In this work, the triangular Lagrangian points L4 and L5 in the circular restricted three body problem are studied under the influence of applying a radial force. The equations of the xy planar motion of the third body with negligible mass compared to the two primaries are formulated with the addition of an external force αr and solved for the case of the triangular Lagrangian points L4 and L5. The positions of L4 and L5 and the stability conditions are found. The results show the dependence of the positions of the artificial libration points on the applied external force αr. Also the original position of the points is shown to be a limiting case when α = 0. The results also show the dependence of the stability conditions on α, and thus giving the possibility of creating artificial stable libration points other than the well-known natural points. The case of the earth-moon system is studied numerically.