An investigation of poorly studied open cluster NGC 4337 using
  multi-color photometric and Gaia DR2 astrometric data
  We present a comprehensive analysis (photometric and kinematical) of poorly
studied open cluster NGC 4337 using 2MASS, WISE, APASS, and Gaia~DR2 database.
By determining the membership probabilities of stars, we identified 624 most
probable members with membership probability higher than $50\%$ by using proper
motion and parallax data taken from Gaia~DR2. The mean proper motion of the
cluster is obtained as $\mu_{x}=-8.83\pm0.01$ and $\mu_{y}=1.49\pm0.006$ mas
yr$^{-1}$. We find the normal interstellar extinction towards the cluster
region. The radial distribution of members provides a cluster radius of 7.75
arcmin (5.63 pc). The estimated age of $1600\pm180$ Myr indicates that NGC 4337
is an old open cluster with a bunch of red giant stars. The overall mass
function slope for main-sequence stars is found as $1.46\pm0.18$ within the
mass range 0.75$-$2.0 $M_\odot$, which is in fair agreement with Salpeter's
value (x=1.35) within uncertainty. The present study demonstrates that NGC 4337
is a dynamically relaxed open cluster. Using the Galactic potential model,
Galactic orbits are obtained for NGC 4337. We found that this object follows a
circular path around the Galactic center. Under the kinematical analysis, we
compute the apex coordinates $(A, D)$ by using two methods: (i) the classical
convergent point method and (ii) the AD-diagram method. The obtained
coordinates are: $(A_{conv}, D_{conv})$ = (96$^{\textrm{o}}$.27 $\pm$
0$^{\textrm{o}}$.10, 13$^{\textrm{o}}$.14 $\pm$ 0$^{\textrm{o}}$.27) $\&$
$(A_\circ, D_\circ)$ = (100$^{\textrm{o}}$.282 $\pm$ 0$^{\textrm{o}}$.10,
9$^{\textrm{o}}$.577 $\pm$ 0$^{\textrm{o}}$.323) respectively. We also computed
the Velocity Ellipsoid Parameters (VEPs), matrix elements ($\mu_{ij}$),
direction cosines ($l_j$, $m_j$, $n_j$) and the Galactic longitude of the
vertex ($l_2$).
