The electric solar wind sail, or E-sail, is a novel deep space propulsion concept which has not been demonstrated in space yet. While the solar wind is the authentic operational environment of the electric sail, its fundamentals can be demonstrated in the ionosphere where the E-sail can be used as a plasma brake for deorbiting. Two missions to be launched in 2023, Foresail-1p and ESTCube-2, will attempt to demonstrate Coulomb drag propulsion (an umbrella term for the E-sail and plasma brake) in low Earth orbit. This paper presents the next step of bringing the E-sail to deep space—we provide the initial modelling and trajectory analysis of demonstrating the E-sail in solar wind. The preliminary analysis assumes a six-unit cubesat being inserted in the lunar orbit where it deploys several hundred meters of the E-sail tether and charges the tether at 10–20 kV. The spacecraft will experience acceleration due to the solar wind particles being deflected by the electrostatic sheath around the charged tether. The paper includes two new concepts: the software architecture of a new mission design tool, the Electric Sail Mission Expeditor (ESME), and the initial E-sail experiment design for the lunar orbit. Our solar-wind simulation places the Electric Sail Test Cube (ESTCube) lunar cubesat with the E-sail tether in average solar wind conditions and we estimate a force of (Formula presented.) N produced by the Coulomb drag on a 2 km tether charged to 20 kV. Our trajectory analysis takes the 15 kg cubesat from the lunar back to the Earth orbit in under three years assuming a 2 km long tether and 20 kV. The results of this paper are used to set scientific requirements for the conceptional ESTCube lunar nanospacecraft mission design to be published subsequently in the Special Issue “Advances in CubeSat Sails and Tethers”.