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Critical System Engineering Analysis For CRITICAL SYSTEM ENGINEERING ANALYSES FOR PLANETARY DEFENSE by Warren G. Greczyn B.S. in Aerospace Engineering, December 1986, The Pennsylvania State University M.S. in Engineering Science and Mechanics, August 1989, The Pennsylvania State University A Dissertation submitted to the Faculty of The School of Engineering and Applied Science of The George Washington University in partial satisfaction of the requirements for the degree of Doctor of Science January 31, 2006 Dissertation directed by Dr. David F. Chichka Assistant Professor of Engineering and Applied Science Abstract The deflection of asteroid and comet Earth-impact threats is studied, and the kinematic requirements for threat object deflections that prevent Earth impact are characterized. This paper uses direct solutions of Kepler’s equation coupled to an Earth gravitational model to determine threat object pre- and post-deflection orbital behaviors. The primary defense scenario considered is the deflection of asteroid threats through the application of a 1 cm/s velocity change, a level generally accepted by the planetary defense community as achievable in the near term. Threat displacement at Earth passage is assessed as the primary metric of deflection success. Key characteristics of defense system performance are analyzed, including optimal selection of the timing, direction, and required directional accuracy of successful deflections, along with duration of the threat engagement window and the effects of variations in deflection velocity. Deflected threat behaviors are developed parametrically for a representative threat set that spans the full range of observed hazardous threat orbits. The resulting trends are presented in conjunction with a broad-based treatment of the threat itself, including its origins, populations, general behaviors, and the history of both Earth impact and of efforts to develop an understanding of potential impactors. This is done with the aim of capturing the motivation for planetary defense in general and of making this paper a more complete and useful tool in the design of planetary defense systems, missions, and programs. ii Table of Contents Abstract............................................................................................................................... ii Table of Contents...............................................................................................................iii List of Figures..................................................................................................................... v List of Tables ..................................................................................................................... xi Chapter 1 - Introduction...................................................................................................... 1 Chapter 2 - The Threat........................................................................................................ 3 2.1 Asteroids ....................................................................................................................... 3 2.2 Comets .......................................................................................................................... 5 2.3 Earth Impact History................................................................................................... 10 2.4 Probability and Consequences of Earth Impact.......................................................... 17 2.5 Our Reaction – General .............................................................................................. 20 2.6 Our Reaction – Surveillance ....................................................................................... 22 2.7 Our Reaction – Mitigation .......................................................................................... 28 2.8 Threat Structure and Response ................................................................................... 33 2.9 Near Earth Object Orbits: Comets .............................................................................. 38 2.10 Near Earth Object Orbits: Asteroids......................................................................... 40 Chapter 3 - Mitigation Modeling ...................................................................................... 46 3.1 Representative Threat Set........................................................................................ 46 3.2 Threat Displacement Simulation ............................................................................. 60 Chapter 4 - Threat Displacement Simulation Products..................................................... 73 4.1 Asteroid Example Case ........................................................................................... 73 4.2 Representative Threat Set Analysis Points.............................................................. 87 iii 4.3 Overall Asteroid Deflection Opportunities.............................................................. 89 4.4 Latest Possible Asteroid Deflection Before Earth Impact....................................... 91 4.5 Threat Displacement Margin Through Earlier Asteroid Deflection........................ 92 4.6 Optimal Deflection Direction .................................................................................. 97 4.8 Deflection Window Duration ................................................................................ 105 4.9 Effect of Various Imparted Velocity Changes on Displacements......................... 110 4.10 Threat Displacement Behavior Over a Range of Threat Inclinations ................. 113 4.11 Comet Deflection Example Case......................................................................... 115 4.12 Comets and Inclination........................................................................................ 122 Chapter 5 - Mission Design Conclusions ....................................................................... 124 5.1 Mission Design Considerations............................................................................. 124 5.2 Follow-on Work .................................................................................................... 128 References....................................................................................................................... 130 Appendix A – Perihelion Offset ..................................................................................... 135 Appendix B – Simulation Code Description .................................................................. 150 iv List of Figures Figure 2-1: Oort Cloud and Kuiper Belt..............................................................................7 Figure 2-2: Size Distribution of Discovered Earth Impact Craters....................................13 Figure 2-3: The Tunguska Event Overlaid on Washington D.C. Metro Area...................15 Figure 2-4: Updated Hazard Curve....................................................................................18 Figure 2-5: Cumulative Total of Known Near-Earth Asteroids vs. Time .........................23 Figure 2-6: Propellant Required for Rocket Engine Deflection of a Threat Object ..........................................................................................................................32 Figure 2-7: Highlighted Impact Craters on Eros ...............................................................35 Figure 2-8: Rotational Motion of Toutatis.........................................................................37 Figure 2-9: Common Orbits for Short Period Comets.......................................................39 Figure 2-10: Extents of Example Aten Orbits ...................................................................42 Figure 2-11: Range of Example Apollo Orbits..................................................................43 Figure 2-12: Representative Amor Orbits..........................................................................45 Figure 3-1: Distribution of Perihelia for Observed PHAs .................................................47 Figure 3-2: Inner Orbit of PHA 2004 UL ..........................................................................48 Figure 3-3: Distribution of Aphelia for Observed PHAs...................................................49 Figure 3-4: Distribution of Aphelia for Observed PHAs Less Outlier ..............................50 Figure 3-5: Orbit of Apollo 1999 XS35 Looking Down on Ecliptic.................................51 Figure 3-6: Orbit of Apollo 1999 XS35 – Oblique View ..................................................51 Figure 3-7: Distribution of Eccentricity for Observed PHAs ............................................52 Figure 3-8: Distribution of Inclination for Observed PHAs ..............................................53 v Figure 3-9: Attainable Single-Passage Inclination Changes for a Kuiper Object Encountering Earth..........................................................................................55 Figure 3-10: Histogram of Radii of Perihelion for Observed PHAs .................................56 Figure 3-11: Histogram of Eccentricities for Observed PHAs ..........................................56 Figure 3-12: Histogram of Inclinations for Observed PHAs.............................................57 Figure 3-13: Scatter Plot of Eccentricity vs. Inclinations for Observed PHAs .................59 Figure 3-14: Scatter Plot of Perihelion vs. Inclination for Observed PHAs......................59 Figure 3-15: Representation of Process
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