  We present analytic estimates of the fractional uncertainties on the mass,
radius, surface gravity, and density of a transiting planet, using only
empirical or semi-empirical measurements. We first express these parameters in
terms of transit photometry and radial velocity (RV) observables, as well as
the stellar radius $R_{\star}$, if required. In agreement with previous
results, we find that, assuming a circular orbit, the surface gravity of the
planet ($g_p$) depends only on empirical transit and RV parameters; namely, the
planet period $P$, the transit depth $\delta$, the RV semi-amplitude
$K_{\star}$, the transit duration $T$, and the ingress/egress duration $\tau$.
However, the planet mass and density depend on all these quantities, plus
$R_{\star}$. Thus, an inference about the planet mass, radius, and density must
rely upon an external constraint such as the stellar radius. For bright stars,
stellar radii can now be measured nearly empirically by using measurements of
the stellar bolometric flux, the effective temperature, and the distance to the
star via its parallax, with the extinction $A_V$ being the only free parameter.
For any given system, there is a hierarchy of achievable precisions on the
planetary parameters, such that the planetary surface gravity is more
accurately measured than the density, which in turn is more accurately measured
than the mass. We find that surface gravity provides a strong constraint on the
core mass fraction of terrestrial planets. This is useful, given that the
surface gravity may be one of the best measured properties of a terrestrial
planet.
