Monday, October 31, 2016

A Simple Analytical Model for Rocky Planet Interior

A Simple Analytical Model for Rocky Planet Interior


Zeng et al


Based on the PREM~\citep{Dziewonski:1981}, the internal gravity of the Earth increases approximately linearly in the core and stays approximately constant in the mantle. Tested with numerical calculations in~\citet{Zeng:2016}, this behavior of internal gravity can be generalized to any two-layer (iron-silicate) rocky exoplanet with core mass fraction (CMF) in between 0.2∼0.35 and mass in between 0.1 and 30 M⊕. Based on this fact, (1) CMF ≈ CRF2 (core radius fraction squared), (2) Pc∼g2s (interior pressure scales as surface gravity squared), (3) energy released of core formation is ∼110 the total gravitational energy, (4) effective heat capacity of the mantle ≈(MpM⊕)⋅7.5⋅1027J/K, (5) moment of inertia ≈13⋅Mp⋅R2p, and some other results can be derived. These results, though approximate, are handy to use owing to their simplicity and lucidity. They lead us deeper into the understanding of the interior structures of those planets.

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