Quasi-Periodic Orbit
Author: Tianjiang Says
Website: https://cislunarspace.cn
Definition
A quasi-periodic orbit is an orbit that traces out a bounded trajectory without exactly closing on itself. In the ephemeris model, where perturbations from the Sun, planets, and other sources are present, periodic orbits of the Circular Restricted Three-Body Problem (CR3BP) evolve into quasi-periodic orbits.
Characteristics
| Feature | Periodic Orbit (CR3BP) | Quasi-Periodic Orbit (Ephemeris) |
|---|---|---|
| Trajectory | Exactly closed | Never exactly closes |
| Motion | Single frequency | Multiple incommensurate frequencies |
| Geometry | 1D curve | Fills a 2D torus surface |
| Long-term behavior | Repeats exactly | Bounded but non-repeating |
Behavior of DRO in Ephemeris Model
When a DRO computed in the CR3BP is propagated in the ephemeris model:
- The trajectory no longer closes exactly
- It winds within a bounded region, tracing out a torus-like structure
- The overall shape remains similar to the CR3BP periodic orbit
- The orbit remains bounded for long durations due to the inherent stability of DROs
Significance
Quasi-periodic orbits are important for mission design because:
- They represent the actual motion in realistic perturbation environments
- They can be used as reference orbits for station-keeping
- Their structure determines the achievable orbit accuracy
Related Concepts
- Distant Retrograde Orbit (DRO)
- Circular Restricted Three-Body Problem (CR3BP)
- Ephemeris Model
- Orbit Keeping
References
- Chen Yuju. DRO Orbit Design and Control Research for Cislunar Space Situation Awareness[D]. 2024.