Motion Near L4, L5 Stable Lagrange Points - Tadpole, Horseshoe Orbits, Trojan Asteroids, Lucy Mission

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.

Lagrange point location review
L4 and L5
Characteristic polynomial
Critical value of mu for L4, L5 instability
Eigenvalues vs. mu mass parameter
Trojan asteroids of Jupiter and Lucy mission trajectory
Analytical approximation of eigenvalues for small mu
Superposition of short period and long period motion
Epicyclic motion, guiding center, large and small ellipse
Zero velocity curves near L4 and L5
Tadpole orbits, encircling L4 or L5
Horseshoe orbits, encircling L3, L4, & L5
Polar coordinate representation of tadpoles and horseshoe
Analytical formula for tadpole & horseshoe orbits
Out-of-plane motion