中文摘要：

在小行星探测任务中，航天器轨道设计需要充分考虑到小行星的非球形引力场的影响．太阳系中大部分小行星具有形状不规则、密度不均匀的特点，因此，在没有绕飞轨道数据的情况下，精确计算其引力场非常困难．利用不规则小行星的多面体模型，采用体积离散方法通过直接积分计算小行星引力场球谐系数和表面重力场分布情况．将该方法与多面体方法进行了比较，并以（433）Eros为例，通过该方法计算得到的结果与NEAR（Near—Earth Asteroid Rendezvous）探测器的轨道数据反演结果比较，C20项误差不超过2％，使用该方法对我国小行星探测任务拟探测的（19961FG3d~行星的重力场进行了计算．以嫦娥二号探测器飞越的（4179）Toutatis小行星为例，结合相应的雷达观测数据提供的小行星形状模型，计算其表面引力势情况，为通过飞越任务获取的光学图像分析其表壤的分布、流向等提供了相应的理论依据．该方法适用于密度不均匀天体，可为小行星探测任务轨道设计和着陆提供可靠的小行星引力场数据．

英文摘要：

In the orbit design procedure of the small bodies exploration missions, it＇s important to take the effect of the gravitation of the small bodies into account. However, a majority of the small bodies in the solar system are irregularly shaped with non-uniform density distribution which makes it difficult to precisely calculate the gravitation of these bodies. This paper proposes a method to model the gravitational field of an irregularly shaped small body and calculate the corresponding spherical harmonic coefficients. This method is based on the shape of the small bodies resulted from the light curve data via observation, and uses finite volume element to approximate the body shape. The spherical harmonic parameters could be derived numerically by computing the integrals according to their definition. Comparison with the polyhedral method is shown in our works. We take the asteroid （433） Eros as an example. Spherical harmonic coefficients resulted from this method are compared with the results derived from the track data obtained by NEAR （Near-Earth Asteroid Rendezvous） detector. The comparison shows that the error of C20 is less than 2%. The spherical harmonic coefficients of （1996） FG3 which is a selected target in our future exploration mission are computed. Taking （4179） Toutatis, the target body in Chang＇e 2＇s flyby mission, for example, the gravitational field is calculated combined with the shape model from radar data, which provides theoretical basis for analyzing the soil distribution and flow from the optical image obtained in the mission. This method is applied to uneven density distribution objects, and could be used to provide reliable gravity field data of small bodies for orbit design and landing in the future exploration missions.