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\section{Introduction}  Using the Kepler Space Telescope, astronomers and planet hunters have discovered and confirmed 1020 1,020  planets from the time of  its launch in 2009 and the time of this writing. There are still over 4600 4,600  extraterrestrial objects that seem to be planets; they just have not been studied enough to be confirmed yet. Along with those confirmed and unconfirmed planets, Kepler has discovered 2165 binary star systems\cite{KeplerWebsite}. The question then becomes, though, are these binary systems stable? The goal of this paper is to \begin{enumerate}  \item Analyze Holman & Wiegert's paper \textit{Long-Term Stability of Planets in Binary Systems} \cite{Holman_1999} to fully understand what makes such a system stable and  \item Apply theses finding to the system PH1 to find if it, too is stable