关于近地小行星轨道演化的初步探索

本文采用改进的显式辛算法和嵌套的PKF7（8）积分器同时对86颗已命名（或编号）的近地小行星的轨道演化进行了数值研究，在103－104年的时间尺度上，给出了这些小行星轨道演化的状况以及它们与几颗大行星靠近的最小距离，特别是与地球接近的最小距离可小于0．01天文单位，甚至可能比月球还更靠近地球．

A PRELIMINARY INVESTIGATION OF THE ORBITAL EVOLUTION OF NEAR-EARTH ASTEROIDS

Both astCroids and comets are small bodies in the solar system, and the near-earthasteroids (NEAs) are a peculiar kind of asteroids. In recent years, the observation andstudy of the NEAs are well developed, and this has become one of the mostimportant fields of the dynamics of the solar system.The NEAs are divided into the following three kindst (1) Atentype with a < 1.0au and Q > 1.0 au, (2) Apollo-type with a > 1.0 au and q < 1.0 au, (3) Amonr-typewith a > 1.0 au and 1.0 au < q < 1.38 au. Here a is orbital semi-major axis, q =a(1 - e) is Perihelion distance, Q = a(1 e) is aphelic distance, e is orbita eccentricity,au is astronomical unit, and 1.38 au is the perihelion distance of Mars.In order to clarify the orbital evolution of the NEAs, it is necessary to performlong-term tracking computations. Hence the requirement for algorithm is very high.Ths means that the algorithm must maintan the global characteristics of the motions.Furthermore, the motion of a NEA corresponds to a Hamiltonian system. Thus thesymplectic algorithms just satisfy the requirement, because the symplectic differenceschemes preserve exactly the symplectic structure, which is one of the most importantfeatures for Hamiltonian phase flows.Based on the property that the motoons of the NEAs can be described by themodel of a two-body problem with perturbations, we use the composition of algorithmto construct an improved explicit symplectic algorithm with higher effciency. By useof the improved symplectic algorithm, the orbital evolutions of 86 NEAs for a timespan of 103-104 years are computed and some impohant results are presented in thepaper, e.g., (1) The orbits of asteroid #3552 and #4015 are unstable, (2) The minimaldistance between the asteroid #4660 and the Earth is close to 0.0018 au, which is lessthan the mean distallce between the Moon and the Earth.