The Strict Transformation Formula between the Expansion of Different Tidal Generating Potential

The establishment of the lunar observation platform can realize the large-scale, continuous and long-term dynamic observation for the Earth, and can better meet the needs of scientific research on global change. In addition, it is also of great significance to study the early history and evolution of the moon and the Earth-moon system, as well as the deep structure and composition analysis. The construction and application of the lunar platform will certainly drive scientific and technological progress, stimulate industrial development, and have a profound impact on human civilization. The study of lunar tidal deformation is the basis of establishing high precision lunar observation platform. The tidal forces on the surface of the moon are about 20 times greater than those on the Earth, and the lunar tidal love number is less than an order of magnitude smaller than the Earth tidal love number. Therefore, the tidal effect on the lunar surface is significant. In this paper, the expression of tidal generating potential for any celestial body (including the moon), which takes into account its shape and can be expanded to any order, is given by using vector method. At the same time, a new Legendre polynomial recurrence relation is given.