Celestial mechanics is the branch of astrophysics that applies the laws of classical mechanics to determine the motion of celestial bodies, such as planets, moons, and stars, under the influence of gravitational forces. It utilizes mathematical principles, particularly those concerning orbital dynamics, to model the gravitational interactions within various astronomical systems. Key concepts include Kepler's laws of planetary motion, the conservation of energy and angular momentum, and the rigorous solution of the N-body problem, which addresses the gravitational interplay of multiple massive objects. The field allows scientists to predict celestial paths, model the formation and evolution of solar systems, and understand phenomena like galactic rotation and gravitational perturbations.