To determine the Earth’s dynamics and their equations, which are crucial for Earth science research, this paper analyzes the interaction forces in the motion of a three-body system (namely, fixed, active, and passive points), based on the orbital motion. The mathematical derivation has been conducted strictly according to trigonometric functions with time and space as variables. In spatial transformation, related data items are simplified and replaced reasonably and necessarily according to the physical phenomenon to conduct derivations of planar to spatial transformation, through which the motion point has universal significance. Moreover, the polynomial equation for the dynamics has been obtained. Results indicate that the polynomial expression for the dynamics comprises the tidal force, the powerful mid-latitude Force (PML Force), and gravitation. Gravitation analysis shows that it is proportional to the dynamics quality, the size of the angular velocity of their deviation from the progenitor–paternal orbital plane’s center position, and the square of the progenitor orbital plane’s distance. However, it is inversely proportional to the distance of the paternal orbital plane and not related to another body’s quality. Some past errors are addressed and some constructive conclusions are offered in the discussion of gravitation.