deletions | additions       diff --git a/PH1 stable?.tex b/PH1 stable?.tex  index cc6adf6..cc99a46 100644  --- a/PH1 stable?.tex  +++ b/PH1 stable?.tex 
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\end{equation}.  So, $a \stackrel{?}{>} a_c$,  \begin{equation}  0.634 \stackrel{\checkmark}{>} 0.0622  \end{equation}! 0.0622!  \end{equation}  This means for an inner region orbit the planet would be stable. however, the planet is orbiting both of the binary stars which means it is an outer orbit so we will next determine its stability with outer region calculations. \subsection{Semimajor Axis Outer Region}  The planet's semimajor axis, eccentricity, the stars' mass ratio, and semimajor axis are all the same as in the last equation. Using Holman & Wiegert's outer region best fit line: $a_c =1.6+5.1e+(-2.22)e^2 +4.12 \mu +(-4.27)e \mu +(-5.09)\mu ^2 +4.61e^2 \mu ^2 $ we get   \begin{equation}  a_c =1.6+5.1e+(-2.22).0539^2 +4.12(.211) +(-4.27)(.0539)(.211) +(-5.09)(.211^2 )+4.61(.0539^2 )(.211^2 )=3.921  \end{equation}  So, $a \stackrel{?}{>} a_c$,  \begin{equation}  0.634 \stackrel{x}{>} 3.921,  \end{equaiton}  which means for an outer region orbit, the planet is \textit{not} stable.  \subsection{Taking into Account the Second Binary}  The last two calculations are derived from simulations involving only two stars, but PH1 is a four star system so the calculations may not be accurate. To get a better understanding of the system's actual stability, we will make a few generalizations. First, we will consider each binary as a single mass. Then using that assumption, we will consider the planet as a test particle with an inner orbit. Lastly, we will make a final calculation considering the second binary as a test particle with an outer orbit.  \begin{tabular}{ c c c c }  & Binary 1 & Planet & Binary 2 \\   Combined Mass & 1.936 & - & 1.5 \\   Semimajor Axis & - & 0.634 & 1000 \\   Eccentricity & - & 0.0539 & 0.5 \\   \end{tabular}