地月空间DRO环月全球定位卫星星座设计

doi:10.12305/j.issn.1001-506X.2024.12.26

摘要/Abstract

摘要：

为了实现环月全球定位卫星星座设计，概述了月球全球定位卫星星座的研究现状，对基于远距离逆行轨道(distant retrograde orbit，DRO)的环月星座进行深入研究。首先，以圆型限制性三体模型的平面DRO为初值，以DRO初始相位角、轨道平均周期和z方向运动振幅作为参数描述三维DRO，计算双圆限制性四体模型中保持3年稳定的DRO。然后，借鉴地球轨道Walker星座概念，提出基于DRO基准轨道等相位差部署的环月星座设计方法。最后，针对卫星总数量均为16的DRO环月星座，分析单基准轨道、双基准轨道和四基准轨道星座的性能，验证了所提方法的有效性。

关键词: 月球全球定位卫星星座, 构型设计, 远距离逆行轨道, 远距离逆行轨道基准轨道

Abstract:

In order to achieve the design of a circumlunar global positioning satellite constellation, this article provides an overview of the current research on the lunar global positioning satellite constellation and conducts in-depth research on circumlunar constellation based on distant retrograde orbit(DRO). Firstly, taking the planar DRO of the circular restricted three-body model as the initial value, the three-dimensional DRO is described with the DRO's initial phase angle, orbital average period, and z-direction motion amplitude as parameters. The DRO that remains stable for three years in the bicircular restricted four-body model is calculated. Then, drawing inspiration from the concept of the Earth orbit Walker constellation, a circumlunar constellation design method based on the phase difference deployments such as DRO benchmark orbits is introduced. Finally, the performance of single-benchmark, double-benchmark, and quadruple-benchmark orbit constellations are analyzed for the DRO lunar constellation with 16 satellites in each constellation, and the effectiveness of the proposed DRO lunar constellation design method is validated.

Key words: lunar global positioning satellite constellation, configuration design, distant retrograde orbit (DRO), DRO benchmark orbit

中图分类号:

周晨光, 张仁勇, 杨驰航. 地月空间DRO环月全球定位卫星星座设计[J]. 系统工程与电子技术, 2024, 46(12): 4173-4182.

Chenguang ZHOU, Renyong ZHANG, Chihang YANG. Design of circumlunar global positioning satellite constellation on DRO in the cislunar space[J]. Systems Engineering and Electronics, 2024, 46(12): 4173-4182.

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物理意义	符号/单位	数值
月球-地球质量比	μ(无量纲)	1.215×10^-2
单位距离	DU/km	3.844 05×10⁵
单位时间	TU/s	3.752×10⁵
单位质量	m^*/(kg³·s^-2)	4.035×10⁵
单位速度	VU/(km·s^-1)	1.024 083 366 852
太阳质量	m_s(无量纲)	3.289 005 41×10⁵
太阳到地月质心的距离	ρ(无量纲)	3.888 111 43×10²
太阳旋转角速度	ω_s/(rad·s^-1)	2.465 9×10^-6

参数	参数含义	表达式
x	设计变量	x₀
g(x, p)	不等式约束	L_mean－L_UB
J(x, p)	目标函数	ΔT
x_LB	设计变量的下界	x₀－[ΔX_LB, ΔY_LB, ΔZ_LB, Δv_{x_LB}, Δv_{y_LB}, Δv_{z_LB}]
x_UB	设计变量的上界	x₀+[ΔX_UB, ΔY_UB, ΔZ_UB, Δv_{x_UB}, Δv_{y_UB}, Δv_{z_UB}]
p	固定参数	[N_s, L_UB]

DRO共振比	月球北极点		月球南极点
DRO共振比	最大仰角/(°)	平均仰角/(°)	最大仰角/(°)	平均仰角/(°)
2∶1	25.24	12.10	24.40	12.16
3∶1	26.80	13.93	26.48	13.91
4∶1	31.96	16.76	31.72	16.80

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