Hydrostatic equilibrium and opacity
===================================

Below is a partial listing of a model of the solar photosphere.
Estimate, using the equation of hydrostatic equilibrium, the gas
pressure in the depth point which has a temperature which is most
similar to the effective temperature.

What is the probability for a typical photon to escape into space
if it moves straight up towards the surface from this depth?

"g" is the surface gravity in units of cm/s2

1 dyn = 1 g cm/s2 (Michelle has a link to cgs units at her course page)

Tau(Ross) and Kappa(Ross) are the Rosseland mean optical depth
and Rosseland mean opacity, respectively.

The Sun          Teff= 5780.   log g= 4.44   [Fe/H]=0.0
==========================================================
 i Tau(Ross)   T      Pgas  Kappa(Ross)   Rho      depth
      [1]     [K]  [dyn/cm2]  [cm2/g]   [g/cm3]     [cm]
==========================================================
 1 6.310E-05 4336. 7.517E+02 4.237E-03 2.716E-09 0.000E+00 
 2 1.000E-04 4369.           5.194E-03 3.467E-09 2.628E+06 
 3 1.585E-04 4409.           6.370E-03 4.425E-09 5.290E+06 
 4 2.512E-04 4450.           7.820E-03 5.650E-09 7.984E+06 
 5 3.981E-04 4491.           9.607E-03 7.216E-09 1.071E+07 
 6 6.310E-04 4532.           1.181E-02 9.220E-09 1.345E+07 
 7 1.000E-03 4571.           1.453E-02 1.178E-08 1.623E+07 
 8 1.585E-03 4610.           1.788E-02 1.506E-08 1.902E+07 
 9 2.512E-03 4647.           2.200E-02 1.926E-08 2.184E+07 
10 3.981E-03 4684.           2.707E-02 2.462E-08 2.467E+07 
11 6.310E-03 4722.           3.331E-02 3.147E-08 2.753E+07 
12 1.000E-02 4761.           4.097E-02 4.020E-08 3.041E+07 
13 1.585E-02 4806.           5.037E-02 5.133E-08 3.332E+07 
14 2.512E-02 4858.           6.189E-02 6.544E-08 3.625E+07 
15 3.981E-02 4923.           7.602E-02 8.325E-08 3.923E+07 
16 6.310E-02 5005.           9.338E-02 1.056E-07 4.225E+07 
17 1.000E-01 5112.           1.149E-01 1.333E-07 4.533E+07 
18 1.585E-01 5252.           1.425E-01 1.671E-07 4.847E+07 
19 2.512E-01 5440.           1.817E-01 2.067E-07 5.165E+07 
20 3.162E-01 5552.           2.100E-01 2.283E-07 5.319E+07 
21 3.981E-01 5683.           2.498E-01 2.502E-07 5.470E+07 
22 5.012E-01 5833.           3.081E-01 2.711E-07 5.614E+07 
23 6.310E-01 6004.           3.959E-01 2.901E-07 5.748E+07 
24 7.943E-01 6197.           5.309E-01 3.058E-07 5.870E+07 
25 1.000E+00 6416.           7.400E-01 3.175E-07 5.977E+07 
26 1.259E+00 6661.           1.067E+00 3.246E-07 6.069E+07 
27 1.585E+00 6941.           1.596E+00 3.269E-07 6.148E+07 
28 1.995E+00 7276.           2.516E+00 3.238E-07 6.212E+07 
29 2.512E+00 7594.           3.798E+00 3.194E-07 6.265E+07 
30 3.162E+00 7867.           5.333E+00 3.157E-07 6.311E+07 
31 3.981E+00 8100.           7.061E+00 3.132E-07 6.354E+07 
32 5.012E+00 8302.           8.961E+00 3.117E-07 6.396E+07 
33 6.310E+00 8482.           1.103E+01 3.110E-07 6.438E+07 
34 7.943E+00 8646.           1.330E+01 3.111E-07 6.481E+07 
35 1.000E+01 8798.           1.578E+01 3.119E-07 6.527E+07 
==========================================================

A suggested solution will be shown next time.