空间碎片的空间密度算法研究

由于空间碎片的影响,空间环境日益恶劣,有必要建立空间碎片环境工程模型对空间碎片撞击航天器进行风险评估.本文研究了空间碎片环境模型中的重要环节,即碎片的空间密度问题,在统计理论与椭圆轨道理论基础上,分析及推导了空间碎片在空间中的分布状况及空间密度,并得出了碎片空间密度的空间坐标函数解析表达式.同时对引入假设条件的合理性进行了讨论,并利用双行元数据对结论进行了验证,利用本文方法得出的结果与双行元数据吻合.

Research on the Spatial Density Algorithm of Space Debris

With the development of human's space technology and activities,the space debris environment is getting more and more deteriorated,which results in a great threat to the safety of on-orbit space vehicles.Due to the threat,it's necessary to establish an engineering model for the space debris environment to access space vehicle's impact risk.Since the spatial density is the most important component in an engineering model of space debris environment,this paper is devoted to study the algorithm of the spatial density of space debris.By introducing the orbital parameters, the paper firstly gives the conception and the mathematical definition of spatial density of space debris.According to the definition,construction of the spatial density is carried out.With the aid of probability theory and orbital mechanics,the paper theoretically derives a general analytical expression for the spatial density.Afterwards,simplification of the general expression is discussed by introducing some assumptions,i.e.,uniform distribution over right ascension of the ascending node and over the perigee argument,independence of orbital parameters and of spatial coordinates.The result is a more simplified expression of the spatial density,which is suitable for computation.It turns out that the SDPA model's algorithm is just a particular case of the paper's general expression.To enlarge the simplified result's for apphcation,the paper proposes the classification method.To verify the paper's result,apphcation to the Two-line elements is presented,which validates the paper's result.The apphcation also shows that the classification method can help to improve accuracy.