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 \({r}_{e}\).