Something Old and Something.... Actually it is all old.

Let define a new constant,

${G}_{o}= {g}_{o}{r}^{2}_{e}$

where ${g}_{o}$ is surface gravity and ${r}_{e}$ is the planet's radius and ${G}_{o}$ is ...well not a constant, not even for specific pairs of  ${g}_{o}$ and ${r}_{e}$.