2016ApJ...819..127Z

Several small dense exoplanets are now known, inviting comparisons to Earth and Venus. Such comparisons require translating their masses and sizes to composition models of evolved multi-layer interior planets. Such theoretical models rely on our understanding of the Earth's interior, as well as independently derived equations of state, but so far have not involved direct extrapolations from Earth's seismic model: the Preliminary Reference Earth Model (PREM). To facilitate more detailed compositional comparisons between small exoplanets and the Earth, we derive here a semi-empirical mass-radius relation for two-layer rocky planets based on PREM, \fracRR_⊕=(1.07-0.21⋅CMF)⋅[?\left?](\fracMM_⊕[?\right?])^1/3.7, where CMF stands for core mass fraction. It is applicable to 1 ∼ 8 M_⊕ and a CMF of 0.0 ∼ 0.4. Applying this formula to Earth and Venus and several known small exoplanets with radii and masses measured to better than ∼30% precision gives a CMF fit of 0.26 ± 0.07.