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\section{Eccentricities}  As the above simulations show, the semimajor axis is the independent variable in determining a planet's stability around a binary star system. It turns out, though, that the eccentricities of these planets' orbits are quite large. In Takeda and Rasio's \cite{Takeda_2005} sample of binary systems, the median eccentricity is 0.28; the largest eccentricity in our solar system is Mercury's 0.206 and our median is only 0.048 \cite{Smith_1975}. It seems, then, that a binary system requires a more eccentric orbit to be stable; as Innanen et al. found, the maximum eccentricity of a stable planet is dependent on the inclination as represented by the formula:  \begin{equation}  e_m e_\textrm{max}  \simeq \sqrt{1-\frac{5}{3} \cos^2 (i_0)} \end{equation} \cite{Innanen_1997}. "In general, as eccentricities increase...high inclination planetary orbits around a component of a binary star cannot remain stable." So, Innanen et al. ran a simulation to prove the statement. The integration was modeled after our solar system but with a second star at a distance of 400 AU and varying masses. For the integration, they considered 10^9 years without any significant orbital evolution stable. At $m_* / M_* =0.05$ (where M_* is the mass of the sun and m_* is the mass of the second star), every level of inclination was stable. Then as predicted, when the mass ratio increased, higher inclinations became unstable. At $m_* / M_* =0.1$, the planet was stable for i_0 = 0$^{\circ}$--60$^{\circ}$. For both $m_* / M_* =0.2$ and $0.4$, only inclinations of i_0 = 0$^{\circ}$--45$^{\circ}$ were stable.