QUANTITATIVE ANALYSIS OF CHAOS IN THE EARTH-MOON SYSTEM: CORRELATION BETWEEN LARGEST LYAPUNOV EXPONENT MAPS AND ESCAPE BASINS IN THE RESTRICTED THREE-BODY PROBLEM

Resumo

The design of low-energy space missions requires a deep understanding of transport mechanisms in the Earth-Moon system, often modeled by the Planar Circular Restricted Three-Body Problem (PCRTBP). While escape basins provide a qualitative classification of trajectory outcomes, they do not provide a quantitative measure of orbital instability. This work presents a quantitative analysis of chaos by correlating the Largest Lyapunov Exponent (LLE) with the basin structures. We implemented the periodic renormalization algorithm to compute the LLE for a grid of initial conditions in the lunar region. Maps of the LLE were generated for three distinct Jacobi constants (C=3.08, 3.15, 3.2004), corresponding to high, intermediate, and low energy levels. The results reveal a direct correlation between the fractal basin boundaries and regions of high LLE. The intermediate energy regime exhibits the most complex dynamical structure, with the highest LLE values, confirming the high sensitivity to initial conditions and the chaotic nature of the transition between escape and confinement. The high-energy regime (C=3.08) shows widespread positive LLE, while the low-energy regime (C=3.2004) is predominantly regular. This quantitative approach provides crucial information for trajectory design, identifying stable regions and unpredictability zones.