE, G. BRIGGS, A. BUNKER, A. COLLINS, C. HANSEN, T. JOHNSON,J. MITCHELL, R. TERRILE, M. CARR, A. COOK, J. CUZZI, J. POLLACK, E. DANIELSON,A. INGERSOLL,M. DAVIES, G. HUNT. H. MASURSKY. E. SHOEMAKER, D. MORRISON, T. OWEN, C. SAGAN, J. VEVERKA, R. STROM, AND V. SUOMIA (1981). Encounter with Saturn: Voyager 1 imaging science results. Science 212, 163-191. SMITH. B. A.. L. SODERBLOM, R. BATSON, P. BRIDGES, J. INGE, H. MASURSKY, E. SHOEMAKER, R. BEEBE, J. BOYCE, G. BRIGGS, A. BUNKER, S. COLLINS, C. HANSEN, T. JOHNSON,J. MITCHELL, R. TERRILE, A. COOK, J. CUZZI, J. POLLACK, G. DANIELSON,A. INGERSOLL,M. DAVIES, G. HUNT, D. MORRISON, T. OWEN, C. SAGAN, J. VEVERKA, R. STROM, AND V. SUOMI (1982). A new look at Saturn: The Voyager 2 images. Science 215, 504-

536. REFERENCES NULL, G., E. LAU, E. BILLER, AND J. ANDERSON (1981). Saturn gravity results obtained from Pioneer

SYNNOTT, S. P.. PETERS, C. F., SMITH, B. A., AND MORAB~TO,L. A. (1981). Orbits of the small satellites of Saturn. Science 212, 191-192.