Kepler's Laws: Elliptical Orbits

This lecture covers Kepler's laws of planetary motion, focusing on the transition from the epicyclic model to elliptical orbits. It explains how Kepler's radical departure from the ancient system led to the formulation of the three laws of planetary motion, emphasizing the elliptical nature of Earth's orbit and the implications for the duration of seasons. The lecture also delves into the mathematical construction of ellipses, the significance of eccentricity, and the characterization of different types of conic sections. It concludes with a detailed exploration of the parametric equations and geometric properties of ellipses, parabolas, and hyperbolas.