Jordan Sligh edited section_Creation_of_a_Magnetosphere__.tex  over 8 years ago

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where $\rho_c$ is the charge density of the outer core and $\omega = 2\pi/2t_"con"$ where $t_con$ 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 $T_inner$ as a function of the the outer core temperature $T_outer$.  Consolidating the necessary equations we find that  $$t_con = [T_outer/g((dT/dr)_ad-\deltaT/\deltar)^-1]$$