The dynamics of a spacecraft propelled by a continuous radial thrust resembles that of a nonlinear oscillator. This is analyzed in this work with a novel method that combines the definition of a suitable homotopy with a classical perturbation approach, in which the low thrust is assumed to be a perturbation of the nominal Keplerian motion. The homotopy perturbation method provides the analytical (approximate) solution of the dynamical equations in polar form to estimate the corresponding spacecraft propelled trajectory with a short computational time. The accuracy of the analytical results was tested in an orbital-targeting mission scenario.