利用形状模型进行火卫一高阶重力场建模

High Degree Phobos Gravity Field Modeling Based on Shape Model

火卫一重力场对探测器的轨道设计及在星体表面着陆等任务而言极其重要。由于缺少探测器轨道跟踪数据,利用形状模型正演计算了火卫一高至80阶次的高阶重力场模型。介绍了基于火卫一形状模型计算引力位的边长法、面积法和体积法3种方法。在计算过程中,将多面体模型所在参考系由行星体固坐标系转换为以质心为原点、坐标轴与主惯性轴重合的坐标系。所计算引力位在45~56 m2/s2范围间变化,整体分布呈现条带状变化,且在Stickney陨石坑附近出现极大值。解算得到相对于x、y、z轴的惯性矩分别为0.355 45、0.418 10和0.491 34,C20项为-0.029 395 4, C22项为0.015 254。通过比较20阶、50阶、80阶重力场所计算的加速度,得出高阶重力场系数对加速度有明显影响的结论。

This paper solved a Phobos gravity field model with degree of 80 by using shape forward modeling method. We introduced three methods that are edge,surface,polyhedron,to generate integral unit and obtain outside potential value from shape model. During computation we rotated the reference coordinate system of the polyhedron model into the principal axis frame. The potential varies from 45-56 m2/s2, basically showing a stripped distribution and indicating a maximal value around the Stickney crater. Meantime, the moment of inertia in x,y,z axes, with values of 0.355 45,0.418 10,0.491 34 are obtained;the spherical coefficient C20 value is-0.029 395 4, and C22 value is 0.015 254. By comparing the acceleration of 20, 50 and 80 degrees gravitational potential fields, we can confirm that the benefits of higher degree of the gravity field can be seen on acceleration.