In this paper, a spacecraft formation flying in the gravitational and magnetic fields of the Earth is investigated. The “direct magnetic dipole” is considered as a model of the geomagnetic field. A system of nonlinear differential equations describing the relative orbital motion of an electrically charged spacecraft is derived, as well as its simplified version. The analytical research of a spacecraft formation flying under the influence of the Lorentz force is carried out. The asymptotic solution of the differential system of the relative motion of a spacecraft with a variable electrical charge is found. The results of numerical modeling according to the derived system of nonlinear differential equations are presented. A comparison between the analytical and numerical solutions is made. The open-loop control algorithm, which is based on a charge change according to a simple harmonic law, is proposed to transfer a spacecraft to new relative orbits. The problem of programmed changing the distance between spacecraft is considered, which is carried out in three stages. The analytical trajectory is obtained, which agrees well with the results of numerical modeling using a nonlinear model.