This paper proposes an improved method for the preliminary evaluation of minimum-propellant trajectories to Near-Earth Asteroids (NEAs). The method applies to missions from Earth to asteroids with small eccentricity and inclination. A planar and a plane-change problem can be distinguished. In the planar problem, the solution assumes that multiple burn arcs are performed in correspondence of the apsides of the target asteroid in order to change the initial spacecraft orbit (i.e., Earth’s orbit) into the target one. The number of arcs is established once the time of flight is given (1 burn at each apsis per revolution, 1 revolution per year can be assumed). The length and propellant consumption of each arc to attain the required changes of semi-major axis and eccentricity are computed by a procedure based on Edelbaum’s approximation, which is well-suited to the problem at hand, as eccentricity changes are expected to be small for feasible missions. No numerical integration is required, but only the numerical solution of a three-unknown algebraic system is needed, making the procedure extremely fast. Plane change is taken into account assuming a constant out-of-plane thrust angle during each burn. A previous simple formulation used an averaged thrust effect over one revolution and neglected the fact that plane changes are more effective at the nodes. Several improvements are here introduced, which greatly increase the method accuracy. The influences of the eccentricity change, the angle between the asteroid line of nodes and line of apsides, and the expected length of the arc are considered: In fact, when the eccentricity is small, the thrust arc can be performed at the nodes where the inclination is efficiently changed, with little penalty in the planar maneuver. An efficient plane change is also performed when the angle between the asteroid line of nodes and line of apsides is small and/or the length of the arc is large, because, in this case, the node is comprised in the apsidal burn. A simple corrective formula accounts for this effect. The new method shows remarkable accuracy. The results comparison with solutions obtained with an indirect optimization method for a set of more than 60 NEAs shows a 0.95 correlation coefficient in the propellant masses. The estimation error is below 10% for 75% of the targets, below 15% for 95% of the targets, and always below 20%.

本文提出了一种改进的方法，用于对近地小行星 (NEA) 的最小推进剂轨迹进行初步评估。该方法适用于从地球到小偏心率和倾角小行星的任务。可以区分平面问题和平面变化问题。在平面问题中，该解假设对应目标小行星的外侧面进行多次燃烧弧，以将初始航天器轨道（即地球轨道）改变为目标轨道。一旦给定飞行时间，弧的数量就确定了（每圈每圈燃烧 1 次，可以假设每年 1 圈）。通过基于埃德尔鲍姆近似的程序计算每个弧的长度和推进剂消耗，以获得所需的半长轴和偏心率变化，这非常适合手头的问题，因为对于可行的任务，预计离心率变化很小。不需要数值积分，而只需要三未知代数系统的数值解，使得该过程非常快。假设在每次燃烧期间具有恒定的平面外推力角，则考虑平面变化。之前的一个简单公式使用了一圈内的平均推力效应，而忽略了平面变化在节点处更有效的事实。这里介绍了几项改进，大大提高了方法的准确性。考虑偏心率变化、交点小行星线与中点线夹角、预期弧长的影响： 事实上，当偏心率较小时，推力弧可以在有效改变倾斜度的节点处执行，对平面机动几乎没有损失。当节点的小行星线和后点线之间的角度很小和/或弧的长度很大时，也执行有效的平面改变，因为在这种情况下，节点包含在顶点烧伤中。一个简单的修正公式说明了这种影响。新方法显示出惊人的准确性。结果与使用间接优化方法获得的解决方案的比较结果显示，推进剂质量的相关系数为 0.95。75% 的目标的估计误差低于 10%，95% 的目标低于 15%，并且始终低于 20%。当节点的小行星线和后点线之间的角度很小和/或弧的长度很大时，也执行有效的平面改变，因为在这种情况下，节点包含在顶点烧伤中。一个简单的修正公式说明了这种影响。新方法显示出惊人的准确性。结果与使用间接优化方法获得的解决方案的比较结果显示，推进剂质量的相关系数为 0.95。75% 的目标的估计误差低于 10%，95% 的目标低于 15%，并且始终低于 20%。当节点的小行星线和后点线之间的角度很小和/或弧的长度很大时，也执行有效的平面改变，因为在这种情况下，节点包含在顶点烧伤中。一个简单的修正公式说明了这种影响。新方法显示出惊人的准确性。结果与使用间接优化方法获得的解决方案的比较结果显示，推进剂质量的相关系数为 0.95。75% 的目标的估计误差低于 10%，95% 的目标低于 15%，并且始终低于 20%。一个简单的修正公式说明了这种影响。新方法显示出惊人的准确性。结果与使用间接优化方法获得的解决方案的比较结果显示，推进剂质量的相关系数为 0.95。75% 的目标的估计误差低于 10%，95% 的目标低于 15%，并且始终低于 20%。一个简单的修正公式说明了这种影响。新方法显示出惊人的准确性。结果与使用间接优化方法获得的解决方案的比较结果显示，推进剂质量的相关系数为 0.95。75% 的目标的估计误差低于 10%，95% 的目标低于 15%，并且始终低于 20%。