基于相对轨道要素的航天器相对运动碰撞分析

采用基于相对轨道要素的方法,建立了计算碰撺概率的数学模型.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....

Collision Analysis of Spacecraft Relative Motion Based on Relative Orbit Elements

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.