Jupiters Lagrange points

In this project, our team investigated the Lagrange points in the Sun–Jupiter system, focusing on the Trojan asteroid groups that cluster near the stable L4 and L5 points. We compared the stability of L1, L2, and L3 (unstable) with L4 and L5 (stable equilateral triangle positions), and examined their significance for both natural celestial mechanics and spacecraft applications.

The analysis involved applying Newton’s law of gravitation and Kepler’s third law to derive conditions for equilibrium, then solving the resulting equations computationally. Using Mathematica and MATLAB, we calculated the approximate distances of the L1 and L2 points from Jupiter and built models to visualize the dynamics of the system.

Our results aligned closely with theoretical expectations: L4 and L5 proved stable regions that naturally accumulate large populations of Trojan asteroids, while L1 and L2 required constant adjustment to maintain position. This work demonstrated how orbital mechanics, computational modeling, and systems analysis can be combined to study both astrophysical phenomena and practical mission design strategies.