Jordan Sligh edited section_Creation_of_a_Magnetosphere__.tex  over 8 years ago

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Consolidating the necessary equations we find that  $$t_con = [T_outer/g((dT/dr)_ad-\deltaT/\deltar)^-1]$$ where the adiabatic gradient  $(dt/dr)_ad = (\gamma - 1)/\gamma T_outer/P_c dP/dr$  and $dP/dr = -4/3\piG\rho^2R_inner$, $g=4/3\piG\rhoR_inner$, and the planet's central pressure $P_c = 2/3\piG\rho^2R_p^4$.