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131 lines
3.8 KiB
TeX
131 lines
3.8 KiB
TeX
\documentclass[12pt]{article}
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%%%%%%%%%Packages%%%%%%%%%%%%%%%
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\usepackage{geometry}
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\geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
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\setlength{\parskip}{7pt}
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\setlength{\parindent}{6pt}
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%\setlength{\parindent}{0pt}
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\usepackage{setspace}
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\doublespacing
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\usepackage{amsmath}
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\usepackage{mathtools}
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\usepackage{amsthm}
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\usepackage{amssymb}
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\usepackage{thmtools, thm-restate}
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\usepackage{cleveref}
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%Add institute to title
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\usepackage{etoolbox}
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\makeatletter
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\providecommand{\institute}[1]{% add institute to \maketitle
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\apptocmd{\@author}{\end{tabular}
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\par
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\begin{tabular}[t]{c}
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#1}{}{}
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}
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\makeatother
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%%%%%%%%%%%%SETUP THEOREMS%%%%%%%%%%%%%%%%%%%%%%
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\declaretheorem[within=subsection]{theorem}
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%%%%%%%%%%%%FORMATTING%%%%%%%%%%%%%%%%%%%%%
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%Math formatting
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\newcommand{\bb}[1]{\mathbb{#1}}
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\newcommand{\parder}[3]{\ensuremath{ \frac{\partial^{#3} #1}{\partial #2~^{#3}}}}
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\newcommand{\likeli}[2]{\text{L}\left( #1 | #2 \right)}
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\newcommand{\induction}[3]{
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\textbf{#1}\\
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\underline{Basis Step:}\\
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#2
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\underline{Induction Step:}\\
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#3
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}
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\newcommand{\mle}[1]{\hat{#1}_{\text{MLE}}}
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\newcommand{\pr}[1]{\text{Pr}\left( #1 \right)}
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\newcommand{\thm}[3]{
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\begin{restatable}[#1]{theorem}{#2}
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\label{thm:#2}
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#3
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\end{restatable}
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}
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%These are some formatting/reminder commands
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\newcommand{\todo}[1]{
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\textbf{\#TODO: \underline{#1}}
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}
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\newcommand{\define}[1]{%for now just highlight, in future, link.
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\underline{\textbf{#1}}
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}
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%%%%%%%%%%%%%%%Math Operators%%%%%%%%%%%%%%%%%%
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\DeclareMathOperator{\argmax}{argmax}
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\DeclareMathOperator*{\plim}{plim}
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\DeclareMathOperator*{\adj}{adj}
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%%%%%%%%%%%%%%INTERNAL REFERENCES%%%%%%%%%%%%%%
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\newcommand{\eref}[1]{Eq. \ref{#1}} %Already defined
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%%%%%%%%%%%%%%Bibliography%%%%%%%%%%%%%%%
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\usepackage[backend=biber,sorting=none,style=numeric]{biblatex}
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\addbibresource{References.bib}
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%%%%% Adjust this at some point.
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%This is how to perform citations.
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% Use \cite{ref} to get a numerical reference to the bibliography
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% Use \citetitle{ref} to get the title as a citation
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% Use \fullcite{ref} to insert the full reference.
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% Use \autcite{ref} to get formatted references
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%%%%%%%%%%%%%%Other commands%%%%%%%%%%%%%%
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\providecommand{\keywords}[1]{\textbf{\textit{Keywords:}} #1}
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\providecommand{\jel}[1]{\textbf{\textit{JEL Codes:}} #1}
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%%%%%%%%%%%%CUSTOMIZATION%%%%%%%%%%%%%%%%%%%%%%
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\title{Dynamic Launch Decisions for Satellite Constellation Operators}
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\author{William King}
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\institute{Washington State University}
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\begin{document}
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\maketitle
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\begin{abstract}
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Over the last 10 years new technology has make low earth orbits (LEOs) more accessible, and
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the resulting increase in LEO satellites has increased the risk of collision.
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Because debris in orbit generates more debris through collisions with objects in orbit
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and the debris created during launch and operation imposes a negative externality
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on other operators,
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optimal use of orbits is believed to not occur under free entry.
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This paper develops a dynamic model of satellite operation incorporating two effects not considered
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in previous models.
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The first effect is complementarity between satellites within the same operator's fleet (called a constellation).
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The second effect is collision avoidance efficiencies that exist within constellations.
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The primary result is a theoretical model and the resulting analysis of the difference in survival ratios between
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constellation operators and society.
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\end{abstract}
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\keywords{Orbits, Pollution, Economies of Scale, Externality }
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\jel{Q29, Q58, L25}
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\textbf{Acknowledgments:} I am the sole author and have recieved no contributions from others as of yet.
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This paper has been approved for dual submission in Econs 529 and Econs 594 by the instructors.
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\end{document}
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