(2010 SO16 is associated with Lagrange point L3 but wanders so far behind and ahead of it that the orbit is called "horseshoe"...
and the comment was made:
Not really. L3 is unstable. Horseshoe orbiters are in effect "alternating trojans" that switch between L4 and L5, with L3 as a transit point.
All of this breaks down in real solar systems with elliptical orbits and many perturbing bodies, but let's constrain ourselves to CR3BP rules
- two bodies have substantial mass (Sun, Earth) and 2010 SO16's mass can be ignored.
- Sun and Earth have circular orbits around a common center of mass
- all motion is in one plane, it's a 2D problem.
- are there closed, periodic 2D planar orbits in the CR3BP that are good models for horseshoe orbits?
- can we say that horseshoe orbits "associated" with any of the Lagrange points at all, or does this kind of language fail us when applied to horseshoe orbits?
- is either of us right? or both? or neither?
note: I'm not looking for opinions or "ways of looking at it". If there is a solid, supportable way to answer, hopefully with a little scholarly, authoritative sourcing, that will be great. But for the purposes of this question just qualitative insights or another way to look at it is's won't be so helpful in this case. Thanks!