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We study the effects of oblateness up to $J_4$ of the primaries and power-lawdensity profile (PDP) on the linear stability of libration location of aninfinitesimal mass within the framework of restricted three body problem(R3BP), by using a more realistic model in which a disc with PDP is rotatingaround the common center of the system mass with perturbed mean motion. Theexistence and stability of triangular equilibrium points have been explored. Ithas been shown that triangular equilibrium points are stable for $0<\mu<\mu_c$and unstable for $\mu_c\leq\mu\leq1/2$, where $\mu_c$ denotes the critical massparameter. We find that, the oblateness up to $J_2$ of the primaries and theradiation reduces the stability range while the oblateness up to $J_4$ of theprimaries increases the size of stability both in the context where PDP isconsidered and ignored. The PDP has an effect of about $\approx0.01$ reductionon the application of $\mu_c$ to Earth-Moon and Jupiter-Moons systems. We findthat the comprehensive effects of the perturbations have a stabilizingproclivity. However, the oblateness up to $J_2$ of the primaries and theradiation of the primaries have tendency for instability, while coefficients upto $J_4$ of the primaries have stability predisposition. In the limiting case$c=0$, and also by setting appropriate parameter(s) to zero, our results are inexcellent agreement with the ones obtained previously. Libration points playvery important role in space mission and as a consequence, our results have apractical application in space dynamics and related areas. The model may beapplied to study the navigation and stationkeeping operations of spacecraft(infinitesimal mass) around the Jupiter (more massive) -Callisto (less massive)system, where PDP account for the circumsolar ring of asteroidal dust, whichhas a cloud of dust permanently in its wake.

Triangular libration points in the R3BP under combined effects of oblateness, radiation and power-law profile