力学中一个趣味问题的讨论

Discussion on an Interesting Mechanical Question

在3维空间和n维空间中,当一个质点受到某一确定质量和密度物体的最大引力时,对该连续分布物体的形状进行物理分析和数学运算可发现,当物体对质点有最大引力时,物体表面任意质量元对质点的引力在引力合力方向上的分量都相等,而且在3维空间中物体的形状并非球形.

Through physical analysis and mathematical operations on the shape of a continuous distribution object with constant mass and density in three - dimensional space and n - dimensional space respectively, find a conclusion： when the resultant gravity of the object on a given particle is maximal, the component of gravity on the given particle of any particle with euqal mass in the object＇s surface in the direction of the resultant gravity is equal, and the shape of the object is not sphericity in three- dimensional space