Changes between Version 22 and Version 23 of PlanetaryAtmospheres
- Timestamp:
- 08/31/15 15:15:43 (9 years ago)
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PlanetaryAtmospheres
v22 v23 86 86 87 87 and numerically solve the following 3 equations for $\xi_s$ and $\chi$, and $\lambda_s$ 88 || $\frac{ 1+\psi\left ( \frac{ 1 - \xi_{bow}}{\xi_s}, \lambda_s \right ) }{ 1+\psi \left ( \frac{\xi_{bow}}{\xi_p}, \lambda_p \right ) } = \frac{q \xi_{ s} \left ( 1 + \sigma_p \right ) }{\xi_{p} \left ( 1 + \sigma_s \right ) } $ ||88 || $\frac{ 1+\psi\left ( \frac{ 1 - \xi_{bow}}{\xi_s}, \lambda_s \right ) }{ 1+\psi \left ( \frac{\xi_{bow}}{\xi_p}, \lambda_p \right ) } = \frac{q \xi_{Ms} \left ( 1 + \sigma_p \right ) }{\xi_{Mp} \left ( 1 + \sigma_s \right ) } $ || 89 89 || $\chi=\chi_{bow} \frac{\phi \left ( \frac{1 - \xi_{bow}}{\xi_s}, \lambda_s \right ) }{\phi \left ( \frac{\xi_{bow}}{\xi_p}, \lambda_p \right )}$ || 90 90 || $\lambda_s=\frac{2 \xi_{Ms}}{\xi_s} $ || … … 97 97 and 98 98 99 $c _s^2=\frac{G M_p}{r_p}$ so $\frac{c_p^2}{c_s^2} = q \frac{\xi_s}{\xi_p}$99 $c^2=\frac{G M}{r \lambda}$ so $\frac{c_p^2}{c_s^2} = q \frac{\xi_s lambda_s}{\xi_p \lambda_p} = q \frac{\xi_Ms}{\xi_Mp}$ 100 100 101 101 102 $\xi_{bow}=\mbox{solve} \left [ \left ( 1 + \psi(\frac{1-\xi_{bow}}{\xi_s}) \right) \left ( 1 + \sigma_s \right ) = q \frac{\xi_ s}{\xi_p} \left ( 1 + \psi(\frac{\xi_{bow}}{\xi_p}) \right) \left ( 1 + \sigma_p \right ) \right ] $102 $\xi_{bow}=\mbox{solve} \left [ \left ( 1 + \psi(\frac{1-\xi_{bow}}{\xi_s}) \right) \left ( 1 + \sigma_s \right ) = q \frac{\xi_Ms}{\xi_Mp} \left ( 1 + \psi(\frac{\xi_{bow}}{\xi_p}) \right) \left ( 1 + \sigma_p \right ) \right ] $ 103 103 104 104
