deletions | additions       diff --git a/section_Creation_of_a_Magnetosphere__.tex b/section_Creation_of_a_Magnetosphere__.tex  index 434f2ee..2b45bae 100644  --- a/section_Creation_of_a_Magnetosphere__.tex  +++ b/section_Creation_of_a_Magnetosphere__.tex 
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Because the convecting currents which generate the magnetosphere are complex and occur within the spherical outer core, we will simplify our calculations by approximating Mars' outer core as a single gigantic rotating cylinder with radius ${R_{outer core} - R_{inner core}}/2$ and height $2R_{outer core}$. With this approximation, we find Mars' magnetic dipole moment to be  $B_0 = \rho_c\omega\mu_0({R_{outer {\rho_c\omega\mu_0}/{16\pi}({R_{outer  core}-R_{inner core}}/2]^42R_{outer core}/{16\pi}$ core}}/2)^42R_{outer core}$  where $\rho_c$ is the charge density of the outer core and $\omega = 2\pi/2t_"con"$ {2\pi}/{2t_{con}}$  where $t_con$ $t_{con}$  is the convective timescale. $t_con$ is mathematically related directly to the adiabatic gradient, and using this we can find the necessary inner core temperature $T_inner$ $T_{inner}$  as a function of the the outer core temperature $T_outer$. $T_{outer}$.  Consolidating the necessary equations we find that  $$t_con $t_{con}  = [T_outer/g((dT/dr)_ad-\delta{T}/\delta{r})^-1]$$ [T_{outer}/g((dT/dr)_{ad}-\delta{T}/\delta{r})^{-1}]$  where the adiabatic gradient  $(dt/dr)_ad $(dT/dr)_{ad}  = (\gamma {\gamma  - 1)/\gamma T_outer/P_c 1}/\gamma T_{outer}/P_c  dP/dr$ and $dP/dr = -4/3\piG\rho^2R_inner$, $g=4/3\piG\rhoR_inner$, and the planet's central pressure $P_c = 2/3\piG\rho^2R_p^4$.