The knowledge of the interior of Mars suggests that it can be modeled as a narrow shell, similar to that of the Earth, a mantle and a core. If the Martian nucleus is dense, composed of iron like that of the Earth or of the SNC meteorites that supposedly come from Mars, then the minimum radius of the nucleus is about 1,300 kilometers.
If the core is composed of less dense materials such as a mixture of sulfur and iron, then the maximum radius would be less than 2,000 kilometers.
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