169451 (2002 BF22) and 853271 (2009 BE162)

Back propagation orbital analysis based on nominal parameters.

Back propagation orbital analysis based on covariance clones.

Covariance clone convergence summary
- 2002 BF22 = 169451 (2002 BF22)
- 2009 BE162 = 853271 (2009 BE162)

Run setup:
- Pair mode, 100 covariance clones per target plus nominal.
- 101 samples per target, 10,201 clone-pair combinations.
- Analysis epoch: JD 2461200.5.
- Window center: 7731.815 yr before analysis epoch.
- Objective: minimize median relative velocity.
- Integrator: REBOUND IAS15, initial dt 1 day, default IAS15 epsilon.
- Massive bodies: Sun; Mercury, Venus, Earth-Moon, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto barycenters; Ceres, Pallas, and Vesta.
- Test particles: all nominal/covariance-clone samples for the two targets; clones are massless and do not perturb the massive bodies or each other.

Best convergence:
- Best time: 7711.893125 yr before analysis epoch.
- Best-time JD: -355617.820022.
- Median relative velocity: 1.477425 m/s.
- Median distance: 28,530.353 km.

Distance distribution at best time:
- Min / p05 / p16: 2,347.644 / 3,492.095 / 8,338.375 km.
- Median / p84 / p95: 28,530.353 / 63,184.025 / 93,165.494 km.
- Max: 168,315.951 km.
- Fractions below thresholds: 19.32% < 10,000 km; 96.01% < 100,000 km; 100% < 1,000,000 km.

Relative-velocity distribution at best time:
- Min / p05 / p16: 0.151787 / 0.203557 / 0.441629 m/s.
- Median / p84 / p95: 1.477425 / 3.271294 / 4.791772 m/s.
- Max: 8.679414 m/s.
- Fractions below thresholds: 35.73% < 1 m/s; 100% < 10 m/s.


Follwing a question from Adrien Coffinet , I tried to search for an answer by plotting all pairwise orbital parameters:

I do  not see any "abrupt" change around -40K but I notice a couple of facts:

Around the -40K marker:

  - e is near a local minimum.

  - q is near a local maximum.

  - Q is near a local minimum.

  That is internally consistent because:

  q = a(1 - e)

  Q = a(1 + e)

  and a is almost constant. So when e reaches a minimum:

  q increases

  Q decreases

 This looks more like a secular-cycle turning point than an abrupt scattering event. A close planetary encounter would more likely produce a sharper discontinuity or step-like change in a, e, or i.

  So the story may be:

  near -40K: the nominal pair is at/near a secular eccentricity turning point

  after -40K: orbital phasing evolves toward lower pair distance and velocity

  near -7.7K: strong nominal convergence

In conclusion: if the phisical truth is a "fission(?) event around -7.7K, the previous plot is not to be taken into consideration, otherwise the plot must be taken into consideration but no clear reason for what happened at -40K besides "secular cycle".

More expert people may find a better explanation (by the way, all this analysis should be peer-reviewed, do not take it as a proof but just as something that might derserve a better study).