deletions | additions       diff --git a/Eccentricities.tex b/Eccentricities.tex  index ea946aa..f635a48 100644  --- a/Eccentricities.tex  +++ b/Eccentricities.tex 
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\begin{equation}  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_ 1,000,000,000  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.