Georgia Institute of Technology College of Sciences

Cislunar space—the region between Earth and the Moon—has reemerged as a critical area for space exploration. From a mathematical perspective, this region is governed by multi-body dynamics that give rise to rich structures, including invariant manifolds, resonant orbits, and homoclinic chaos. This talk will introduce classical and modern tools from celestial mechanics to analyze motion in the Earth–Moon system, with an emphasis on restricted 3- and 4-body problems. We will discuss how perturbative methods (normal forms) and invariant manifold theory (parameterization method) reveal the underlying organization of the phase space. Particular attention will be placed on connecting the perturbative regime, where classical methods apply, with the realistic system, which often lies far outside that regime, using computer-assisted techniques. Our ultimate goal is to establish rigorous results for the real solar system while enhancing the engineering capabilities needed to design and fly missions, highlighting how mathematics contributes both to theory and to the practical challenges of contemporary space exploration.

No prior knowledge is needed; the talk will be self-contained and accessible. Undergraduates are encouraged to attend.