We use a new method of solving equations in variations for perturbed central force fields to obtain first order perturbations of Cartesian coordinates of a small body moving in a perturbed central force field. In the case of Newtonian field, we derive formulae for first order perturbations of coordinates of a small body moving under piecewise polynomial (in true anomaly) low-thrust. We suppose that the small body under consideration is initially moving in an elliptic orbit.