Ellipse: Astronomical Evolution to Mathematical Formulation

This lecture delves into the evolution of astronomical systems from antiquity to the Renaissance, focusing on the transition from geocentric to heliocentric models. It covers Kepler's laws, the concept of elliptical trajectories, and the fundamental parameters of an ellipse. The instructor discusses the mathematical principles behind the ellipse, including its parametric equations and geometric properties. The lecture also explores the historical context of Copernicus, Galileo, and Newton in shaping our understanding of celestial mechanics.