A Study of Open Clusters Frolov 1 and NGC 7510 using CCD UBV Photometry and Gaia DR2 Astrometry

We present reddening, photometric metallicity, age and distance estimates for the Frolov 1 and NGC 7510 open clusters based on CCD UBV photometric and Gaia data. Photometric observations were collected using the 1-m telescope of the T\"UB\.ITAK National Observatory. Gaia DR2 proper motion data in the direction of two groupings were used to identify cluster membership. We determined mean proper motion values ($ \mu_{\alpha}\cos\delta, \mu_{\delta}$) = ($-3.02\pm 0.10$, $-1.75 \pm 0.08$) and ($-3.66 \pm 0.07$, $-2.17 \pm 0.06$) mas yr$^{-1}$ for Frolov 1 and NGC 7510, respectively. We used two-colour diagrams to obtain $E(B-V)$ colour excesses for Frolov 1 and NGC 7510 as $0.65\pm0.06$ and $1.05\pm0.05$ mag, respectively. We derived the photometric metallicity of Frolov 1 as [Fe/H] = 0.03$\pm$0.03 dex and adopted a solar metallicity for NGC 7510. Based on these reddening and metallicities we determined the distance moduli and ages of the clusters via fitting PARSEC isochrones to the cluster colour-magnitude diagrams. Isochrone fitting distances for Frolov 1 and NGC 7510 are $2864 \pm 254$ and $2818 \pm 247$ pc, respectively, which correspond to the ages $35\pm 10$ Myr and $18\pm 6$ Myr. We also calculated mean Gaia distances and compared them with those given in the literature and in this study, concluding that our results are in good agreement with previous work. Finally, we calculated the mass function slopes as being $X=-1.21\pm0.18$ for Frolov 1 and $X=-1.42\pm0.27$ for NGC 7510.