Comparison Between Indirect Methods and Approximate Methods for the Optimization of Low-Thrust Transfers Between LEO Orbits with J2 Perturbation

In recent years, space exploration has experienced an exponential increase in activities within low Earth orbit (LEO), a trend that is expected to continue in the coming years. This growth has drawn attention to the problem of orbital debris overcrowding and the need to design missions capable of actively mitigating this issue. As a result, there is a growing interest in developing more efficient missions, particularly in optimizing transfer manoeuvres to minimize either time or propellant consumption. LEO is an environment where the Keplerian orbit approximation alone is insufficient to accurately describe all relevant dynamics. In particular, the perturbation due to Earth’s J2 effect must be considered to obtain precise results. However, these perturbations can also be exploited to optimize transfer trajectories. Electric propulsion is a promising candidate for future missions, offering significant advantages in terms of propellant efficiency. Numerous methods exist for optimizing low-thrust, multi-revolution transfers. Among these, the indirect method is a robust approach that relies on the numerical integration of differential equations and the shooting method to achieve optimal transfers. However, it poses significant challenges in terms of implementation and computational cost. Conversely, the arc-impulse method is based on an approximate analytical optimal solution and requires only a few iterations to converge. Although the optimal strategies derived from approximate methods may differ from those obtained using the indirect method, within its range of applicability, the arc-impulse method proves to be an effective approach for quickly estimating both propellant costs and the minimum time required for a mission. This becomes particularly advantageous when studying multi-target solutions.