Abstract This study focuses on the construction of a Lissajous orbit in the Circular Restricted Three-Body Problem in the Earth-Moon-particle system using Richardson’s analytical Methodology with a third-order frequency correction. The motivation for this poster is the growing prominence of analytical methods in translunar orbit and trajectory propagation due to the increasing interest of the private and public space sector. Analytical methods do not rely on numerical integration, they rather use algebraic expansions; they provide prominent data regarding the geometry of the orbit. The key finding is the realistic representation of a Lissajous orbit with a solely analytical calculation framework and the quasi-periodic beating property of Lissajous orbits.
Silye et al. (2026) studied this question.