-
Notifications
You must be signed in to change notification settings - Fork 1
/
main_thesis.lof
57 lines (57 loc) · 9.08 KB
/
main_thesis.lof
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
\contentsline {part} {\figurenameToC }{\relax }{}
\addvspace {10\p@ }
\addvspace {10\p@ }
\contentsline {figure}{\numberline {2.1}{\ignorespaces Diagram of solar radiation, absorption, and YORP re-radiation\relax }}{10}{}%
\contentsline {figure}{\numberline {2.2}{\ignorespaces Body frame diagram which shows $\hat {u}$, the sun-pointing vector, $\hat {u}_{||xy}$, the projection of the sun-pointing vector into the body x-y plane, $\hat {u}_{\perp }$, the perpendicular vector to the sun-pointing vector, the body frame unit vectors $\hat {x}_B, \hat {y}_B$, and $\hat {z}_B$, as well as the solar inclination angle $i_s$, the longitude of the ascending node $\Omega _s$, and the spin pole obliquity angle $\eta $. \relax }}{13}{}%
\contentsline {figure}{\numberline {2.3}{\ignorespaces First-order YORP spin coefficient variation per facet on Bennu and Itokawa\relax }}{16}{}%
\contentsline {figure}{\numberline {2.4}{\ignorespaces Wedge shape boulders provide asymmetry that induces YORP effect\relax }}{17}{}%
\contentsline {figure}{\numberline {2.5}{\ignorespaces Boulder model with frame\relax }}{18}{}%
\contentsline {figure}{\numberline {2.6}{\ignorespaces Difference of per-facet distance from body center of mass and the average radius for three asteroid shape models: Bennu, Ryugu, and Itokawa. Darker points represent equatorial facets. Itokawa exhibits the greatest variation over longitude.\relax }}{19}{}%
\contentsline {figure}{\numberline {2.7}{\ignorespaces Cumulative number of boulders per square km\relax }}{22}{}%
\contentsline {figure}{\numberline {2.8}{\ignorespaces Orientation of Prism Boulder Rotating from West to East, from $0$ to $\pi $\relax }}{27}{}%
\contentsline {figure}{\numberline {2.9}{\ignorespaces Sinusoidal relationship of boulder orientation to YORP torque. Asymmetric boulder at equator and perfectly tangent to spin pole\relax }}{29}{}%
\contentsline {figure}{\numberline {2.10}{\ignorespaces Frequency distribution of YORP with 500 random boulder populations for Bennu\relax }}{32}{}%
\contentsline {figure}{\numberline {2.12}{\ignorespaces Bennu distribution comparison of normalized frequencies of boulder latitude and orientation in the > 1\% YORP spin coefficient boulder population.\relax }}{33}{}%
\contentsline {figure}{\numberline {2.11}{\ignorespaces Size distribution and mean diameter of boulders where $C_{0,z,i} > 1\%$ on Bennu\relax }}{33}{}%
\contentsline {figure}{\numberline {2.13}{\ignorespaces Frequency distribution of total boulder YORP spin coefficients for Itokawa\relax }}{35}{}%
\contentsline {figure}{\numberline {2.14}{\ignorespaces Size distribution and mean diameter of boulders where $C_{0,z,i} > 1\%$ for Itokawa\relax }}{36}{}%
\contentsline {figure}{\numberline {2.15}{\ignorespaces Itokawa distribution comparison of normalized frequencies of boulder latitude and orientation in the > 1\% YORP spin coefficient boulder population.\relax }}{37}{}%
\contentsline {figure}{\numberline {2.16}{\ignorespaces Change in Bennu's global YORP spin coefficient with boulders, shown in Fig.\ref {fig:bennu_results}, when removing boulders < 1m, roughly $99\%$ of original population.\relax }}{39}{}%
\contentsline {figure}{\numberline {2.17}{\ignorespaces Overlaid distribution of normalized YORP with and without 1 m boulders\relax }}{39}{}%
\contentsline {figure}{\numberline {2.18}{\ignorespaces Boulder spin coefficients for Bennu, separated by size bins. Percentages represent the proportion of boulders in each bin to the size of the sample population.\relax }}{40}{}%
\contentsline {figure}{\numberline {2.19}{\ignorespaces Change in global YORP spin coefficient when enforcing a percentage of boulders with a westward orientation bias. Each profile is a histogram of global YORP spin coefficients. The black histogram represents the 100\% west bias for all boulders\relax }}{41}{}%
\contentsline {figure}{\numberline {2.20}{\ignorespaces Change in asteroid global YORP spin coefficients when removing boulders outside of $\pm 30^{\circ }$ latitude, varying the percentage until $100\%$ are outside of the the bounds equivalent to a liberal cushion about Bennu's Roche lobe\relax }}{43}{}%
\contentsline {figure}{\numberline {2.21}{\ignorespaces Area reduced by shaving off triangle areas from boulder tops and the subsequent reduction in the YORP spin coefficient\relax }}{45}{}%
\contentsline {figure}{\numberline {2.22}{\ignorespaces Graphical representation of area removal causing reduced YORP torque for more realistic boulder shapes where the percentage is the amount of face area leftover after removal versus the original flat wedge face\relax }}{45}{}%
