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-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 pa- rameter with respect to the zero-order Keplerian motion. An implicit formula- tion is thus obtained which allows for the determination of the low–thrust transfer trajectory driving the equinoctial parameters from the initial to their fi- nal values in a prescribed time. Three test cases are presented, which demon- strate 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.