  The Three-Body Problem has fascinated scientists for centuries and it has
been crucial in the design of modern space missions. Recent developments in
Generative Artificial Intelligence hold transformative promise for addressing
this longstanding problem. This work investigates the use of Variational
Autoencoder (VAE) and its internal representation to generate periodic orbits.
We utilize a comprehensive dataset of periodic orbits in the Circular
Restricted Three-Body Problem (CR3BP) to train deep-learning architectures that
capture key orbital characteristics, and we set up physical evaluation metrics
for the generated trajectories. Through this investigation, we seek to enhance
the understanding of how Generative AI can improve space mission planning and
astrodynamics research, leading to novel, data-driven approaches in the field.
