deletions | additions       diff --git a/section_Creation_of_a_Magnetosphere__.tex b/section_Creation_of_a_Magnetosphere__.tex  index b668469..923131e 100644  --- a/section_Creation_of_a_Magnetosphere__.tex  +++ b/section_Creation_of_a_Magnetosphere__.tex 
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Consolidating the necessary equations we find that  $t_{con} = \frac{T_{outer}}{g}[(\frac{dT}{dr})_ad-\frac{\delta{T}}{\delta{r}})^{-1}]$ \frac{T_{outer}}{g}[(\frac{dT}{dr})_{ad}-\frac{\delta{T}}{\delta{r}})^{-1}]$  where the adiabatic gradient  $(dt/dr)_ad $(\frac{dT}{dr})_{ad}  = (\gamma - 1)/\gamma T_outer/P_c dP/dr$ \frac{\gamma-1}{\gamma} \frac{T_{outer}}{P_c} \frac{dP}{dr}$  and $dP/dr \frac{dP}{dr}  = -4/3\piG\rho^2R_inner$, $g=4/3\piG\rhoR_inner$, -\frac{4\pi}{3}G\rho^2R_{inner}$, $g=\frac{4\pi}{3}G\rhoR_{inner}$,  and the planet's central pressure $P_c = 2/3\piG\rho^2R_p^4$. \frac{2\pi}{3}G\rho^2R_p^4$.  Plugging in all equations and solving for $T_inner$, $T_{inner}$,  we find that $T_{inner} > 1.035T_outer$ 1.035T_{outer}$  Plugging in $T_{outer} ~= 2400K$, we see that we will need a minimum temperature of $T_inner $T_{inner}  ~= 2500K$ in order to induce convection in the outer core and create a magnetic field.