  Classical Cepheids (CCs) are at the heart of the empirical extragalactic
distance ladder. Milky Way CCs are the only stars of this class accessible to
trigonometric parallax measurements. Until recently, the most accurate
trigonometric parallaxes of Milky Way CCs were the HST/FGS measurements
collected by Benedict et al. (2002, 2007) and HST/WFC3 measurements by Riess et
al. (2018). Unfortunately, the second Gaia data release (GDR2) has not yet
delivered reliable parallaxes for Galactic CCs, failing to replace the HST as
the foundation of the Galactic calibrations of the Leavitt law. We aim at
calibrating independently the Leavitt law of Milky Way CCs based on the GDR2
catalog of trigonometric parallaxes. As a proxy for the parallaxes of a sample
of 23 Galactic CCs, we adopt the GDR2 parallaxes of their spatially resolved
companions. As the latter are unsaturated, photometrically stable stars, this
novel approach allows us to bypass the GDR2 bias on the parallax of the CCs
that is induced by saturation and variability. We present new Galactic
calibrations of the Leavitt law in the J, H, K, V, Wesenheit WH and Wesenheit
WVK bands based on the GDR2 parallaxes of the CC companions. We show that the
adopted value of the zero point of the GDR2 parallaxes, within a reasonable
range, has a limited impact on our Leavitt law calibration.
