采用球面几何方法,严格定义了相对轨道要素(ROE),推导了其与绝对轨道要素(AOE)之间精确的相互转换关系;针对近圆和椭圆基准轨道相对运动情况,给出相对轨道要素和绝对轨道要素之间相互转换的近似式,以满足不同任务的要求;分析了卫星近距离相对运动时相对轨道要素的一些特性;基于相对轨道要素,推导了无奇点问题的、适用于近圆和椭圆基准轨道的近距离相对运动方程;据此分析了椭圆基准轨道卫星的相对运动特性,对比近圆基准轨道相对运动模型和精确解的结果进行了误差分析,通过典型算例验证了本文提出的方法和结果的正确性和有效性。论文研究结果完善了相对轨道要素的基本理论,统一了近圆轨道和椭圆轨道的卫星近距离相对运动的描述形式。

In this paper, the relative orbit elements (OREs) are strictly defined using the spherical geometry method. The accurate transformation between relative orbit elements and absolute orbit elements (AOEs) is deduced. Under the elliptical and circular reference orbit relative motion conditions, the approximate transformation equations between relative orbit elements and absolute orbit elements are derived to meet the needs of different missions. Some characteristics of the relative orbit elements are also analyzed for the case of close relative motion. A new relative linear model is derived based on the relative orbit elements with no singularity, which is suitable for close relative motion under elliptical or circular reference orbit conditions. The characteristics of elliptical relative motion are analyzed. Then an error analysis is carried out through a comparison of near-circular relative motion equations with the results of exact solutions. The proposed method and conclusions are validated by simulation through some typical examples. The study improves the basic theory of relative orbit elements, and unifies the expressions of elliptical and near-circular close relative motion.