# Calculating angular diameter amplitude from angular diameter variations of Cepheid variable

I'm a high school student but have as much interests in Cepheid variable as the professionalists. I'm trying to derive independent distances to Cepheid with the Baade-Wesselink method.

I got the angular diameter variations data from the paper Cepheid distances from infrared long-baseline interferometry but I'm stuck from the afterward. I want to know how equation 9 in that paper is derived. Where did the number 9.305 suddenly came up?

The equation is the following:

θLimb-darkened model angular diameter = amplitude of limb-darkened observed angular diameter + 9.305 (∆D/d)

It seems like I need that equation to derive the distance from the angular diameter values with radial velocity values.

• "This is done by applying a classical χ^2 minimization algorithm between our angular diameter measurements and a model of the star pulsation." It's simply a constant derived from fitting a model to data by minimizing the chi squared value of the fit. – zephyr Oct 13 '16 at 14:53
• @zephyr Yeah but the X^2 minimization algorithm is done for angular diameter values but in the equation 9 suddenly distance d and radial amplitude D came up! I don't get this point.. – 7_G.S.N Oct 14 '16 at 7:02
• The minimization is done for $\theta_{LD,model}$ which is a function of $d$ and $D$. That's just geometry. – zephyr Oct 14 '16 at 13:35