The mantle is solid (but plastic), not liquid. The mantle deforms elastically due to tidal effects caused by the Moon, which is part of what causes the Earth to not be a perfect sphere & may be relevant to the formation of mantle plumes (hotly debated)
The outer core behaves like a liquid (it’s a low-viscosity fluid that convects turbulently), but the level of tidal influence here is another argued-about planetary science thing, especially the relationship to the planet’s magnetic field. Some subscribe to the classic “geodynamo” hypothesis, but there’s an alt theory that most of the mag field is generated by “tidal eddies” in the fluid outer core. We do all tend to agree that tidal forces shear the fluid outer core into distinct sub-layers.
Further reading (high level): [https://www.nature.com/articles/nature09643](https://www.nature.com/articles/nature09643)
Even more info on ‘Earth Tides’: [https://en.wikipedia.org/wiki/Earth_tide](https://en.wikipedia.org/wiki/Earth_tide)
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