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\title{Summary of my work on Satellite Constellations}
\author{William King}

\begin{document}
\maketitle

\section{Introduction}
\subfile{sections/00_Introduction} %Currently from past semesters.
%roughly done 2021-07-15

%Describe sections
The paper is organized as follows.
\cref{SEC:Environment}, describes the laws of motion 
governing satellites and debris(\ref{SEC:Laws}), 
%discusses the laws of motion that govern satellite constellations and debris.
places limits on various measures of risk (\ref{SEC:Survival}),
%uses the laws of motion to put upper bounds on average, fleetwide marginal survival rates.
and reviews various definitions of kessler syndrome in 
the context of dynamic modeling, their advantages, and their disadvanteges (\ref{SEC:Kessler}).
In \cref{SEC:Models} the dynamic problem faced by constellation operators and 
social planners is first described.
Finally \cref{SEC:Computation} describes the computational approach and results.


\section{Modeling the Environment}\label{SEC:Environment}
\subsection{Laws of motion}\label{SEC:Laws}
\subfile{sections/01_LawsOfMotion} %Roughly done 2021-07-15

\subsection{Marginal survival rates}\label{SEC:Survival}
\subfile{sections/03_SurvivalAnalysis} %roughly done 2021-07-14

\subsection{Kessler Syndrome}\label{SEC:Kessler}
\subfile{sections/02_KesslerSyndrome}  %roughly done before 2021-07-14
\subfile{sections/06_KesslerRegion}  %roughly done before 2021-07-14




\section{Model}\label{SEC:Models}
\subsection{Constellation Operator's Program}\label{SEC:Operator}
\subfile{sections/04_ConstellationOperator} %TODO

\subsection{Social Planner's Program}\label{SEC:Planner}
\subfile{sections/05_SocialPlanner} %TODO

\section{Computation}\label{SEC:Computation}
\subfile{sections/07_ComputationalApproach} %TODO

\section{Conclusion}\label{SEC:Conclusion}

\newpage
\section{References}
\printbibliography
\newpage
\section{Appedicies}
\subsection{Mathematical Notation}
Needs completed.
%\subsection{Deriving Marginal Survival Rates}\label{APX:Derivations:SurvivalRates}
%\subfile{sections/apx_01_MarginalSurvivalRates} 

\subsection{Deriving Euler Equations}\label{APX:Derivations:EulerEquations}
\subfile{sections/apx_02_GeneralizedEuEqSteps} 


\subsection{Collected Assumptions and Caveats}\label{APX:CollectedAssumptions}
I hope to write a section clearly explaining assumptions, caveats, and shortcomings here.
These will later get written back into the other sections, but I want to collect them 
in a single place first.
%time periods are long enough for debris to disperse after collisions.
%Only a single type of debris
%With my current computational idea; each constellation provides the same risk to each other constellation
% That can be easily adjusted in the computational models.

\end{document}

%%% Notes to keep track of
% Possible other things to investigate
%   - Free-entry conditions: which of the following?
%       - When for every operator, the current stocks imply no more launches(x = 0).
%       - When for every type of operator, the current stocks plus an own stock of 0 imply no more launches(x = 0).
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