卫星运动近点角间的差异极值符号表达式

Symbolic Expressions of Difference Extrema Betw een Anomalies for Satellite Movement

卫星星历的计算涉及三种近点角,利用近点角间的几何关系,借助计算机代数系统推导出近点角间的差异极值点及对应的差异极值符号表达式,并将其表示为关于偏心率e的幂级数形式。分别取偏心率e=0.01、e=0.1和e=0.2(小偏心率)为例,将近点角间的差异明确在数值上面。结果表明,近点角间的差异极值的绝对值与偏心率e密切相关,近似为偏心率e的一倍或者两倍的关系。这些分析结果可为研究近点角之间的关系、卫星星历计算以及卫星精密定轨提供理论基础。

In the calculation of satellite ephemeris, three different anomalies are defined in the two- body problem. According to the three kinds of anomalies＇ geometrical relationship, symbolic expressions of difference extreme points with corresponding extrema between these anomalies are derived and expressed in a power series of eccentricity e by the computer algebra system.Taking eccentricity e equals to 0.01,0.1 or 0.2 for the example, differences between anomalies are shown through numerical values. The results show that the absolute value of its extremum is approximately equal to once or thice the eccentricity e, which is not less than the eccentricity e. The findings could provide theoretical basis for the relationship between the three kinds of anomalies, satellite ephemeris calculation and the precise orbit determination.