Central force optimization (CFO) is a new deterministic multi-dimensional search metaheuristic based on the metaphor of gravitational kinematics. CFO is a deterministic algorithm that explores a decision space by "flying" a group of probes whose trajectories are governed by Newton's laws. Based on in-deph studies on the probes movement governed by the equations of gravitational motion, this paper utilizes Celestial Mechanics theory to deduce moving formulas, establishes the relationship between CFO algorithm and Celestial Mechanics, and analyzes CFO convergence through mathematics analysis of Celestial Mechanics. It concludes that no matter how initial probe distribute, all probes converge deterministically in CFO space with optimal solution. To test CFO's effectiveness, a hybrid CFO-BP algorithm is proposed for joint optimization of three-layer feed forward artificial neural network (ANN) structure and parameters (weights and bias). The experimental results show that the proposed hybrid CFO-BP algorithm is better than other algorithms in convergent speed and convergent accuracy.