I Density fluctuations and the color of the sky

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The color of the sky is primarily explained by Rayleigh scattering, which requires density fluctuations in the atmosphere. Despite atoms being localized and not uniform, their density can still exhibit significant deviations, leading to blue light scattering. The discussion raises the question of whether the positions of atoms need to be correlated yet disordered for the sky to appear blue. It suggests that even in an ordered state, the inherent density fluctuations due to atomic positioning can still result in blue scattering. Ultimately, the relationship between atomic arrangement and light scattering remains a complex topic.
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From posts like this I get that the color of the sky is explained by Rayleigh scattering, but needs density fluctuations. However as atoms are not uniform and are localized, the density is
$$\rho(\mathbf r)=\sum_i \delta(\mathbf r-\mathbf r_i)$$
where ##i## sums over all the atom positions ##\mathbf r_i##. So even if the atoms were ordered and not moving in any way, the average of the density is very different from its deviations, that can be quite large (because there are deltas), and one would still have blue light scattering. Right? The fluctuations are already a given due to the form of the density.


Or do the position of the atoms needs to be correlated but disordered in order for the sky to be blue?
 
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