Abstract

The study considers the problem of calculating the low-energy trajectories of a low-thrust spacecraft to the Moon during the ballistic capture. The transfer is carried out using a transit trajectory in the vicinity of one of the collinear libration points L₁ or L₂ of the Earth-Moon system. Using a transit trajectory allows us to reduce fuel consumptions for the transfer by applying spacecraft dynamic in the Earth-Moon system. After exit from the orbit of ballistic capture, depending on the goal of mission the required lunar orbit can be formed, or the maneuver can be completed for inserting into the required interplanetary trajectory. A method for solving the problem is proposed, which consists in selecting the suitable transit trajectory to ensure sufficiently long duration of staying a spacecraft in the sphere of influence of the Moon, and in calculating the optimal low-thrust trajectories from initial lunar orbit to the transit trajectory to the Moon. To solve the problem of optimal control and calculate the optimal exit point to the transit trajectory, the Pontryagin’s maximum principle is used in combination with the continuation method by parameter. Numerical examples are given for calculating low-energy trajectories to the Moon during the ballistic capture with the optimization of exit point to the transit trajectory.

中文翻译：

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设计在临时捕获轨道上的低能量低推力飞往月球的飞行

摘要

该研究考虑了计算低推力航天器在弹道捕获过程中到达月球的低能轨迹的问题。使用共线振动点L ₁或L ₂之一附近的过渡轨迹进行转移地月系统的一部分。使用传输轨道使我们能够通过在地月系统中应用航天器动力学来减少传输的燃料消耗。退出弹道捕获轨道后，根据任务目标，可以形成所需的月球轨道，或者可以完成机动以插入所需的行星际轨道。提出了一种解决该问题的方法，该方法包括选择合适的过境轨道以确保航天器在月球影响范围内停留足够长的时间，并计算从初始月球轨道到月球轨道的最佳小推力轨道。前往月球的轨道。解决最优控制问题并计算过境轨迹的最优退出点，庞特里亚金极大值原理与参数连续法结合使用。给出了计算弹道捕获过程中到月球的低能轨迹的数值例子，并优化了过境轨迹的出口点。