In this paper, a time- and space-coordinate transformation, commonly known as the Kustaanheimo–Stiefel (KS)-transformation, is applied to reduce the order of singularities arising due to the motion of an infinitesimal body in the vicinity of a smaller primary in the three-body system. In this work, the Sun–Earth system is considered assuming the Sun to be a radiating body and the Earth as an oblate spheroid. The study covers motion around collinear Lagrangian L 1 and L 2 points. Numerical computations are performed for both regularized and non-regularized equations of motion and results are compared for non-periodic as well as periodic motion. In the transformed space, time is also computed as a function of solar radiation pressure ( q ) and oblateness of the Earth ( A 2 ). The two parameters ( q , A 2 ) have a significant impact on time in the transformed space. It is found that KS-regularization reduces the order of the pole from five to three at the point of singularity of the governing equations of motion.