We present here the fundamental parameters of ten open star clusters, nominated from Kronberger et al. (2006) who presented some new discovered stellar groups on the basis of 2MASS photometry and DSS visual images. Star counts and photometric parameters (radius, membership, distances, color excess, age, luminosity function, mass function, total mass, and the dynamical relaxation time) have been determined for these ten clusters for the first time. In order to calibrate our procedures, the main parameters (distance, age, and color excesses) have been re-estimated for another five clusters, which are studied by Kronberger et al. (2006) as well.

In this work, the astrophysical parameters of the open cluster Gulliver 1 are calculated using Gaia DR2 catalogue. The parameters that covered under this study are the radius, distance, colour excess, age, total mass and relaxation time also the parallax and proper motion values in both coordinates Ra and Dec beside studying the luminosity and mass functions of the cluster. Using the radial density profile, radius is found to be 6.8 ± 0.2 arcmin. We get the distance and age from the colour magnitude diagram to be 2818.38 ± 11 pc and 1.78 Gyr ±20 Myr, respectively. the horizontal-projected distances from the sun on the galactic plane X ⊙ & Y ⊙ , the distance from the galactic plane Z and the distance from the galactic centre R gc are obtained as 507.5 ± 2 pc, −2222 ± 8.7 pc, −1657.4 ± 6.5 pc and 3609 ± 14 pc respectively. Also, astrometric parameters are obtained such as parallax and proper motions in both coordinates Ra and Dec as 0.31 ± 0.08 mas, −7.9 ± 0.14 mas/yr and 3.6 ± 0.08 mas/yr, respectively. From the estimated relaxation time we inferred that the cluster is relaxed and has a mass of 146.2 M ʘ. Some parameters are presented for the first time.

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