  The orbits about Lagrangian equilibrium points are important for scientific
investigations. Since, a number of space missions have been completed and some
are being proposed by various space agencies. In light of this, we consider a
more realistic model in which a disk, with power-law density profile, is
rotating around the common center of mass of the system. Then, we analyze the
periodic motion in the neighborhood of Lagrangian equilibrium points for the
value of mass parameter $0<\mu\leq 1/2$. Periodic orbits of the infinitesimal
mass in the vicinity of equilibrium are studied analytically and numerically.
In spite of the periodic orbits, we have found some other kind of orbits like
hyperbolic, asymptotic etc. The effect of radiation factor as well as
oblateness coefficients on the motion of infinitesimal mass in the neighborhood
of equilibrium points are also examined. The stability criteria of the orbits
examined by the help of Poincar\'{e} surfaces of section (PSS) and found that
stability regions depend on the Jacobi constant as well as other parameters.
