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My question is:

Does the relative position of the barycenter of the Earth-Moon system change due to mass distribution changes in the system and would this affect the Earth-Moon distance?

For example: Could the sea level rise change the Earth-Moon distance?

The only formula I found looks like this one:

But this is obviously a formula which does not take mass distributions of the two objects into account.

Any suggestions for calculations regarding this question are highly appreciated! Thanks in advance!

Best regards,

Sven