Space Gravitational Wave (GW) mission proposals often use constellation or formation flying for the required interferometry implementation. The spacecraft of most of these mission proposals go to deep space and many have Earthlike orbits around the Sun. ASTROD-GW, Big Bang Observer and DECIGO have spacecraft distributed in Earthlikc orbits in formation. LISA has three spacecraft arranged in a nearly equilateral triangle formation with 5 million kilometer arms, inclined by 60° with respect to the ecliptic and flying along an Earth-like heliocentric orbit trailing Earth by 20°. ALIA-Descope (Taiji) arc proposed to work on time delay intcrfcrometry for 3, 4, 6 Mkm arm-length LISA-like orbits. ASTROD-GW has 3 spacecraft near Lagrange points to range interferometrically with one another with arm length about 260 million kilometers. The formation design is an important issue for these missions. In this paper, a 4th-order compact finite-difference method for the multi-body two-point boundary-value problem is proposed to design the transfer orbits. The deployment of the formations is studied systematically for fixed travel time transfer. A compact finite-difference method is used to calculate the delta-V for the deployment of various LISA-like formations for fixed travel time transfer from LEO. Although the delta-Vs of three spacecraft are different, the mean delta-V is nearly constant for different configurations of the formation, and linearly related to the arm length.
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机译：太空引力波（GW）任务建议通常使用星座图或编队飞行来实现所需的干涉测量。这些任务提议中的大多数航天器都进入了深空，许多航天器绕着太阳运行着类似地球的轨道。 ASTROD-GW，Big Bang Observer和DECIGO的航天器分布在编队的Earthlikc轨道上。 LISA的三架航天器排列成几乎等边的三角形结构，臂数为500万公里，相对于黄道倾斜60°，并沿与地球类似的日心定心轨道飞行，其后沿地球20°。 ALIA-Descope（Taiji）弧线建议对3、4、6 Mkm臂长LISA样轨道进行时延积分测量。 ASTROD-GW在拉格朗日点附近有3艘太空船，彼此干涉测距，臂长约2.6亿公里。编队设计是这些任务的重要问题。提出了一种解决多体两点边值问题的四阶紧致差分方法来设计传递轨道。系统地研究了编队的部署，以实现固定的旅行时间转移。紧凑的有限差分方法用于计算增量V，以部署各种LISA类地层，以实现从LEO的固定行进时间转移。尽管三个航天器的增量V不同，但对于地层的不同构型，平均增量V几乎是恒定的，并且与臂长线性相关。
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