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

This paper discusses a method for solving the so called low-thrust Lambert’ s problem. The problem is formulated as a two-points boundary value one, where the initial and final positions are provided in terms of equinoctial variables. A first-order perturbative method is used for investigate the development of orbital elements generated by the low-thrust propulsion system, which acts as a perturbative 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. Furthermore the paper presents three test cases, which demonstrate the flexibility of the method for different missions: the first example is a spiral multi-revolution transfer from low Earth orbit to the International Space Station, the second is a interplanetary transfer from Earth to Mars, while the third is a geostationary transfer orbit to a geostationary orbit.