Abstract: Based on the principle of coincidence between the surfaces of equal density and the surfaces of equal geopotential inside the rotating fluid Earth, a differential equations is established to determine the parameters of the surfaces of equal geopotential inside the Earth. Using internationally recognized Earth models, obtain theoretical values of the shape parameters of the rotating Earth through numerical solutions and compare them with actual values. Comparison shows that the solutions of the differential equations derived in this article are closer to the actual values than the solutions of existing related differential equations, and the differential equations in this article are more suitable as the basic equations for studying the shape of the Earth. Due to the complexity of the process of establishing differential equations, attempts are made to adapt the teaching approach and omit those cumbersome mathematical formulas. Emphasis is placed on introducing the physical concepts and solutions involved, as well as the key steps, key nodes, key formulas, and important results in mathematical derivation.

Key words:  rotating earth, Earth shape, surfaces of equal density, surfaces of equal geopotential, earth model