Celestial Mechanics: Newton's Gravitational Law

This lecture delves into the concepts of angular momentum and Newton's law of gravitation. The instructor guides the audience through a historical perspective, exploring how Newton derived the gravitational force expression. The lecture demonstrates the central nature of the gravitational force, its relationship with centripetal acceleration, and the proportionality to mass and the inverse square of distance. The discussion extends to the application of Newton's third law, emphasizing the equal and opposite forces between celestial bodies. The lecture concludes with an analysis of the energy and potential in gravitational fields, showcasing the conservation of energy and the implications for orbital motion, including elliptical trajectories and escape velocities.