月球和地球正常重力特征差异及成因探讨

Difference of normal gravity characteristics between the Moon and the Earth and its causes

月球和地球都非常接近于旋转椭球,基于正常椭球求定的正常重力场占据了月球和地球真实重力场的主要部分,比较月球和地球的正常重力,可以更好地理解这两个天体的重力变化特征.基于Clairaut定理求解月球和地球的正常重力,正常重力随纬度的变化呈现了相反趋势,即地球是两极的正常重力大于赤道的正常重力,而月球是两极的正常重力小于赤道的正常重力.从截断误差及椭球形状与自转角速度的协调关系分析了月球和地球正常重力随纬度变化产生相反趋势的原因:月球的椭球扁率与自转角速度之间的数值关系不满足行星流体静力学平衡条件,即利用Clairaut定理求解正常重力并不严格适用于月球.

The Moon and the Earth are very similar to a rotating ellipsoid.The normal gravity of such a ellipsoid accounts for the main part of their real gravity.Comparing the normal gravity of the Moon and the Earth calculated by the Clairaut theorem permits to improve understanding the characteristic of the gravity for these two celestial bodies.The normal gravity variations with latitudes between the Moon and the Earth show an opposite trend,i.e.the polar normal gravity is smaller than that of the equator on the Moon while the polar normal gravity is greater than that of the equator on the Earth.This paper analyses the reasons for such a difference from the truncation error,and the relationship between the shape of the normal ellipsoid and rotation angular velocity.Our research suggests that the relationship between the flattening and rotation velocity of the Moon does not satisfy the hydrostatic equilibrium conditions,which means the Clairaut theorem cannot be used to calculate the normal gravity of the Moon.