This work aims at exploring the scaling relations among rocky exoplanets .
With the assumption of internal gravity increasing linearly in the core , and staying constant in the mantle , and tested against numerical simulations , a simple model is constructed , applicable to rocky exoplanets of core mass fraction ( CMF ) \in 0.1 \sim 0.4 and mass \in 0.1 \sim 10 M _ { \oplus } .
Various scaling relations are derived : ( 1 ) core radius fraction CRF \approx \sqrt { CMF } , ( 2 ) Typical interior pressure P _ { \text { typical } } \sim g _ { s } ^ { 2 } ( surface gravity squared ) , ( 3 ) core formation energy E _ { diff } \sim \frac { 1 } { 10 } E _ { grav } ( the total gravitational energy ) , ( 4 ) effective heat capacity of the mantle C _ { p } \approx \left ( \frac { M _ { p } } { M _ { \oplus } } \right ) \cdot 7 \cdot 10 ^ { 27 } J K ^ { -1 } , and ( 5 ) the moment of inertia I \approx \frac { 1 } { 3 } \cdot M _ { p } \cdot R _ { p } ^ { 2 } .
These scaling relations , though approximate , are handy for quick use owing to their simplicity and lucidity , and provide insights into the interior structures of rocky exoplanets .
As examples , this model is applied to several planets including Earth , GJ 1132b , Kepler-93b , and Kepler-20b , and made comparison with the numerical method .