引用本文: 张赛, 杨震, 罗亚中. 地固系下航天器单脉冲轨道机动可达域求解算法. 力学与实践, 2022, 44(6): 1286-1296.
Zhang Sai, Yang Zhen, Luo Yazhong. An algorithm for solving spacecraft reachable domain with single-impulse maneuvering in ECEF coordinate system. Mechanics in Engineering, 2022, 44(6): 1286-1296.
 Citation: Zhang Sai, Yang Zhen, Luo Yazhong. An algorithm for solving spacecraft reachable domain with single-impulse maneuvering in ECEF coordinate system. Mechanics in Engineering, 2022, 44(6): 1286-1296.

## AN ALGORITHM FOR SOLVING SPACECRAFT REACHABLE DOMAIN WITH SINGLE-IMPULSE MANEUVERING IN ECEF COORDINATE SYSTEM

• 摘要: 航天器轨道机动可达域是空间态势的有效表征方法，对空间目标机动监测、威胁评估和碰撞预警等有重要意义。特别地，地固系下的轨道机动可达域对分析机动卫星星下点轨迹变化、静止轨道机动卫星可达区域等作用显著。现有关于可达域的研究多针对惯性系下绝对可达域的求解，地固系下可达域的求解方法目前尚无研究。由于存在坐标系旋转引起的时间变量耦合，地固系下可达域的求解不如地心惯性系下容易。针对该问题，本文提出了一种基于可达性约束和时间约束的可达域计算方法。首先，在地惯系下通过两点边值问题的边界速度双曲线建立近心点坐标系下任意方位是否可达的可达性判据；其次，通过地固系和地惯系之间的转换关系建立地固系下任意方位可达的时间约束方程，从而建立地固系下轨道机动可达域的求解模型，将可达域包络求解问题转为可达方向矢径极值求解问题；再次，根据转移轨道面内航天器真近点角变化量推导可达方向上矢径大小方程，通过计算极值点确定地固系下航天器轨道机动可达域。通过蒙特卡洛仿真验证表明，本文所提出的地固系下航天器单脉冲轨道机动可达域求解方法正确有效。

Abstract: The spacecraft reachable domain (RD) is an effective tool in space situational awareness, which can be used in maneuver detection, threat assessment and collision warning. In particular, the RD in earth-centered earth-fixed (ECEF) coordinate system plays a significant role in analyzing the variation of maneuvering satellite’s subastral point and the reachable region of a maneuvering satellite in geostationary orbit (GEO). The majority of available literature provided the calculation of the absolute RD in earth-centered inertial (ECI) coordinate system. Nevertheless, the solution of RD in ECEF has not been studied before, which is still a hard nut to crack due to time coupling caused by the transformation of different coordinate systems. To solve this problem, an algorithm is developed in this paper by handling time constraint and accessibility constraint. The accessibility constraint of arbitrarily given orientation in ECI is firstly established by means of terminal velocity hyperbola in two-body orbital boundary-value problem. In addition, the coordinate transforming relation between ECEF and ECI is applied to construct the time constraint of the accessibility of arbitrarily given orientation in the ECEF coordinate system. Based on these two constraints, a solution model for solving the RD in ECEF is presented. The problem of determining the entire envelope of RD is consequently transformed into finding the extremum of spacecraft position vector in an accessible orientation. Then the RD in ECEF can be obtained by finding out the extremum of expression of position vector in any accessible orientation, which is derived by virtue of the variation of spacecraft's true anomaly in transfer orbit. Finally, the method proposed in this paper is verified by Monte Carlo simulation to show its feasibility and effectiveness.

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