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Description
On the one hand, the second data release of the Gaia mission (GaiaDR2, Cat. I/345) has opened a trove of astrometric and photometric data for Galactic clusters within a few kpc 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, a time sufficient to apply its results to the calculation of orbits of some massive multiple systems within ~1kpc of the Sun. 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 both clusters is a multiple system with an O-type primary: HD 193322 and 15 Mon, respectively. For each of those two multiple systemsI aim to derive new astrometric orbits for the Aa,Ab components. First, I present a method that usesGaiaDR2 G+G_BP_+G_RP_ photometry, positions, proper motions, and parallaxes to obtain the membership and distance of a stellar group and apply it 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,Abusing as input literature data from the Washington Double Star Catalog (WDS) and the AstraLux measurements recently presented by Maiz Apellaniz et al. (2019, Cat. J/A+A/626/A20) I obtain GaiaDR2 distances of 1006^+37^_-34_pc for Collinder 419 and 719+/-16pc for NGC 2264, with the main contribution to the uncertainties coming from the spatial covariance of the parallaxes. The two NGC 2264 subclusters are at the same distance (within the uncertainties) and they show a significant relative proper motion. The distances are shown to be robust. HD 193322 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^_-7.4_M_{sun}_. The orbit of 15 Mon Aa,Ab is even more eccentric (e=0.770^+0.023^_-0.030_), with a period of 108+/-12 a and a total mass of 45.1^+3.6^_-3.3_M_{sun}_ for its two stars.
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