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Dynamical Evolution of Small Bodies in the Solar System

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Dynamical Evolution of Small Bodies in the Solar System Dynamical evolution of small bodies in the Solar System by Seth A. Jacobson B.S., Cornell University, 2008 M.S., University of Colorado, 2010 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Astrophysical and Planetary Sciences 2012 This thesis entitled: Dynamical evolution of small bodies in the Solar System written by Seth A. Jacobson has been approved for the Department of Astrophysical and Planetary Sciences Daniel Scheeres Glen Stewart J. Michael Shull Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. Jacobson, Seth A. (Ph.D., Astrophysical and Planetary Sciences) Dynamical evolution of small bodies in the Solar System Thesis directed by Prof. Daniel Scheeres This thesis explores the dynamical evolution of small bodies in the Solar System. It focuses on the asteroid population but parts of the theory can be applied to other systems such as comets or Kuiper Belt objects. Small is a relative term that refers to bodies whose dynamics can be significantly perturbed by non-gravitational forces and tidal torques on timescales less than their lifetimes (for instance the collisional timescale in the Main Belt asteroid population or the sun impact timescale for the near-Earth asteroid population). Non-gravitational torques such as the YORP effect can result in the active endogenous evolution of asteroid systems; something that was not considered more than twenty years ago. This thesis is divided into three independent studies. The first explores the dynamics of a bi- nary systems immediately after formation from rotational fission. The rotational fission hypothesis states that a rotationally torqued asteroid will fission when the centrifugal accelerations across the body exceed gravitational attraction. Asteroids must have very little or no tensile strength for this to occur, and are often referred to as \rubble piles." A more complete description of the hypothesis and the ensuing dynamics is provided there. From that study a framework of asteroid evolution is assembled. It is determined that mass ratio is the most important factor for determining the outcome of a rotational fission event. Each observed binary morphology is tied to this evolutionary schema and the relevant timescales are assessed. In the second study, the role of non-gravitational and tidal torques in binary asteroid systems is explored. Understanding the competition between tides and the YORP effect provides insight into the relative abundances of the different binary morphologies and the effect of planetary flybys. The interplay between tides and the BYORP effect creates dramatic evolutionary pathways that lead to interesting end states including stranded widely separated asynchronous binaries or tightly iv bound synchronous binaries, which occupy a revealing equilibrium. The first results of observations are reported that confirm the theoretically predicted equilibrium. In the final study, the binary asteroid evolutionary model is embedded in a model of the entire Main Belt asteroid population. The asteroid population evolution model includes the effects of collisions as well as the YORP-induced rotational fission. The model output is favorably compared to a number of observables. This allows inferences to be made regarding the free parameters of the model including the most likely typical binary lifetimes. These studies can be combined to create an overall picture of asteroid evolution. From only the power of sunlight, an asteroid can transform into a myriad number of different states according to a few fundamental forces. Dedication I dedicate this thesis to my family: Bob, Renee, Alec, Tess and Elli. vi Acknowledgements For the construction of this thesis and my graduate career in general, I would like to acknowl- edge a number of people. Foremost, I acknowledge the incredible guidance provided by my advisor Daniel J. Scheeres. I found both challenge and inspiration inside his laboratory, the Celestial and Spaceflight Mechanics Lab, and amongst his other students including Jay McMahon, Masatoshi Hirabayashi, Paul Sanchez, Christine Hartzell, Marcus Holtzinger, Zubin Olikara, Yu Takahashi, Dylan Boone, and Kohei Fujimoto. Within the Astrophysical and Planetary Sciences Department, I have found many individuals that have provided positive role models, good advice, and friendship: John Bally, John Stocke, Jeremy Darling, Robbie Citron, Julia Kamenetzky, Susanna Kohler, Erik Larson, Adam Ginsburg, Tyler Mitchell, Tim Ellsworth-Bowers, and Jessica Lovering. I would like to specially acknowledge the members of my thesis committee: Phil Armitage, Larry Esposito, Glen Stewart, Mike Shull, Seth Hornstein. I must also acknowledge the assistance of a number of individuals outside of the univer- sity including Petr Pravec, Petr Scheirich, Francesco Marzari, and Alessandro Rossi. Special ac- knowledgements to the observatory staffs of Apache Point Observatory and Kitt Peak National Observatory especially Russet McMillan and Dianne Harmer. Lastly, I must acknowledge the role of my family and friends in keeping me motivated and sane especially Caroline Sczcepanski, Drew Eisenberg, Robbie Citron and Erik Larson. Contents Chapter 1 Study of Post-rotational Fission Dynamics 1 1.1 Introduction . 