We address the heliocentric in-orbit repositioning problem of an E-sail-based spacecraft that covers a circular parking orbit of given radius, with the assumption that the propulsive acceleration is directed along the Sun-spacecraft line. According to the recent literature, the analysis exploits the possibility of reducing the mathematical problem to the dynamics of an equivalent nonlinear oscillator with a single degree of freedom. The analytical expression of the spacecraft heliocentric trajectory, which is available in polar form when its motion is periodic, is used to obtain approximate relationships among the E-sail performance, the flight time, and the desired phasing angle. The approximate analytical model is validated through numerical simulations, whereas the last part of the paper discusses a comparison with the optimal in-orbit repositioning transfers available in the literature. •The paper analyzes the heliocentric in-orbit repositioning of an E-sail.•A Sun-facing attitude is assumed in the analysis.•The problem is reduced to the dynamics of an equivalent nonlinear oscillator.•The paper proposes an analytical approximation of the E-sail trajectory.•A comparison with optimal results from the literature is discussed in detail.