\contentsline {figure}{\numberline {2.23}{\ignorespaces Normalized CYORP Contribution scaled by crater diameter frequency\relax }}{47}{}%
\contentsline {figure}{\numberline {2.24}{\ignorespaces Incorporating the assumption of smooth transitions below and above the ideal thermal inertia length, $L_{cond}$ with a logarithmic scale factor\relax }}{48}{}%
\contentsline {figure}{\numberline {2.25}{\ignorespaces Comparison of analytical YORP spin components for Bennu as a function of obliquity\relax }}{50}{}%
\contentsline {figure}{\numberline {2.26}{\ignorespaces Comparison of mean and standard deviation from several YORP models\relax }}{51}{}%
\contentsline {figure}{\numberline {2.27}{\ignorespaces Differing amounts of YORP spin acceleration for boulders within 4 degrees in longitude but varying latitudes\relax }}{53}{}%
\contentsline {figure}{\numberline {2.28}{\ignorespaces The change in YORP spin acceleration from boulder motion with the latitude degree change shown on the x-axis\relax }}{54}{}%
\addvspace {10\p@ }
\contentsline {figure}{\numberline {3.1}{\ignorespaces Solar Inclination Rates for entire asteroid with 5000 boulders added in 500 different configurations of size, orientation, and location on Bennu and Itokawa shape models\relax }}{59}{}%
\contentsline {figure}{\numberline {3.2}{\ignorespaces Boulder diameter power laws: dashed line is the model and histogram represents the population sampled from power law\relax }}{60}{}%
\contentsline {figure}{\numberline {3.3}{\ignorespaces Full histogram of boulder diameters compared to the subsampled set that represents boulders contributing $> 1\%$ to solar inclination change\relax }}{60}{}%
\contentsline {figure}{\numberline {3.4}{\ignorespaces Varying bins of percent contribution to solar inclination change, with darker colors representing higher \% change from a single boulder, distributed over dominant pointing direction\relax }}{61}{}%
\contentsline {figure}{\numberline {3.5}{\ignorespaces Boulder locations separated by percent contribution, showing a departure of boulders from equator at rates of > 1\% and > 10\% for both bodies\relax }}{62}{}%
\contentsline {figure}{\numberline {3.6}{\ignorespaces Differing amounts of YORP obliquity acceleration for boulders within 4 degrees in longitude but varying latitudes\relax }}{63}{}%
\contentsline {figure}{\numberline {3.7}{\ignorespaces The change in YORP obliquity rate from boulder motion with the latitude degree change shown on the x-axis\relax }}{64}{}%
\addvspace {10\p@ }
\contentsline {figure}{\numberline {4.1}{\ignorespaces Example Images\relax }}{68}{}%
\contentsline {figure}{\numberline {4.4}{\ignorespaces Four Edge Results Overlaid in Image Space\relax }}{70}{}%
\contentsline {figure}{\numberline {4.3}{\ignorespaces 25 Examples of Canny Parameters and Impact on Edge Detection\relax }}{71}{}%
\contentsline {figure}{\numberline {4.5}{\ignorespaces Limb and Terminator in Bennu Mission Image\relax }}{72}{}%
\contentsline {figure}{\numberline {4.6}{\ignorespaces Geometry of Two Intersecting Planes\relax }}{73}{}%
\contentsline {figure}{\numberline {4.7}{\ignorespaces Geometric Depiction of Patch Crossing Calculations\relax }}{75}{}%
\contentsline {figure}{\numberline {4.8}{\ignorespaces Intersection Ray from Two Patches - Ten Sampled Points and Associated Ray Normals\relax }}{76}{}%
\contentsline {figure}{\numberline {4.9}{\ignorespaces Ball-Pivoting Surface Reconstruction Results of Itokawa and Bennu Point Clouds\relax }}{78}{}%
\contentsline {figure}{\numberline {4.10}{\ignorespaces Pre- and Post-Processed Point Cloud of Itokawa Limb-Trimmed Shape\relax }}{79}{}%
\contentsline {figure}{\numberline {4.11}{\ignorespaces Limb-based Itokawa shape compared to SPC, with surface error in units of kilometers\relax }}{80}{}%
\contentsline {figure}{\numberline {4.12}{\ignorespaces Pre- and Post-Processed Point Cloud of Bennu Limb-Trimmed Shape\relax }}{80}{}%
\contentsline {figure}{\numberline {4.13}{\ignorespaces Limb-based Bennu shape compared to SPC, with surface error in units of kilometers\relax }}{81}{}%
\contentsline {figure}{\numberline {4.14}{\ignorespaces Bennu Shape Model from Real Images, compared to SPC, surface error in kilometers\relax }}{82}{}%
\contentsline {figure}{\numberline {4.15}{\ignorespaces Test image and Library Image, Expected Match Pair\relax }}{85}{}%
\contentsline {figure}{\numberline {4.16}{\ignorespaces Test Image and Library image, Actual Match Pair\relax }}{86}{}%
\contentsline {figure}{\numberline {4.17}{\ignorespaces 2D Correlation scores between all library images and all test images, based on longitude\relax }}{87}{}%
\addvspace {10\p@ }