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Jordan Sligh edited section_Creation_of_a_Magnetosphere__.tex
over 8 years ago
Commit id: bdbb4e07f38744fca8a9eaed3a563298ea1810d3
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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 $P_c = 2/3\piG\rho^2R_p^4$.