小行星轨道演化研究中的数值方法

小行星是太阳系最重要的一类小天本，主要分布在两个区域；火星和木星轨道之间的一条主带和近地空间，近地小行星轨道的最大特点是其轨道半长径与地理轨道半长径相近，或近日距离接近甚至小于日地平均距离，其运动可深入到地球轨道的内部，迷将导致该类小行星与地球（还有金星、火星等）十分靠近甚至发生碰撞，这一特征给其轨道演化数值研究带来一些困难，包括天体力学方法中一般消除碰撞奇点的正规化处理以及对定性研究十分成功的辛算法都将在不同程度上失败，通过对几种常用数值方法（包括辛算法）计算效果的比较，根据小天体运动自身的特性，给出了相应处理措施，从而可提高计算结果的可靠性。

THE NUMERICAL METHODS OF THE RESEARCH IN THE ORBITAL EVOLUTION OF THE ASTEROIDS

The asteroids are the most important small bodies in the solarsystem,and they mainly lies in the two locations-a main belt between the Mars's orbit and the Jupiter's and the near-Earth space.The most feature of the orbits of Near-Earth Asteroids(NEAs) is that the semi-major axes of the orbits are nearly equal to that of the Earth or the perihelia distances are approximate to or even less than the mean distance between the Sun and the Earth,thus they could move into inside of the Earth's orbit,so that they might close approach or even colliside with the Earth (or other planets,such as the Venus,the Mars,etc.).The characteristic brings about some difficulties in the numerical research during their orbital evolution,which leads to the failure of the normalization technique in the general removal impact singularities of celestial mechanics methods and the Symplectic Algorithm which is successfully applied to the investigation in quality.By comparing the computation effects of several common numerical methods(including Symplectic Algorithm),and considering the nature of the movement of the small bodies,the corresponding treatments are provided here to improve the reliability of the computation.