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Matteo Cantiello edited MLT.tex
over 9 years ago
Commit id: 1a337ce7cfbfb80dac3832bfc9c54fbff45ef536
deletions | additions
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index 1851464..9eda2c4 100644
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\begin{equation}
\Delta \T (\Delta r) = \Delta r \, \T \bigg[ -\frac{\D \ln \T}{\D r}- \bigg(-\frac{\D \ln \T'}{\D r}\bigg)\bigg],
\end{equation}
and using the assumption of pressure equilibrium, the definitions of pressure scale height $\hp$ and the gradients $\nabla$ and $\nabla'$
we obtain
\begin{equation}
\Delta \T (\Delta r) = - \frac{\D \ln \P}{\D r} \Delta r \, \T \bigg[ \frac{\D \ln \T}{\D \ln \P}- \bigg(\frac{\D \ln \T'}{\D \ln \P}\bigg)\bigg] = \Delta r \frac{\T}{\hp}\, (\nabla - \nabla'),
\end{equation}