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The concept of Lorentz force can provide a propellantless electrostatic propulsion, through the interaction between an electrostatically charged satellite and the Earth\'s magnetic field to provide a useful thrust, which can be used for control both orbital and attitude motion. This idea needs to install an ion collector on the satellite to increase the level of charging as artificial charging. In this work the Lorentz force has been developed for two terms, a) first term, which was experienced with the magnetic field in the case of absolute charging of the spacecraft; b) the second term, which was experienced with the electric field in the case of differential charging of the spacecraft. We developed a mathematical model of fuel-optimal satellite formation keeping using a low thrust propulsion system using Electrostatic forces The linear time-varying relative dynamics which describe the relative motion in the presence of second zonal harmonic perturbation and total Lorentz force have developed. The proposed controller includes a feedback control using a real-time fuel-optimal control approach are considered. Application of a Legendre pseudospectral method is presented using quadratic programming for the fuel-optimal control problem. Feedforward control (iterative learning control) is used to improve formation keeping accuracy by eliminating the effects of periodic perturbations due to second zonal harmonics. The simulation results confirm the capability of using Lorentz force to provide an optimal propellantless to control the of formation keeping.