A method for solving the so called low–thrust Lambert’s problem is proposed. After formulating it as a two-point boundary value problem, where initial and final positions are provided in terms of equinoctial variables, a first-order perturbative approach is used for investigating the variation of orbital elements generated by the low–thrust propulsion system, which acts as a perturbing parameter with respect to the zero-order Keplerian motion. An implicit formulation is thus obtained which allows for the determination of the low–thrust transfer trajectory driving the equinoctial parameters from the initial to their final values in a prescribed time. Three test cases are presented, which demonstrate the flexibility of the method for different missions: (i) an interplanetary transfer from Earth to Mars, (ii) a spiral multi-revolution transfer from low Earth orbit to the International Space Station, and (iii) a geostationary transfer orbit to a geostationary orbit.
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