Satellite formation establishment may consume considerable fuel if cross-track distance (CTD) is a mission requirement. This work proposes a strategy for significantly reducing the required fuel. Instead of direct out-of-plane maneuvers, it is suggested to use in-plane maneuvers, while using the nodal precession caused by the $J_2$ perturbation. The CTD dynamics are analyzed, and representative formation geometries are considered. Analytical expressions for the CTD and related establishment timing are derived for the case of impulsive thrust. For most cases, the expected CTD establishment duration is reasonable, and the fuel saving with the $J_2$-assisted CTD establishment strategy is considerable. For the case of $J_2$-assisted CTD establishment with continuous thrust, optimal control methods are used. The proposed strategy is proven to be optimal for two cases: limited and unlimited thrust magnitude. Finally, the cases of $J_2$-assisted CTD establishment with impulsive and with continuous thrust are compared. It is shown that continuous thrust is preferable in terms of fuel, for similar CTD establishment durations.

如果跨轨道距离 (CTD) 是一项任务要求，那么卫星编队的建立可能会消耗大量燃料。这项工作提出了一种显着减少所需燃料的策略。建议使用平面内机动而不是直接的平面外机动，同时使用由平面引起的节点进动。$J_2$扰动。分析了 CTD 动力学，并考虑了具有代表性的地层几何形状。CTD 和相关建立时间的解析表达式是针对脉冲推力的情况推导出来的。在大多数情况下，预期的 CTD 建立持续时间是合理的，并且可以节省燃料$J_2$- 辅助CTD建立策略可观。对于以下情况$J_2$- 连续推力辅助 CTD 建立，采用最优控制方法。所提出的策略被证明对于两种情况是最佳的：有限的和无限的推力大小。最后，以下案例$J_2$比较了脉冲和连续推力的辅助 CTD 建立。结果表明，对于类似的 CTD 建立持续时间，就燃料而言，连续推力更可取。