中文摘要：

两个不同半球沿对称轴方向（第1种情形）或者接触面分开（第2种情形），球心间的距离是h．在情形1中，计算得到了展开到h一次项的引力势能表达式．由这个引力势能的解析表达式，得到了两个半球间的引力表达式．在情形2中，计算得到了展开到h二次项的引力势能表达式．当大的半球固定时，小的半球作简谐振动，并给出了周期公式．以上的解析式得到了数值计算值的验证．

英文摘要：

Two different hemispheres are separated from each other along symmetric axis （case one） or a contact plane （case two）. The distance between their centers is denoted as h. In the case one, the gravitational potential energy containing first order of h is derived. The attrac- tion force between two hemispheres is obtained from the analytical expression of the gravita- tional potential energy. In the case two, the gravitational potential energy containing second order of h is derived. When the bigger hemisphere is fixed, the smaller one＇s motion is a sim- ple harmonic vibration. The period time is given. All of those analytical expressions are con- firmed by numerical calculation results.