Lambert solution and application for interplanetary low-thrust trajectories

In order to improve the precision of primary design for an interplanetary low-thrust transfer trajectory, a semi-analytical Lambert algorithm based on the N-degree inverse polynomial approach is proposed, and a primary design method is developed accordingly. First, the N-degree inverse polynomial is used to approximate the low thrust trajectory, and the partial coefficients as well as the analytical solution of the thrust are derived with the thrust direction assumption and trajectory boundary conditions. Next, the existent feasibility of the Lambert solution is analyzed and the feasible region of the key coefficient is presented taking into consideration the fly time and orbit dynamical constraints. Then, a computation model for the Lambert problem is established using the spacecraft mass equation. Finally, based on the Lambert algorithm, a primary design approach for a multi-revolution, free-time transfer trajectory is presented through reducing the dimensions of the thrust constraints. The proposed Lambert algorithm and primary design method are validated by computer simulations. The numerical results demonstrate that, for a target orbit with 5 AU semi-major axis, the Lambert algorithm can reduce the velocity increment by 36.63% as compared with the traditional six order algorithm. The primary design solution, which is very close to that of the optimal method, can provide a feasible guess for an accurate design problem.