deletions | additions       diff --git a/The_reason_for_the_lengthy__.tex b/The_reason_for_the_lengthy__.tex  index 9378da5..6840680 100644  --- a/The_reason_for_the_lengthy__.tex  +++ b/The_reason_for_the_lengthy__.tex 
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The second simulation is focusing on the outer region --- meaning the planet is orbiting both stars --- using $\mu=0.3, e=0.4$. This follows an opposite pattern to that of the first simulation, and the semimajor axes are much bigger (this makes sense since the planet is orbiting two stars now instead of one). Holman and Wiegert start this simulation at $a=3.1$ and run it through $a=4.0$. This time, as the semimajor axis gets bigger, the stability increases. There is a strange phenomenon between $a=3.6$ and $a=3.8$. At $a=3.6$, every planet is stable for 10,000 binary periods but at $a=3.7$ the median number of periods drops back down to 3,500. Then at $a=3.8$, the planets all become stable again. So it seems that the critical semimajor axis is 3.8, but there is also a region of stability at 3.6.    \subsubsection{Comparison with Earlier Work}  When looking at previous simulations done by Dvorak et al., Holman and Wiegert again found their results were similar. Holman and Wiegert found a best fit line for the critical semimajor axis of  \begin{equation}  a_c = 2.37+2.76e-1.04e^2 ,  \end{equation}  and Dvorak et al. found   \begin{equation}  a_c = 2.278+3.824e-1.71e^2 .  \end{equation}