RADIO OCCULTATION OF SATURN’S RINGS WITH THE CASSINI SPACECRAFT: RING MICROSTRUCTURE INFERRED FROM NEAR-FORWARD RADIO WAVE SCATTERING A DISSERTATION SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Fraser Stuart Thomson July 2010 © 2010 by Fraser Stuart Thomson. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/pb657pg3502 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Howard Zebker, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Per Enge I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Essam Marouf Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii iv Abstract The Cassini spacecraft is a robotic probe sent from Earth to orbit and explore the planet Saturn, its moons, and its expansive ring system. Between May 3 and Au- gust 2 of 2005, we undertook a series of radio occultation experiments, during which the Cassini spacecraft operated in conjunction with the NASA Deep Space Network (DSN) to probe the rings at three distinct radio wavelengths. During our occultation experiments, Cassini flies behind the rings of Saturn as viewed from Earth and transmits coherent radio signals at wavelengths of 13 cm, 3.6 cm, and 0.94 cm, in the radio bands known as S, X, and Ka, respectively. These signals pass through the rings and are received and recorded on Earth at the large antenna complexes of the DSN. At each of the three transmitted frequency channels, the received signal comprises two components, i) a direct (coherent) component, which is the transmitted sinusoid, attenuated and phase shifted by the average effect of its interaction with the interceding ring material, and ii) a scattered (incoherent) signal component, comprising energy that is forward-scattered towards the receiver from all of the ring particles illuminated by the transmitting antenna’s beam. The time- and spatially-averaged diffraction signature of ring microstructure—which forms when individual ring particles organize into large clusters or groups under the influence of collisional and self-gravitational forces—is superimposed on the scattered signal. Coherent radio waves transmitted by the Cassini spacecraft are diffracted at vari- ous locations in Ring A and B and indicate the presence of fine-scale structure showing periodic variation in optical depth, which we refer to as periodic microstructure (PM). We interpret the observed spectral signature using simple diffraction grating models, yielding estimates of the structural period λgr ≈ 100–250 meters. In particular, two v regions in Ring A at radial locations 123.05–123.4 × 103 km and 123.6–124.6 × 103 + + km yield average estimates of λgr=163−6 meters and λgr=217−8 meters, respectively. Three regions in Ring B at radial locations 92.1–92.6 × 103 km, 99.0–104.5 × 103 × 3 +20 + km, and 110.0–115.0 10 km yield average estimates of λgr=115−15, 146−14, and +150 250−75 meters, respectively. In all regions, the structure appears to be azimuthally o ≤ ≤ o symmetric with mean orientation angles ranging between -2.8 φgr 1.5 . Prior to Cassini, axisymmetric periodic microstructure was predicted by fluid dynamical theory and by the results of dynamical simulations of the rings, but was not observed experimentally. Our observations are the first to directly observe PM in the rings, and to report estimates of its structural period and orientation in five distinct regions across Rings A and B. vi Acknowledgements I would like to extend my heartfelt thanks to Howard Zebker for taking over from Len Tyler as my primary advisor in early 2008. Without his support, it is unlikely that I would have completed this degree program. I will always be in his debt for his acts of kindness and support. Sincere thanks are due to Essam Marouf, who always made the effort to find time in his busy schedule for my many questions. Essam has been a model of patience, diligence, and excellence during our years of collaboration, and his steady provision of guidance, tutelage, and financial support has made this work possible. His ethics and commitment to excellence in his work form an ideal that all scientists should aspire to, and which many on the Cassini radio science team depend on and are indebted to. One of the most memorable moments in my life is being at JPL during the first planned Cassini radio occultation experiment, and watching how excited Essam and Dick French were as we all watched the spectrum of the received signal varying in real time, as the experiment revealed hints of ring structure. Throughout my years at Stanford, it has been a great privilege and joy for me to observe Essam’s passion for the rings firsthand. Thanks also to Per Enge for serving as my third reader, for serving on my oral defense committee, and for teaching me about orbital mechanics and GPS. He is an excellent professor and a friend to many students, myself included. I extend many thanks to my teacher and friend Ivan Linscott, who always has time to discuss new ideas and old ones, and for being such a generous friend to many students over the years. Thanks also to Antony Fraser-Smith for stepping in to save the day on several occasions, for serving on my defense committee, and for being such vii a great guy in general. Special thanks go to Len Tyler for all of his time, energy, and support, and for being a mentor to me for several years prior to his semi-retirement. Len is a polymath, and memories of times when I have glimpsed his brilliance will always bring a smile to my face. On those rare occasions when Len did not know the answer, his honest and free willingness to admit gaps in his knowledge provide an inspirational lesson to us all; there is no better way to get started solving a problem than to admit what is known and what is not known. Len’s insistent attention to detail has taught me to choose my words more carefully, and has made me a better technical writer. As Len would say, a key goal in writing is to minimize the impedance mismatch between the writer and their audience. I hope I have done that here. A very special thanks to Sami Asmar of NASA’s Jet Propulsion Laboratory, for being a friend and a great boss during my all-too-brief work terms at the lab. I would be honored to work with him or for him again, anytime and anywhere. I would also like to thank Christopher Chyba, my friend and mentor, and one of the kindest and smartest people I’ve ever known. The nine months that we collaborated before I chose to join Cassini was the most exciting and fulfilling period of time that I spent at Stanford. Lots of love and thanks to my parents, who provided access to all of the oppor- tunities that anyone could ever ask for in life. I would not be writing this without them. There are many other people who, either knowingly or unknowingly, helped to make this dissertation possible. To the anonymous, I offer my thanks also. I dedicate this dissertation to my wife Katherine and to my son Kaiden (b. June 7, 2009), for showing me how simple life really is, and for being a constant reminder of what is truly important. This work was supported by the NASA Cassini Project through JPL Contract No. 1214216. The support is gratefully acknowledged. viii Contents Abstract v Acknowledgements vii 1 Introduction and Historical Review 11 1.1 The Discovery of Saturn’s Rings ..................... 12 1.2 Occultation Studies of Saturn’s Rings: A Brief History ........ 20 1.3 Contents and Contributions of this Dissertation ............ 22 2 Saturn Ring Structure and Dynamics 27 2.1 Ring Macrostructure ........................... 33 2.1.1 Gaps and Ring Boundaries .................... 34 2.1.2 Spiral Density and Bending Waves ............... 38 2.2 Ring Microstructure ........................... 40 2.2.1 Gravitational Wakes ....................... 40 2.2.2 Periodic Microstructure ..................... 42 2.3 Models of Ring Microstructure ...................... 44 2.4 Summary ................................. 47 3 EM Scattering and Diffraction from Ring Particle Clusters 49 3.1 Introduction ................................ 50 3.2 Theoretical Background ......................... 53 3.2.1 Coherent Scattering from a Sphere: Mie Theory ........ 56 3.2.2 Multi-ParticleScatteringUsingMieTheory.......... 60 ix 3.2.3 Diffraction from an Amplitude Screen .............. 64 3.2.4 Mie and Diffraction Theory: Some Practical Considerations . 66 3.3SimulationResults............................ 68 3.3.1 Scattering from a Single Sphere ................. 70 3.3.2 Scattering from Two and Three Spheres ............ 71 3.3.3 Scattering from Ten Spheres ................... 77 3.4 Discussion ................................. 83 3.5 Amplitude Screen Model Results for Thick, Homogeneous Rings .