Abstract: In theoretical mechanics textbooks, the center of gravity is usually defined as the simplest simplification center of gravity as a parallel force system, that is, the point of action of the resultant gravitational force. According to the property of the simplest simplification center of a force system, the simplest simplification center is not unique. On the other hand, almost all theoretical mechanics and university physics textbooks provide expressions for the position of the center of gravity, stating that the center of gravity is uniquely determined, which contradicts the non-uniqueness of the simplest simplification center of a force system. This article rigorously elaborates on the relevant concepts of the simplest simplification center and the center of gravity, and clarifies some ambiguous understandings of the simplification center of parallel force systems and the center of gravity.