The goal of this work is to formulate an explicit analytical solution that approximates the SRP perturbed motion. The method of solution starts with embedding the non-conservative motion within an extended conservative system, followed by using canonical perturbation mitigation methods. The proposed method is entirely canonical and is following the Lie-Deprit-Hori perturbation paradigm. The computations given are carried out for the first-order approximation. Providing such analytical propagator reveals qualitative, as well as quantitative insights, regarding the short-term and long-term effect of the SRP upon a solar-sailing spacecraft. As practical outcome, we present an analytic orbit propagator for interplanetary orbits (Earth to Mars travel) with a relevant solar radiation pressure influence.