backpropagation of the 2016 HO3 quasi stable (QS) orbit around Earth

[NoamTene]

I understand that backpropagation of the 2016 HO3 quasi stable (QS) orbit around Earth for several thousand years would show multiple transitions between QS and horseshoe (HS) orbits in a rotating reference frame with:

• a constant rate of one rotation per sidereal year
• the origin at the Solar System Barycenter (SSB)
• Earth moves in an ellipse centered around x=1 AU y=z=0

According to "Lunar ejecta origin of near-Earth asteroid Kamo`oalewa is compatible with rare orbital pathways", 2016 HO3 could be Lunar ejecta from a collision more than 100ky ago. If this is the case, it should be theoretically possible to back propagate the orbit over hundreds of QS/HS transitions all the way back to the Moon.

It is very likely, however, that small numerical errors will grow exponentially especially during each close approach to the Earth/Moon system which triggers the HS/QS transitions. Trying to propagate these unstable orbits for a million year may not be feasible even with infinite machine precision due to inaccuracy in our current knowledge of the 2016 HO3 orbit and of other solar system ephemerides (Luna, Sun, Jupiter and Venus).

What should still be possible, however, is looking for boundary conditions on both the starting and ending states of 5000 year runs that would remain within 10% of 1 AU without being ejected. For long enough simulations, orbits that satisfy that condition should converge to one of several fixed cycles that avoid resonance conditions with frequent Earth approaches and have a periodic sequence of flyby effects that helps keep the semimajor axis close to 1AU over several millennia.

For these orbit families to be meaningful, it may eventually be necessary to account for the sensitivity to YORP effects, Milankovitch cycles and variations in planetary ephemerides. While these inputs may be unknown, it may be possible to map them into equivalent small variations in the boundary conditions that have similar and predictable effects.

How hard would it be to build a baseline for such a simulation that can then be pertubed for the sensitivity analysis?

Can you recommend targeting and/or optimization tools that would be compatible with rebound?

[hannorein]

Are you aware of ASSIST? It's an add-on for REBOUND which would be the right tool. Another thing you might want to look into are variational equations. I'm not sure which optimization tool works well for this system. I'd maybe do a rough grid-based parameter search first.

https://github.com/matthewholman/assist https://academic.oup.com/mnras/article/459/3/2275/2595117

[NoamTene]

My background is from spacecraft orbit design (STK/astrogator, Freeflyer and Swingby). I was not even aware of rebound until recently, but I would like to start using it. I learn fast when I can program by example, making changes to existing code and scripts instead of trying to create it from scratch.

Are you suggesting that I might need ASSIST even for the basic simulation? Or was that only relevant to pertubations due to YORP effects, Milankovitch cycles and variations in planetary ephemerides?

[hannorein]

I suggest you consider using ASSIST for your problem.