deletions | additions       diff --git a/section_Creation_of_a_Magnetosphere__.tex b/section_Creation_of_a_Magnetosphere__.tex  index 923131e..b82cf9f 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  $B_0 = \frac{\rho_c\omega\mu_0}{16\pi}(\frac{R_{outer core}-R_{inner core}}{2})^42R_{outer core}}{2})^4*2R_{outer  core}$ where $\rho_c$ is the charge density of the outer core and $\omega = 2\pi/2t_{con}$ where $t_{con}$ is the convective timescale. 
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$(\frac{dT}{dr})_{ad} = \frac{\gamma-1}{\gamma} \frac{T_{outer}}{P_c} \frac{dP}{dr}$  and \frac{dP}{dr} $\frac{dP}{dr}  = -\frac{4\pi}{3}G\rho^2R_{inner}$, $g=\frac{4\pi}{3}G\rhoR_{inner}$, and the planet's central pressure $P_c = \frac{2\pi}{3}G\rho^2R_p^4$. Plugging in all equations and solving for $T_{inner}$, we find that