deletions | additions       diff --git a/PH1 stable?.tex b/PH1 stable?.tex  index 1f1f1a1..a118707 100644  --- a/PH1 stable?.tex  +++ b/PH1 stable?.tex 
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\item use Holliday and REsnick's simulation results to compare PH1b's inclination and eccentricity with that of the expected stability zones.  \end{itemize}  \subsection{Semimajor Axis Inner Region}  The planet's semimajor axis is approximately 0.634 AU. The eccentricity is $e \approx 0.0539$, and the mass ratio is $\mu=m_2 /(m_1 +m_2 )=0.408/(1.528+.408)=.211$. The binary semimajor axis is $a_b =0.1744$. So, using Holman & Wiegert's best fit equation: $a_c \begin{equation}  a_c  =[0.464+(-0.380)\mu +(-.631)e+(.586)\mu e +.15e^2 +(-0.198)\mu e^2 ]a_b $ ,  \end{equation}  we can find the critical semimajor axis, $a_c =[0.464+(-0.380).211 +(-.631).0539+(.586)(.211) .0539 +.15(.0539^2)$  $+(-0.198)(.211) .0539^2 ].1744=0.0622$  For the inner region, the test particles with a semimajor axis less than the critical semimajor axis were stable so, $a \stackrel{?}{<} a_c$,  \begin{equation} a_c \Rightarrow  0.634 \nless 0.0622  \end{equation} 0.0622$  This means for an inner region orbit the planet would not 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 \begin{equation}  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 $ ,  \end{equation}  we get   $a_c =1.6+5.1e+(-2.22).0539^2 +4.12(.211) +(-4.27)(.0539)(.211)$   $+(-5.09)(.211^2 )+4.61(.0539^2 )(.211^2 )=3.921$  So, $a \stackrel{?}{>} a_c$,  \begin{equation} a_c \Rightarrow  0.634 \ngtr 3.921  \end{equation} 3.921$  which means for an outer region orbit, the planet is \textit{not} stable.  \subsection{Taking into Account the Second Binary}