How does the pull of the moon affect the earths atmosphere? Compare the air tide to the water tide for height fluctuations. I would expect the varience in depth affects the air tide the same as water tide, so it would make a simple comparison improbable. Feel free to give a simplified comparison, for this answer of a set thickness.
I’ll take this silence to mean that nobody has ever concidered this happening, so we have no answer for it. Another black hole of science. I couldn’t decide if the mass difference would cause more, less, or equal pull, and then the different amounts of each item comes into play.
The question in the first place is ill-phrased. The atmosphere doesn’t have height. It just fades out. So it is more reasonable to ask if there is detectable pressure changes due to tidal changes in the atmosphere.
Such things are just barely detectable. The daily cycle of pressure change due to heating and cooling from the sun is far greater. Since the daily tidal cycle is just a few hours off from that, you are basically talking about noise in the data.