STELLAR OCCULTATION STUDIES OF SATURN'S RINGS WITH THE HUBBLE SPACE TELESCOPE by Amanda Sachie Bosh S.B. (Earth, Atmospheric, and Planetary Sciences) S.B. (Materials Science and Engineering) Massachusetts Institute of Technology (1987) Submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 1994 © Massachusetts Institute of Technology 1994, All Rights Reserved q Aithnr'c lriernntim- · uss&v, o Ulbll~~~r·LYIY-_ J~~- I r · w Department of Earfti, Atmospheric, and Planetary Sciences 31 December 1993 I Certified by ^ · ! g - -- Professor James L. Elliot Thesis Supervisor Depoamnpt*ef Earth, Atmospheric, and Planetary Sciences Accepted by rw - -- - Professor Thomas Jordan Chairman, Department Graduate Committee MASSACHUSETTSINSTITUTE OFT'c-JOLOGY 1 JAN 18 1994 LIBRARIES ARCHIt rSr . 2 ACKNOWLEDGMENTS I would like to acknowledge the Instrument Definition Team of the Hubble Space Telescope High Speed Photometer for guidance in the understanding of the intricacies of HST data. I also thank Peg Stanley, Andy Lubenow, and Jim Younger, all of whom worked very hard to schedule a very difficult occultation observation on the HST. Alex Storrs has my extreme gratitude for help on every occultation but this first one. Without him in the planetary scheduling department at the Space Telescope Science Institute, we would have gotten much less data than we did. Colleen Townsley has been extremely helpful as our liaison at STScI. Cathy Olkin did the initial work on the equations for the vector code formulation of the occultation geometry; this has proven very helpful for this work, as have the many discussions we've had. Other past and present graduate students have always been a source of friendship, advice, and good times. I would also like to thank Dick French, Phil Nicholson, and Bruno Sicardy for the use of non-circular feature data before publication. I extend a special thanks to Phil for a very long, very helpful discussion about the gravitational harmonics problem. Maren Cooke also provided some helpful insight into ringlet kinematics, and measured feature times as part of our Elliot et al. (1993) paper in the Astronomical Journal. I thank my thesis advisor, Jim Elliot, or his patient reading of many drafts of this thesis, for his guidance throughout most of my career at MIT, and for letting me spend my last year in graduate school at Lowell Observatory. Last, I thank Matthew Holman, my family, Chicky the cat, and many others for their friendship and support over the years. This work was supported, in part, by HSP GTO Grant NASG5-1613. The author is partially supported by the NASA Graduate Student Researcher Program. 3 4 TABLE OF CONTENTS Acknowledgments...................................................................................................3 Table of Contents......................................... 5 Abstract ...................................................................................................................7 1. Introduction....................................................................................................9 2. Data ......................................... 13 3. Model for Geometric Analysis of Occultation Data ................................... 21 4. Ring Orbit Models ................................................................................... 34 5. Implementation of Models ........................................................................... 38 6. Ring-plane Pole Solution ......................................... 43 7. Comparison with CLhe.rMethods of Radius Determination ........................66 8. Pole precession.............................. 68 9. Non-circular Features ......................................... 71 10. Ringlet Masses ........................................................................... ................. 92 11. Gravitational Harmonic Coefficients ...........................................................99 12. B-Ring Features ...................................................................................... 111 13. Conclusions ............................................................................................... 117 Appendix A: Occultation Observations with the Hubble Space Telescope....... 122 Appendix B: Reprint of Elliot et al. (1993) ........................................ 126 References .......................................................................................................... 