应用Lane-Emden方程分析下月幔厚度与月核半径大小

文中取圈层结构和球对称形态为月球的基本结构假设，并以月球平均密度和无量纲惯性矩作为约束，数值求解月球Lane-Emden方程，得到下月幔厚度和月核大小的变化范围.结果表明月核的密度在4.7 ~7.0 g/cm3范围内变化时，月核半径的变化范围为704~356 km，相应的月幔厚度的变化范围约为33～381 km，月核占月球总质量的百分比在0.6%～7%之间变化.所得结果可为后续的关于月球内部结构的研究提供一定的参考.

Analysis of the lower mantle thickness and core size of lunar based on the solution of the Lane-Emden equation

On the premise of the layering structure of the lunar and spherically symmetric interior of lunar, We calculated numerically the lunar Lane-Emden equation based on the similar properties between lower mantle and core of lunar and the earth. Also constrained by the mean density and nondimensional moment of inertia of the lunar. Then obtained the lower mantle thickness and the core size of the lunar. The results were that： if the density variation of the lunar core changed from 4.7 g/cm³ to 7.0 g/cm³ ,then the corresponding variation of lower mantle thickness of the lunar would be varied from 33 km to 381 km, as well as the core size would be changed from 704 to 356 km. The ratio of the core mass to the total mass of the lunar spanned from 0.6% to 7%.In order to show a clue to further work about the lunar inner structure, A further discussion about the result which derived from the specifically condition was proposed at last.