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Clohessy-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。

In this article, a collision probability model is introduced based on the relative orbit elements. Under the two-body circular orbit conditions, its equivalence relation with the collision model based on Clohessy-Wiltshire (C-W) equation is derived and verified. Some remained problems of the C-W equations are also solved. A new method for collision analysis based on the relative elements is proposed for the configuration design of the close relative motion. Then the role of the relative orbital elements is highlighted on configuration design and collision analysis. The impact of the earth gravity harmonics perturbation (mainly J₂ perturbation) on the orbit error is analyzed. The drift equation of the relative elements in the unit time is derived, the propagation equation of the covariance matrix is given, and the collision probability model is established with the consideration of the impact of J₂ perturbation. Finally, the proposed calculation method is validated by simulation through a typical example.