This study analyzes the application limitations of Newton’s law of gravitational force in the many-body problem and reveals the fundamental problems with the application of Newton’s gravitational formula in the current central configuration theory widely used in celestial mechanics. A new method suitable for the synthesis of gravitational vectors in many-body systems is proposed, and a new central gravity theory system is constructed accordingly. The proposed theory provides a concise framework for the dynamic modeling and analysis of complex celestial systems. Based on the many-body mechanical equation established by the central gravity formula, the analytical solution of the many-body problem was successfully solved, and an important theoretical breakthrough in this field was achieved in the field. It has been more than 300 years since Newton proposed the three-body and many-body problems. The central gravitational formula has undergone rigorous mathematical derivation and logical verification, and this formula now has theorem properties, marking the substantial progress of celestial mechanics. The theory of central gravity is expected to have a profound impact on the theoretical development of astrophysics.