基于二叉树的太阳系小天体数值历表建立方法

The Design of Ephemerides for Solar System Minor Bodies Based on Binary Tree

在小天体深空探测任务中,经常需要调用力模型较完备的精确小天体数值历表,然而由于部分小天体可能有较大的轨道偏心率以及存在近距离飞越大行星的可能,导致传统的等区间分段切比雪夫多项式插值方法不适用于构建这些小天体的数值历表.在传统方法基础上采用结合误差自适应的二分法对原始轨道进行分段,并采用二叉树结构来组织所有的分段区间,能解决历表读取中的系数反查问题.以大偏心率近地小行星4179 Toutatis和3200 Phaethon、大偏心率彗星2P/Encke以及将近距离飞越地球的99942 Apophis小行星为例,通过数值仿真证实了该算法的有效性.由于该方法没有对小天体的轨道性质做任何要求,因此能够作为构建太阳系小天体数值历表的通用方法,可应用于大量目标小天体的精确轨道设计中.

In minor body missions, the numerical ephemerides constructed with complete force model integration are often used. However, some minor bodies may have high eccentricities, and some may flyby planets in close distance, which makes the traditional ephemerides construction method based on equal-section division not suitable for these bodies. Based on the traditional method, in this article, the original orbit section is divided in dichotomy way, and combined with error-adaptive method. We use binary tree to represent all sections, which resolves the coefficient search problem. The three high eccentrical minor bodies, 4179 Toutatis, 3200 Phaethon, and 2P/Encke, and 99942 Apophis, an asteroid that will flyby Earth in close distance, are taken as examples to show the validity of our method. Because this method does not restrict the orbit characteristics of minor bodies, it may be used as a general way to design the ephemerides of minor bodies in solar system, and it is suitable to deal with the precise orbit design for a large amount of target asteroids.