Does the barycenter of the Earth-Moon system change?

[Sven E]

Hi to all!

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

 

[Vanadium 50]

It's already changing because it's moving around the sun. If you say "that doesn't count!", fine, but then this discussion will hinge around what "counts" and what doesn't.

 

[Chronos]

Unsurprisingly, the Earth moon barycenter is located about 1000 miles inside the earth. Unsurprising, considering the Earth is about 81 times more massive than the moon. The precise mass distribution of the Earth and moon is not known with great precision. Gravitational studies to date suggest the Earth's mass distribution is very homogenous. the moon/s mass distribution is less well known although the data indicate it too is fairly homogeneous. The Earth is very close to being a perfect sphere, it deviates from spherical only by about 3%. The moon is much less spherical from earth. I think it deviates about 10% from spherical,. The huge gravity of Earth is part of the reason. The moon was largely molten when it first formed and its surface got tugged out of spheroidal by the earth. It also has a much thicker crust on the far side vs the near side thus giving it a lemon-like appearance. Still it is pretty round compared to most moons in the solar system.