The Moon does exert a gravitational force on Earth, including its fluid layers such as the oceans and the molten outer core. The gravitational interaction between the Moon and Earth creates tidal forces, which result in the rise and fall of ocean tides. However, the influence of the Moon's gravitational force on Earth's fluid core is relatively small compared to its effect on the oceans.
The tides caused by the Moon primarily affect the water on Earth's surface due to its fluidity and proximity to the Moon. The gravitational force of the Moon pulls on the water, causing it to bulge on the side facing the Moon and the side opposite it, creating high tides. The areas perpendicular to these bulges experience low tides.
While the Moon's gravitational force also acts on Earth's molten outer core, the core's fluid nature and its distance from the Moon result in a much smaller response compared to the surface tides. The gravitational force of the Moon on the fluid core may induce some subtle deformations or motions, but they are not significant enough to cause noticeable effects on Earth's geological processes or the planet's overall behavior.
It's worth noting that other factors, such as the gravitational interactions between Earth and other celestial bodies like the Sun or other planets, also contribute to the complex dynamics of Earth's core and its geophysical processes. The Moon's influence on Earth is primarily observed through its impact on ocean tides, while its effect on the fluid core is relatively minor in comparison.