Geodesic Engineering for Propulsionless Spaceflight: Symbolic Optimization of Curved Spacetime Trajectories via the NEXUS Framework

Traditional propulsion systems are inherently constrained by fuel mass, energy inefficiency, and diminishing returns over interplanetary distances. This work proposes a radical shift in spaceflight methodology: rather than applying external force, we engineer the geometry of spacetime or field analogs such that desired trajectories emerge naturally as geodesics. We introduce NEXUS, a symbolic-discovery engine that autonomously derives governing equations from first principles using variational calculus, symmetry constraints, and geometric priors. Leveraging this framework, we derive new classes of spacetime metrics and field configurations that enable directed, propulsionless motion purely through curvatureinduced geodesics. Numerical simulations confirm spiral-like, slingshot, and drift-corridor trajectories that require no energy input, conserving relativistic invariants throughout. These findings establish a new paradigm in space navigation, enabling station-keeping, orbital insertion, and interplanetary drift with zero thrust—laying the groundwork for future curvature-engineered field architectures across gravitational, electromagnetic, and synthetic domains.