A charged spacecraft is subject to the Lorentz force when it orbits a central body with a magnetic field. The induced Lorentz force provides a new mean of propellantless electromagnetic propulsion for orbital control. Modeling the Earth magnetic field as a tilted dipole that co-rotates with the Earth, this paper develops a nonlinear dynamical model that describes the relative motion of the Lorentz spacecraft about an arbitrary reference orbit. Based on the proposed dynamical model, feasibility of Lorentz-propelled rendezvous with no restrictions on the initial states is investigated. The rendezvous problem is then formulated as an optimal control problem, and solved with the Gauss pseudospectral method(GPM). Numerical simulations substantiate the validity of proposed model and method, and results show that the propellantless rendezvous is achieved at both fixed and free final time. A charged spacecraft is subject to the Lorentz force when it orbits a central body with a magnetic field. The induced Lorentz force provides a new mean of propellantless electromagnetic propulsion for orbital control. Modeling the Earth magnetic field as a tilted dipole that co-rotated with the Earth, this paper develops a nonlinear dynamical model that describes the relative motion of the Lorentz spacecraft about an arbitrary reference orbit. Based on the proposed dynamical model, feasibility of Lorentz-propelled rendezvous with no restrictions on the initial states is investigated. The rendezvous problem is then formulated as an optimal control problem, and solved with the Gauss pseudospectral method (GPM). Numerical simulations substantiate the validity of proposed model and method, and results show that the propellantless rendezvous is achieved at both fixed and free final time.