New Period-Luminosity and Period-Color relations of classical Cepheids: I. Cepheids in the Galaxy

321 Galactic fundamental-mode Cepheids with good B, V, and (in most cases) I photometry by Berdnikov et al. ([CITE]) and with homogenized color excesses $E(B-V)$ based on Fernie et al. ([CITE]) are used to determine their period-color (P-C) relation in the range $0.4<\log P\la1.6$. The agreement with colors from different model calculations is good to poor. – Distances of 25 Cepheids in open clusters and associations (Feast [CITE]) and of 28 Cepheids with Baade-Becker-Wesselink (BBW) distances (Gieren et al. [CITE]) are used in a first step to determine the absorption coefficients ${\cal R}_{B}=4.17$, ${\cal R}_{V}=3.17$, and ${\cal R}_{I}=1.89$ appropriate for Cepheids of intermediate color. The two sets of Galactic Cepheids with known distances define two independent P-L relations which agree very well in slope; their zero points agree to within $0\fm12\pm0\fm04$. They are therefore combined into a single mean Galactic P-L$_{B,V,I}$ relation. The analysis of HIPPARCOS parallaxes by Groenewegen & Oudmaijer ([CITE]) gives absolute magnitudes which are brighter by $0\fm21\pm0\fm11$ in V and $0\fm18\pm0\fm12$ in I at $\log P=0.85$. Agreement with P-L relations from different model calculations for the case [Fe/H] = 0 is impressive to poor. Galactic Cepheids are redder in $(B-V)^0$ than those in LMC and SMC as shown by the over 1000 Cloud Cepheids with good standard B, V, I photometry by Udalski et al. ([CITE],c); the effect is less pronounced in $(V-I)^0$. Also the $(B-V)^0$, $(V-I)^0$ two-color diagrams differ between Cepheids in the Galaxy and the Clouds, attributed both to the effects of metallicity differences on the spectral energy distributions of the Cepheids and to a shift in the effective temperature of the middle of the instability strip for LMC and SMC relative to the Galaxy by about $\Delta \log T_{\rm e}\sim 0.02$ at $M_{V}=-4\fm0$, hotter for both LMC and SMC. Differences in the period-color relations between the Galaxy and the Clouds show that there cannot be a universal P-L relation from galaxy-to-galaxy in any given color. The inferred non-uniqueness of the slope of the P-L relations in the Galaxy, LMC, and SMC is born out by the observations. The Cloud Cepheids follow a shallower overall slope of the P-L relations in B, V, and I than the Galactic ones. LMC and SMC Cepheids are brighter in V than in the Galaxy by up to $0\fm5$ at short periods ($\log P = 0.4$) and fainter at long periods ($\log P \ga 1.4$). The latter effect is enhanced by a suggestive break of the P-L relation of LMC and SMC at $\log P = 1.0$ towards still shallower values as shown in a forthcoming paper