  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 core radius,
presence of light elements in the core and an upper-mantle consisting of
low-pressure silicates have the largest effect on the final calculated mass at
a given radius, none of which are included in current mass-radius models. We
expand these results 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 to Earth's Si/Fe = 1 and Sun's Si/Fe =
1.19.
