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.
