銀河縮影 - 桌面磁力位能井系統的航道與混沌動力學 Orbits and Escape Dynamics of Potential well Landscape at Tabletop Scale
Compared with earlier studies on space trajectory that are mostly theoretical, our study uses magnetic potential well as an experimental analog of a gravitational potential well, making table scaled experiments to better understand physical model for spacecraft trajectories. In our theoretical model, we account for the finite size of real planets and used a finite magnetic force model to avoid singularities, fully deriving the equations of motion and have great predictive power against experiments. The experiments: (1) single-well trajectories—analyzing in-flight acceleration and quantitatively characterizing the flower trajectories; (2) Escape dynamics in multi-well landscapes—finding the escape conditions (escape velocity), also when a spacecraft falls into multiple wells and the patterns of wells capturing the spacecraft. We further examine special conditions, including gravity assists, relative motion with planets, and tangential velocity releases, to systematically identify the key parameters for trajectories. An extended discussion summarizes phase diagrams and quantifies chaotic behavior and quantized trends. The results provide concrete understanding for real mission planning and fuel-efficiency optimization.