Equation 8 · From Origins to Frontier: A History of Planetary Science and Exploration
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This is a first-order model, not a complete theory of core formation — real planetary interiors involve diapirism, iron rain, and turbulent entrainment rather than single isolated blobs — but it exposes the essential dependency: differentiation requires a large enough density contrast, a large enough body (so gravity g and blob size r are non-trivial), and a mantle viscosity low enough (i.e., hot enough) for sinking to complete within the age of the solar system. This is exactly why small, cold bodies — many asteroids among them — never fully differentiated and instead preserve primitive, unprocessed material from the solar system’s earliest few million years, which is the physical…
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This is a first-order model, not a complete theory of core formation — real planetary interiors involve diapirism, iron rain, and turbulent entrainment rather than single isolated blobs — but it exposes the essential dependency: differentiation requires a large enough density contrast, a large enough body (so gravity g and blob size r are non-trivial), and a mantle viscosity low enough (i.e., hot enough) for sinking to complete within the age of the solar system. This is exactly why small, cold bodies — many asteroids among them — never fully differentiated and instead preserve primitive, unprocessed material from the solar system’s earliest few million years, which is the physical reason sample-return missions target asteroids rather than differentiated planets when the goal is recovering pristine early solar system chemistry.
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