This work is a theoretical breakthrough in the study of the many-body problem. Breaking the long-standing myth that the many-body problem cannot be solved analytically, the analytic solutions of the orbit equation, periodic formula, and the motion equation of the many-body problem are obtained skillfully herein. Furthermore, this study offers a rigorous mathematical proof of the coplanarity and common direction of celestial bodies within such systems. The conclusions are mathematically accurate and complete, potentially marking a culmination of over 300 years of inquiry since Newton first posed the problem. From a physics perspective, this study provides a theoretical basis for the stable operation of celestial systems that is fully aligned with astronomical observation across large and small galactic structures. Notably, the discovery that the orbital period of celestial bodies is related to their own mass is of great significance for studying the formation and evolution of galaxies and planetary systems.