  Context. One challenge for measuring the Hubble constant using Classical
Cepheids is the calibration of the Leavitt Law or period-luminosity
relationship. The Baade-Wesselink method for distance determination to Cepheids
relies on the ratio of the measured radial velocity and pulsation velocity, the
so-called projection factor and the ability to measure the stellar angular
diameters. Aims. We use spherically-symmetric model stellar atmospheres to
explore the dependence of the p-factor and angular diameter corrections as a
function of pulsation period. Methods. Intensity profiles are computed from a
grid of plane-parallel and spherically-symmetric model stellar atmospheres
using the SAtlas code. Projection factors and angular diameter corrections are
determined from these intensity profiles and compared to previous results.
Results. Our predicted geometric period-projection factor relation including
previously published state-of-the-art hydrodynamical predictions is not with
recent observational constraints. We suggest a number of potential resolutions
to this discrepancy. The model atmosphere geometry also affects predictions for
angular diameter corrections used to interpret interferometric observations,
suggesting corrections used in the past underestimated Cepheid angular
diameters by 3 - 5%. Conclusions. While spherically-symmetric hydrostatic model
atmospheres cannot resolve differences between projection factors from theory
and observations, they do help constrain underlying physics that must be
included, including chromospheres and mass loss. The models also predict more
physically-based limb-darkening corrections for interferometric observations.
