Explore the fascinating world of motion near L4 and L5 stable Lagrange points in this comprehensive 47-minute lecture. Delve into the intricacies of tadpole and horseshoe orbits, Trojan asteroids, and the Lucy mission. Learn about the characteristic polynomial, critical mass parameter values, and eigenvalue analysis for L4 and L5 stability. Discover analytical approximations, epicyclic motion, and zero velocity curves. Examine the polar coordinate representation of orbits and analytical formulas for tadpole and horseshoe trajectories. Gain insights into out-of-plane motion and the effective potential energy in the circular restricted 3-body problem. Perfect for those interested in orbital mechanics, dynamical systems, and space mission design.