Gaia DR2 distances to Collinder 419 and NGC 2264 and new astrometric orbits for HD 193 322 Aa,Ab and 15 Mon Aa,Ab

Context. On the one hand, the second data release of the Gaia mission (Gaia DR2) has opened a trove of astrometric and photometric data for Galactic clusters within a few kiloparsecs of the Sun. On the other hand, lucky imaging has been an operational technique to measure the relative positions of visual binary systems for a decade and a half. This time is sufficient to apply the results of the technique to the calculation of orbits of some massive multiple systems within ∼1 kpc of the Sun. Aims. As part of an ambitious research program to measure distances to Galactic stellar groups (including clusters) containing O stars, I start with two of the nearest examples: Collinder 419 in Cygnus and NGC 2264 in Monoceros. The main ionizing source for each cluster is a multiple system with an O-type primary: HD 193 322 and 15 Mon, respectively. For each of the two multiple systems, I aim to derive new astrometric orbits for the Aa,Ab components. Methods. First, I present a method that uses Gaia DR2 G + GBP + GRP photometry, positions, proper motions, and parallaxes to obtain the membership and distance of a stellar group and applied these values to Collinder 419 and NGC 2264. Second, I present a new code that calculates astrometric orbits by searching the whole seven-parameter orbit space and apply it to HD 193 322 Aa,Ab and 15 Mon Aa,Ab using, as input, literature data from the Washington Double Star Catalog and the AstraLux measurements recently presented by our group in another paper published this year. Results. I obtain Gaia DR2 distances of 1006+37−34 pc for Collinder 419 and 719 ± 16 pc for NGC 2264; the main contribution to the uncertainties comes from the spatial covariance of the parallaxes. The two NGC 2264 subclusters are at the same distance (within the uncertainties) and show a significant relative proper motion. The distances are shown to be robust. HD 193 322 Aa,Ab follows an eccentric (e = 0.58+0.03−0.04) orbit with a period of 44 ± 1 a and the three stars it contains have a total mass of 76.1+9.9−7.4M⊙. The orbit of 15 Mon Aa,Ab is even more eccentric (e = 0.770+0.023−0.030); it has a period of 108 ± 12 a and a total mass of 45.1+3.6−3.3M⊙ for its two stars.