Final answer:
The Moon's mantle is thinner than Earth's mantle and, due to its smaller size and proportionally less heavy metal content, the Moon's core would also be expected to be smaller than its mantle. Due to the lack of specific thickness measurements for the Moon's core in the provided material, we cannot state the exact thickness of the Moon's core.
Step-by-step explanation:
The question asks about the comparison between the thickness of the Moon's mantle and its core. The Moon's mantle is far less in thickness when compared to Earth's mantle. While the Earth's mantle is about 2,900 kilometers thick, the Moon's mantle would be significantly thinner, as the Moon itself is smaller and has proportionally less iron and other metals. However, it is important to note that this question contains an error because it assumes that the Moon's core and Earth's core have the same thickness. Earth's core is about 3,500 km thick, but we cannot directly apply this to the Moon due to differences in size and composition.
The Moon's average density is lower than that of Earth, which suggests that the Moon does not contain as much iron or heavy metals, and this results in a different internal structure. Therefore, when comparing the Moon's mantle to its core, one should consider the Moon's smaller size and lower density. The details of the exact thickness of the Moon's mantle and core are not provided in the reference material, and thus we cannot conclusively state the thickness of the Moon's core.
However, we can infer that since the Mantle constitutes a significant portion of the Moon's volume, similar to Earth, the core would be proportionally smaller than the mantle.