We can calculate the strength of a wind and its velocity structure by simply solving Newton’s second law
However, the force on a given parcel depends on how much radiation flux it is receiving…in other words, on its redshift, which is a function of its acceleration
Note that the force, as I’ve convinced you, is a function of the rate at which a line is blueshifted out of the Doppler shadow, which depends on how the velocity changes with distance, dv/dr, and the acceleration is proportional to this quantity through t
This is a highly non-linear set of equations to solve!
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