157 5 6 STELLAR OCCULTATION STUDIES OF SATURN'S RINGS WITH THE HUBBLE SPACE TELESCOPE by Amanda Sachie Bosh Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on 31 December 1993 in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Earth, Atmospheric, and Planetary Sciences ABSTRACT Recent determinations of Saturn's ring-plane pole and radius scale incorporated subsets of currently available data (Elliot, et al. 1993. Astron. J. 106, 2544-2572; French, et al. 1993. Icarus 103, 163-214; Hubbard, et al. 1993. Icarus 103, 215-234). We present a solution for Saturn's pole and radius scale using the following occultation data: (i) the 1991 occultation of GSC6323-01396, observed with the Hubble Space Telescope, (ii) the 1989 occultation of 28 Sgr, observed from 11 Earth-based sites, (iii) the 1981 occultation of 8 Sco, observed with the photopolarimeter on Voyager 2, and (iv) the 1980 occultation of the Voyager I radio science signal, received at Earth. To these data, we fit a solar- system barycentric vector geometric model that includes in-track errors for Voyager (in the form of clock offsets), general relativistic bending by an oblate planet, and pole precession. Since the magnitude of errors in ring-plane radii calculated from this geometric model varies significantly across features, we employ a weighting scheme that assigns higher weights to those features with lower rms residuals. From these model fits, we find a ring plane pole position of ap = 40.59287 ± 0.00470 degrees, p = 83.53833 ± 0.00022 degrees at the Voyager 1 epoch, consistent with the results of all above-mentioned works. We search for inclined rings and find none that are statistically significant. We also find one new feature that is probably non-circular: the inner edge of the C ring, feature 44. This feature appears to be freely precessing (due to Saturn's non-spherical gravity field). In modeling previously determined non-circular features, we find that models for the Titan and Maxwell ringlets agree well with previous models (Porco et al. 1984. Icarus 60, 1-16). The center and inner edge of the 1.470 RS ringlet appear circular, while the outer edge is best fit by a Prometheus 2:1 Lindblad resonant model. The outer edge of the 1.495 RS ringlet is described by a superposition of Mimas 3:1 Lindblad resonance model and a freely precessing model. These two ringlets were previously thought to be purely freely precessing (Porco & Nicholson, 1987. Icarus 72, 437-467), but now it appears that this is not the case. Despite the proximity of the inner edge of the 1.990 RS ringlet to the Pandora 7 9:7 inner Lindblad resonance, this features appears to be freely precessing. The outer edges of the B and A rings were previously shown to be influenced by the Mimas 2:1 and Janus/Epimetheus 7:6 Lindblad resonances, respectively (Porco et al., 1984. Icarus 60, 17-28). We find that both ring edges fit best to a superposition of resonant and freely precessing models. However, residuals are still much larger than for any other ringlet, indicating that there may be other dynamics at work on these features. Finally, the Huygens ringlet is best described by a model that combines freely precessing and Mimas 2:1 Lindblad resonance models. This may be a result of the proximity of this ringlet to the B ring and the strong Mimas 2:1 resonance. We combine constraints from the location of the Titan ringlet (in an apsidal resonance with Titan) and the measured precession rates of the Maxwell and 1.495 RS ringlets with previously published constraints from Pioneer tracking data and satellite precession rate measurements (Null et al., 1981. Astron. J. 86, 456-468) to determine new values for -6 -6 Saturn's gravitational harmonics: J2 = (16301 + 6) x 10 , J4 = (-894 + 9) x 10 , and J6 = (124 + 5) x 10-6 (for Saturn equatorial radius 60330 km). Values of higher-order - 6 - 6 - 6 harmonics are held fixed: J8 =-10x10 , J10 =2x10 , J12 =-0.5x10 , J14 J16== 0. The formal errors in these parameters are greatly reduced from those of Nicholson & Porco (1988, J. Geophys. Res. 93, 10209-10224), particularly the error in J6 . J6 is now determined precisely enough to provide a useful constraint on models of Saturn's interior. The value we find suggests that the interior may be in a state of complex rotation. Thesis Supervisor: Professor James L. Elliot Department of Earth, Atmospheric, and Planetary Sciences 8 1. INTRODUCTION The study of planetary rings blossomed in the 1970's and 1980's, with the discovery of the Uranian rings (Elliot et al. 1977; Millis et al. 1977), the Jovian ring (Owen et al. 1979), and the Neptunian rings (Covault et al. 1986; Hubbard et al. 1986; Lane et al. 1989; Sicardy et al. 1991; Smith et al. 1989). Before this time, only one ring system was known, that of Saturn. All the recently-discovered ring systems share features with the Saturnian ring system: the ethereal Jovian ring resembles Saturn's E ring;