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采用基于相对轨道要素的方法,建立了计算碰撞概率的数学模型。在二体圆轨道条件下,推导验证了与基于Clo-hessy-Wiltshire(C-W)方程的碰撞模型的等价关系,并解决了C-W方程存在的若干问题。在航天器近距离相对运动构型设计中提出了基于相对轨道要素的碰撞分析方法,突出了相对轨道要素在构型设计以及碰撞分析中的作用。分析了地球非球形引力摄动(主要是J2项摄动)对轨道误差的影响,推导了相对轨道要素在单位时间内的漂移量方程,及考虑J2项摄动的协方差矩阵的传播方程,建立了考虑J2项摄动的碰撞概率计算模型。最后,通过典型算例验证了本文方法的正确性。
Using the method based on relative orbital elements, a mathematical model for calculating the probability of collision is established. Under the condition of two-body circular orbit, the equivalence relation with the collision model based on the Clo-hessy-Wiltshire (C-W) equation is verified and some problems existing in the C-W equation are solved. A collision analysis method based on relative orbital elements is proposed in the configuration of spacecraft near relative motion, which highlights the role of relative orbital elements in the configuration design and collision analysis. The influence of non-spherical gravitational perturbation (mainly J2 perturbation) on orbit error is analyzed. The drift equation of relative orbit elements in unit time and the propagation equation of covariance matrix considering J2 perturbation are deduced. The collision probability calculation model considering J2 perturbation is established. Finally, the correctness of the method in this paper is verified by a typical example.