  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) $\in 0.1\sim0.4$ and mass $\in 0.1 \sim 10 M_{\oplus}$. Various
scaling relations are derived: (1) core radius fraction $\rm CRF \approx
\sqrt{CMF}$, (2) Typical interior pressure $P_{\text{typical}} \sim
g_{\rm{s}}^2$ (surface gravity squared), (3) core formation energy $E_{\rm
diff} \sim \frac{1}{10} E_{\rm grav}$ (the total gravitational energy), (4)
effective heat capacity of the mantle $C_{\rm p}\approx \left(
\frac{M_{\rm{p}}}{M_{\oplus}} \right) \cdot 7 \cdot 10^{27}$ J K$^{-1}$, and
(5) the moment of inertia $I\approx \frac{1}{3} \cdot M_{\rm{p}} \cdot
R_{\rm{p}}^2$. 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.
