Low-Thrust Interplanetary Transfers, Including Escape and Capture Trajectories

Abstract

O PTIMAL low-thrust interplanetary transfers in the heliocentric frame have been studied in many documented articles in which the planetary escape and capture maneuvers were not addressed. For example, [1–4] demonstrated different methods to find optimum steering programs for heliocentric orbital transfers. Moreover, a number of state-of-the-art low-thrust trajectory optimization tools are also available for mission designers. The Jet Propulsion Laboratory (JPL) developed the well-known SEPTOP and VARITOP [5] (SEPTOP’s predecessor) programs that have been used for decades. More recently, JPL has demonstrated devotion to developing new low-thrust programs such as MYSTIC [6] and MALTO [7], which are more sophisticated and capable of designing complicated low-thrust trajectories. On the other hand, optimizing low-thrust planetocentric escape and capture trajectories has also been studied (see [8–11]). These prior efforts and studies reveal that mission designers are interested in low-thrust transfers from a lowEarth orbit (LEO) to a low-planet orbit. However, the literature dealing with optimizing the entire mission, including both heliocentric and planetocentric transfer trajectories, still appears to be somewhat limited. The most commonly used method is the patched-conic approximation, which was used by Melbourne and Sauer [12] in the 1960s. The interplanetary leg and planetocentric spirals are optimized separately and then patched together. Currently, this approximation method is still in wide use by mission designers. In this Note, an approach is proposed to estimate the mission performances (e.g., flight time and propellant mass) of low-thrust interplanetary transfers, including escape and capture trajectories. During the escape or capture phases, the continuous tangential or antitangential thrust (null in shadow) is used and J2 perturbations are considered. The low-thrust escape or capture spirals are computed by a fast algorithm (an analytic orbital averaging technique plus a shortduration integration process) that significantly reduces the trajectory propagation time. With the patched-conic approximation, the proposed approach makes it possible to formulate the entire lowthrust interplanetary transfer trajectory in a single nonlinear programming parameter optimization problem. It should be noted that the shadow conditions may significantly affect propellant consumption, flight time, and the ephemeris time that the capture or escape begins. The inclusion of shadowing distinguishes this work from most previous research. The purpose of the proposed approach is not to generate highfidelity trajectory solutions but to provide a preliminary analysis tool for mission designers to quickly estimate the mission performances of low-thrust interplanetary transfers that include escape and capture trajectories. Themany-revolution planetocentric spiral trajectories in the presence of shadowing and J2 perturbations are propagated using orbital averaging, which results in much fewer steps than precise numerical integration. The proposed approach is particularly useful for determining a particular mission’s trendwith respect to variations in system parameters. An optimal Earth–Mars transfer is obtained in this Note to provide an example. Furthermore, the preliminary solutions obtained with the proposed method could be used as good initial guesses for further trajectory optimization to generate highfidelity solutions.