If you know the speed of the photon -- and you do! -- then you can figure out the time it takes for the photon to make the trip. Assume that the average mean free path of a photon everywhere in the Su...If you know the speed of the photon -- and you do! -- then you can figure out the time it takes for the photon to make the trip. Assume that the average mean free path of a photon everywhere in the Sun is the same as the mean free path in the photosphere. Assume that the average mean free path of a photon everywhere in the Sun is the same as the mean free path in the core the Sun.
\[\begin{split} \ln P\ns_{N,X}&\simeq N\ln N - N - \half N (1+x) \ln\Big[\half N (1+x)\Big] + \half N (1+x) \\ & - \half N (1-x) \ln\Big[\half N (1-x)\Big] + \half N (1-x) + \half N(1+x)\,\ln p + \hal...\[\begin{split} \ln P\ns_{N,X}&\simeq N\ln N - N - \half N (1+x) \ln\Big[\half N (1+x)\Big] + \half N (1+x) \\ & - \half N (1-x) \ln\Big[\half N (1-x)\Big] + \half N (1-x) + \half N(1+x)\,\ln p + \half N(1-x)\,\ln q \\ &= -N\Big[ \big(\frac{1+x}{2}\big) \ln\big(\frac{1+x}{2}\big) + \big(\frac{1-x}{2}\big) \ln\big(\frac{1-x}{2}\big) \Big] +N\Big[\big(\frac{1+x}{2}\big)\ln p + \big(\frac{1-x}{2}\big)\ln q\Big]\ . \end{split}\]