1 1.1.1 Observed NEA Classes . 1 1.1.2 Motivation . 5 1.2 Methods . 6 1.2.1 Initial Conditions . 6 1.2.2 Rotational Fission Model . 7 1.2.3 Dynamical Model . 8 1.3 Results . 10 1.3.1 Chaotic Binary . 10 1.3.2 Two Regimes . 12 1.3.3 High Mass Ratio Regime . 15 1.3.4 Low Mass Ratio Regime . 18 1.3.5 Secondary Spin Fission . 22 1.3.6 Chaotic Ternaries . 25 1.3.7 Stable Binaries . 30 1.3.8 Asteroid Pairs . 38 1.4 Discussion . 38 1.5 Conclusion . 40 viii 1.6 Derivation of the Two-Body Equations of Motion . 41 1.7 Derivation of the Three-Body Equations of Motion . 45 1.8 Derivation of the Tidal Theory . 49 1.9 Secondary Fission Condition . 50 1.10 Impact Mass Redistribution . 51 1.11 Modeling Tidal Timescales . 52 1.12 Limit on the Mass Ratio of Next Secondary Fission . 52 2 Study of the Role of Non-gravitational and Tidal Torques on Binary Asteroid Systems 54 2.1 Introduction . 54 2.2 Asynchronous Binary Evolution . 60 2.2.1 The YORP effect and mutual body tides . 61 2.2.2 The tidal YORP coefficient . 63 2.2.3 Application to systems with unknown status . 72 2.3 Synchronous Asteroid Evolution . 73 2.3.1 Tidal Evolution . 74 2.3.2 BYORP Evolution . 76 2.3.3 Joint Evolution . 77 2.4 Joint Expansive Evolution . 78 2.4.1 Expansive De-synchronization Hypothesis . 79 2.4.2 Adiabatic Invariance . 81 2.4.3 Derivation of the Adiabatic Invariance . 81 2.4.4 Onset of Circulation . 86 2.4.5 Libration Energy . 86 2.4.6 Derivation of the libration tides . 86 2.4.7 Energy Dissipation in a number of systems . 90 2.4.8 Libration growth due to BYORP effect . 90 ix 2.4.9 Comparison to Observation . 91 2.5 Joint Opposing Evolution . 92 2.5.1 Implications for the Synchronous Binary Asteroid Population: . 94 2.5.2 Proposed Equilibrium Hypothesis . 97 2.5.3 Test of the Hypothesis . 98 2.5.4 Observation Design and Methods . 99 2.5.5 First Results . 102 3 Study of the Effects of Rotational Fission on the Main Belt Asteroid Population 105 3.1 Introduction . 105 3.2 Single Asteroid Evolution . 108 3.2.1 YORP Evolution . 109 3.2.2 Collisional Evolution . 110 3.2.3 Spin Limits . 112 3.2.4 Outcomes of Rotational Fission . 115 3.2.5 Mass Ratio Fraction . 118 3.3 Binary Asteroid Evolution . 120 3.3.1 \Instantaneous" Binary Evolution . 122 3.3.2 \Long-term" Binary Evolution . 124 3.3.3 Binaries and Collisions . 140 3.3.4 Contact Binaries . 140 3.3.5 Asteroid Pair Observability . 141 3.4 Results of the asteroid population evolution model . 141 3.4.1 Steady-State Binary Fraction . 142 3.4.2 Steady-State Mass Ratio Fraction . 145 3.4.3 Contact Binary Fraction . 150 3.4.4 Best Fit Parameters . 150 x 3.5 Discussion . 154 Bibliography 155 Appendix Chapter 1 Study of Post-rotational Fission Dynamics 1.1 Introduction The Near-Earth asteroid (NEA) population has a relatively large amount of data compared to other small body populations, including detailed information on asteroid figures and binary struc- ture, often made possible through the combination of lightcurve and radar techniques. Observers have discovered a wide and complex set of asteroid systems that before this study have not been tied together into a coherent theory. The emergence of radiative forces as a major evolutionary mechanism for small bodies, in particular for NEA systems due to their small size and proximity to the Sun, makes the development of such a theory possible. A simple model of NEA evolution constructed from the Yarkovsky-O'Keefe-Radzievskii- Paddack (YORP) and binary YORP (BYORP) effects, \rubble pile" asteroid geophysics, and gravitational interactions can incorporate all of the diverse observed asteroid classes as shown in Figure 1.1: synchronous binaries, doubly synchronous binaries, contact binaries, asteroid pairs, re-shaped asteroids, and stable ternaries. 1.1.1 Observed NEA Classes Binary asteroid systems comprise a significant fraction (15 4%) of the NEA population (Mar- ± got et al., 2002; Pravec et al., 2006) and include all compositional classes and size scales (Pravec and Harris, 2007). Most of these systems are synchronous binaries{the orbital and secondary spin periods are equal, but the primary has a faster spin rate. Observed synchronous systems have mass 2 YORP Process Tidal Process 5 6 ContactC ttB Binary 10 10 yrs 104 106 yrs ∼ − ∼ − BYORPBYORP ProcessProc q 0.2 105 106 yyrsrs ∼ − Chaotic Binary Doubly Synchronousous Binary Asteroid Pair Tidal Process 106 107 yrs ∼ − ChaoticChaotic TernarTer ary Stable.
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