An exoplanet's structure and composition are first-order controls of the planet's habitability. We explore which aspects of bulk terrestrial planet composition and interior structure affect the chief observables of an exoplanet: its mass and radius. We apply these perturbations to the Earth, the planet we know best. Using the mineral physics toolkit BurnMan to self-consistently calculate mass–radius models, we find that the core radius, the presence of light elements in the core, and an upper mantle consisting of low-pressure silicates have the largest effects on the final calculated mass at a given radius, none of which are included in current mass–radius models. We expand these results to provide a self-consistent grid of compositionally as well as structurally constrained terrestrial mass–radius models for quantifying the likelihood of exoplanets being "Earth-like." We further apply this grid to Kepler-36b, finding that it is only ~20% likely to be structurally similar to the Earth with Si/Fe?=?0.9 compared with the Earth's Si/Fe?=?1 and the Sun's Si/Fe?=?1.19.
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