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ADAPTED SYZYGY FUNCTIONS FOR THE PRELIMINARY DESIGN OF MULTIPLE GRAVITY ASSISTED TRAJECTORIES

机译:适用于多重重力辅助轨迹的初步设计的Syzygy功能

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In the design of Multiple Gravity Assisted (MGA) trajectories, the most critical and time-consuming phase is the definition of the sequence of planets at which to perform the flybys. A general approach tackles the MGA problem using a branch and bound technique to resolve the combinatorial problem arising by the possible sequences of planets to be flown in order to reach the destination in reasonable amount of time. It is clear how, depending on the associated launch window and the total time of flight, not a unique optimal configuration exists. Possible solutions are searched selecting each planet at a time, resolving the associated Lambert problem for a specific time of flight and choosing the minimum delta-v solution. Such an approach is extremely expensive from a computational point of view: depending on the orbital distance to be reached and the associated number of planets that could be flown, the process requires at each stage the evaluations of the remaining possibilities in cascade and for different encounter epochs. The goal of this paper is to provide a quick estimate of the possible planet configurations for the preliminary design of suboptimal MGA trajectories. For such purpose, the Syzygy function, commonly used in astronomy for the identification of planet alignment, is mimicked and adapted to satisfy the needs of trajectory design. Different strategies to exploit this approach are presented. At a first stage, a simple modification of the classical Syzygy function is considered: the alignment condition is maintained but with a time shift, ensuring that, between one planet and the following one, the time of flight between two planets is exactly a Hohmann semi-period. The limitation of this approach, which always enforces a Hohmann transfers between one planet and the following, is resolved by the use of a shape-based approach for the trajectory model, which modifies the Syzygy line condition into a conic section one. Shaping the trajectory on the eccent
机译:在多重重力辅助(MGA)轨迹的设计中,最关键且耗时的阶段是执行鹅卵沟的行星序列的定义。一般方法使用分支和绑定技术来解决MGA问题,以解决待飞行的行星可能序列而产生的组合问题,以便在合理的时间内到达目的地。很清楚如何,根据相关的启动窗口和总飞行时间,不存在独特的最佳配置。一次搜索可能的解决方案,一次选择每个行星,解决相关的LAMBERT问题,用于特定的飞行时间并选择最小的DELTA-V解决方案。这种方法从计算的观点来看非常昂贵:取决于达到的轨道距离以及可以飞行的相关行星,该过程需要在每个阶段进行级联和不同遭遇的剩余可能性的评估时代。本文的目的是提供对次优MGA轨迹初步设计的可能行星配置的快速估计。出于这种目的,常用于天文学的Syzygy功能用于识别行星对准,模仿并适合满足轨迹设计的需求。提出了利用这种方法的不同策略。在第一阶段,考虑了古典Syzygy函数的简单修改:保持对准条件,但是随着时间的推移,确保在一个行星和下面的一个星球之间,两个行星之间的飞行时间正好是Hohmann半-时期。这种方法的限制始终在一个行星和下面实施的Hohmann传送,通过使用基于形状的轨迹模型来解决,该方法是将Syzygy线条件修改为一个圆锥部分。在换档上塑造轨迹

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