Although CR3BP can be highly chaotic, it present a lot of variety of periodic and quasi-periodic orbits (PO) types, esspecially in around M2 region and in relatively high energy (such as both L1 and L2 gates are open). Because the disturbance effect of bigger body (M1) influences on M2 very much, many alternative orbits, which are quaite useful as any science orbits, can be appeared. Therefore, it is better to classifed these huge amount of orbits for convenience.
Here the periodic orbits (PO) types around M2;
- Retrograde ones, whose motions are reverse relative to rotation axis. They are quite stable, but they may not be suitable as transfer orbits that they are too close in their orbits. They can be easily appear in both low and high energy levels. And their places can be found using Poincaré mapping method.
- Direct ones, whose motions are same direction as rotation axis. In 2D-CR3BP, they can be stable in low-enegy levels (while both L1 and L2 gates close), but they are highly unstable in high energy levels. On the other hand, in 3D-CR3BP, it is observed that some medium inclined direct orbits can be stable in high energy level, too (this phenomenon will be explained later, now see). They are very suitable for transfer orbits and they can be perfect parking orbits for stabilizng capture transfer orbits. In the litarature, low energy transfer operations can be done thanks to them. They can be also clasified as Low and High energy level ones;
- Low energy ones; as it is mentioned above; if orbits in the energy level both L1 and L2 gates close, then they are in low-energy level. And they can be called Low energy-orbits. These orbits are mainly restricted and imprisoned in zero velocity curves. They can be either found using Differantial corrector (DC) method or Poincaré mapping method.
- High energy ones; opposite the above, if orbits in the energy level both L1 and L2 gates are open, then they are in high-energy level. And they can be called high energy periodic orbits. Although they are not imprisoned in zero velocity curves, they can be still bounded and become either stable or unstable periodic orbits;
- Unstable ones; They are dynamicly very sensitive that they can easily escape their neighborhood, unless artifical control mechanism. Depend on the space mission, they can be very useful.
- Stable ones; They make periodic motion spontaneously in effect of gravitational forces, without needed any control mechanisim to keep them their orbits. According to my reserach and thesis, (I’ll later present), large amount of stable-high enegy PO are located in around medium inclination (~45°) relative to M2. ^_^
These are very simple classification of PO’s around M2, and in addition to them, there are also Homoclinic and Heterocilinic cycles in neck region of CR3BP, so around M2. I’ll later update this page, putting some periodic orbits figures around M2. But in advance, you may look this catalog by Ryan P. Russell, Global Search for Planar and Three-dimensional Periodic Orbits Near Europa, see the appendix.