We present CCD $UBVRI$ photometry of the field of the open cluster NGC 6866. Structural parameters of the cluster are determined utilizing the stellar density profile of the stars in the field. We calculate the probabilities of the stars being a phys
ical member of the cluster using their astrometric data and perform further analyses using only the most probable members. The reddening and metallicity of the cluster were determined by independent methods. The LAMOST spectra and the ultraviolet excess of the F and G type main-sequence stars in the cluster indicate that the metallicity of the cluster is about the solar value. We estimated the reddening $E(B-V)=0.074 pm 0.050$ mag using the $U-B$ vs $B-V$ two-colour diagram. The distance modula, the distance and the age of NGC 6866 were derived as $mu = 10.60 pm 0.10$ mag, $d=1189 pm 75$ pc and $t = 813 pm 50$ Myr, respectively, by fitting colour-magnitude diagrams of the cluster with the PARSEC isochrones. The Galactic orbit of NGC 6866 indicates that the cluster is orbiting in a slightly eccentric orbit with $e=0.12$. The mass function slope $x=1.35 pm 0.08$ was derived by using the most probable members of the cluster.
Lutz-Kelker bias corrected absolute magnitude calibrations for the detached binary systems with main-sequence components are presented. The absolute magnitudes of the calibrator stars were derived at intrinsic colours of Johnson-Cousins and 2MASS (Tw
o Micron All Sky Survey) photometric systems. As for the calibrator stars, 44 detached binaries were selected from the Hipparcos catalogue, which have relative observed parallax errors smaller than 15% ($sigma_{pi}/pileq0.15$). The calibration equations which provide the corrected absolute magnitude for optical and near-infrared pass bands are valid for wide ranges of colours and absolute magnitudes: $-0.18<(B-V)_{0}<0.91$, $-1.6<M_{V}<5.5$ and $-0.15<(J-H)_{0}<0.50$, $-0.02<(H-K_{s})_{0}<0.13$, $0<M_{J}<4$, respectively. The distances computed using the luminosity-colours (LCs) relation with optical (BV) and near-infrared ($JHK_{s}$) observations were compared to the distances found from various other methods. The results show that new absolute magnitude calibrations of this study can be used as a convenient statistical tool to estimate the true distances of detached binaries out of Hipparcos distance limit.
