Implicit Solution for the Low-Thrust Lambert Problem by Means of a Perturbative Expansion of Equinoctial Elements

A method for solving the so called low-thrust Lambert’ s problem is proposed. After formulating it as a two-points 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.