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Classical Cepheids provide the foundation for the empirical extragalacticdistance ladder. Milky Way Cepheids are the only stars in this class accessibleto trigonometric parallax measurements. However, the parallaxes of Cepheidsfrom the second Gaia data release (GDR2) are affected by systematics because ofthe absence of chromaticity correction, and occasionally by saturation. As aproxy for the parallaxes of 36 Galactic Cepheids, we adopt either the GDR2parallaxes of their spatially resolved companions or the GDR2 parallax of theirhost open cluster. This novel approach allows us to bypass the systematics onthe GDR2 Cepheids parallaxes that is induced by saturation and variability. Weadopt a GDR2 parallax zero-point (ZP) of -0.046 mas with an uncertainty of0.015 mas that covers most of the recent estimates. We present new Galacticcalibrations of the Leavitt law in the V, J, H, K_S , and Wesenheit W_H bands.We compare our results with previous calibrations based on non-Gaiameasurements and compute a revised value for the Hubble constant anchored toMilky Way Cepheids. From an initial Hubble constant of 76.18 +/- 2.37 km/s/Mpcbased on parallax measurements without Gaia, we derive a revised value byadopting companion and average cluster parallaxes in place of direct Cepheidparallaxes, and we find H_0 = 72.8 +/- 1.9 (statistical + systematics) +/- 1.9(ZP) km/s/Mpc when all Cepheids are considered and H0 = 73.0 +/- 1.9(statistical + systematics) +/- 1.9 (ZP) km/s/Mpc for fundamental modepulsators only.

The Milky Way Cepheid Leavitt law based on Gaia DR2 parallaxes of companion stars and host open cluster populations