基于数值延拓的日月综合借力DRO入轨策略

Low-energy transfer from Earth into DRO with hybrid gravity assist and numerical continuation

远距离逆行轨道(DRO)是地月空间中的一类周期轨道,这类轨道具有长期稳定、入轨能量低的特点,可作为未来载人月球和载人火星任务的中转站。对于地球至DRO的两脉冲入轨任务,采用日月综合借力(即同时使用弱稳定边界(WSB)和月球借力(LGA))可以最大化入轨质量,但是这类轨道对初值非常敏感。使用日月综合借力拓展DRO入轨脉冲包络,改进构造方法和提供解析梯度大幅提高多步打靶收敛率,提出2层伪弧长延拓方法进一步降低任务总脉冲。数值仿真采用共振比为2∶1的DRO,脉冲最低解采用“LGA+WSB+2LGA”的飞行模式,飞行时间为123天,近地轨道发射脉冲为3.125 km/s,DRO入轨脉冲仅为19.7 m/s。

Distant retrograde orbits(DRO)are well-known trajectory types in cislunar space,such orbits have long-term stability and low insertion cost.In cislunar space,DRO are well-known trajectory types with minimal insertion costs and long-term stability.A cislunar station deployed on DRO might be expected to deliver a crew to the moon or Mars for exploration missions in the future.For low-energy transfer from Earth into DRO,the maximum delivery mass can be achieved by utilizing a weak stability boundary(WSB)and multiple lunar gravity assist(LGA)simultaneously,but this kind of transfer is very sensitive to initial values.A novel two-level pseudo-arc continuation method was proposed to explore local solution space,and this paper aims to improve both computational and transfer efficiency when leveraging hybrid gravity assist in cislunar space.Additionally,a modified problem description with an analytical gradient is used to improve multiple shooting efficiency under a bicircular restricted four-body problem.In the numerical simulation,the minimum cost solution shows“LGA+WSB+2LGA”,where the time of flight is 123 days,the LEO launching cost is 3.125 km/s and the 2:1 DRO insertion maneuver only needs 19.7 m/s.