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I have a conceptual and mathematical question about gases in stars.

The information we have from stars is due to the motion of particles in one dimension: along our line of sight.

We assume that this motion is isotropic and that regardless of where on the star we look, we'll get the same motion.

So, when calculating the temperature of the star's chromosphere, do we use the one dimensional kinetic energy E=1/2kT, the three-dimensional kinetic energy E=3/2kT or the average kinetic energy E=kT to equate to 1/2mv^2, where v is the one dimensional velocity?