251223 (2006 UA211) and 814159 (2008 EM188)

Covariance clone convergence summary: minimize nominal velocity

Run setup:

- Pair mode, 100 covariance clones per target plus nominal.

- 101 samples per target, 10,201 sample cross-combinations.

- Analysis epoch: JD 2461200.5.

- Objective: minimize nominal velocity.

- Nominal sample source: covariance.

- Integrator: REBOUND IAS15 in AU-yr-Msun, initial dt 0.3652564 day (0.001 yr), 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 2 targets; clones are massless and do not perturb the massive bodies or each other.

Window window_1:

- Window center: 2803.000000 yr before analysis epoch.

- Selected best time: 2802.818859 yr before analysis epoch.

- Selected-time JD: 1437452.973716.

- Median relative velocity at selected time: 0.721601 m/s.

- Median distance at selected time: 43,032.279 km.

Distance distribution at selected time:

- Minimum combination at selected time: 22,704.637 km.

- p05 / p16: 23,742.091 / 28,904.316 km.

- Median / p84 / p95: 43,032.279 / 57,237.225 / 66,740.024 km.

- Max: 91,420.166 km.

- Nominal at selected time: 42,504.950 km.

- Fractions below thresholds: 0.00% < 10,000 km; 100.00% < 100,000 km; 100.00% < 1,000,000 km.

Relative-velocity distribution at selected time:

- Minimum combination at selected time: 0.294131 m/s.

- p05 / p16: 0.308852 / 0.359331 m/s.

- Median / p84 / p95: 0.721601 / 1.517238 / 2.105724 m/s.

- Max: 4.090306 m/s.

- Nominal at selected time: 0.526255 m/s.

- Fractions below thresholds: 65.32% < 1 m/s; 100.00% < 10 m/s.

Covariance clone convergence summary: minimize median velocity

Run setup:

- Pair mode, 100 covariance clones per target plus nominal.

- 101 samples per target, 10,201 sample cross-combinations.

- Analysis epoch: JD 2461200.5.

- Objective: minimize median velocity.

- Nominal sample source: covariance.

- Integrator: REBOUND IAS15 in AU-yr-Msun, initial dt 0.3652564 day (0.001 yr), 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 2 targets; clones are massless and do not perturb the massive bodies or each other.

Window window_1:

- Window center: 2803.000000 yr before analysis epoch.

- Selected best time: 2802.813520 yr before analysis epoch.

- Selected-time JD: 1437454.923699.

- Median relative velocity at selected time: 0.720172 m/s.

- Median distance at selected time: 43,035.937 km.

Distance distribution at selected time:

- Minimum combination at selected time: 22,647.707 km.

- p05 / p16: 23,705.650 / 28,868.694 km.

- Median / p84 / p95: 43,035.937 / 57,243.968 / 66,745.529 km.

- Max: 91,420.269 km.

- Nominal at selected time: 42,508.718 km.

- Fractions below thresholds: 0.00% < 10,000 km; 100.00% < 100,000 km; 100.00% < 1,000,000 km.

Relative-velocity distribution at selected time:

- Minimum combination at selected time: 0.290953 m/s.

- p05 / p16: 0.306359 / 0.357196 m/s.

- Median / p84 / p95: 0.720172 / 1.516254 / 2.106361 m/s.

- Max: 4.089507 m/s.

- Nominal at selected time: 0.526748 m/s.

- Fractions below thresholds: 65.36% < 1 m/s; 100.00% < 10 m/s.

The run using the median objective closely reproduces the nominal-objective result, strengthening the robustness of the convergence.

The low dispersion shows that the nominal solution might not be simply a lucky realization. This agreement is more significant for the relative velocity than for the distance, therefore, the case is intriguing but not conclusive evidence of a common origin.

2018 BM33 and (206673) = 2003 YC111

Covariance clone convergence summary: - Objective: minimize nominal velocity

Prefix: 2018_BM33_2003_YC111_nominal_100

Run setup:

- Pair mode, 100 covariance clones per target plus nominal.

- 101 samples per target, 10,201 sample cross-combinations.

- Analysis epoch: JD 2461200.5.

- Objective: minimize nominal velocity.

- Nominal sample source: covariance.

- Integrator: REBOUND IAS15 in AU-yr-Msun, initial dt 0.3652564 day (0.001 yr), 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 2 targets; clones are massless and do not perturb the massive bodies or each other.

Window window_1:

- Window center: 7536.000000 yr before analysis epoch.

- Selected best time: 7612.261607 yr before analysis epoch.

- Selected-time JD: -319226.770450.

- Median relative velocity at selected time: 4.887196 m/s.

- Median distance at selected time: 119,529.208 km.

Distance distribution at selected time:

- Minimum combination at selected time: 2,990.397 km.

- p05 / p16: 13,314.389 / 45,322.580 km.

- Median / p84 / p95: 119,529.208 / 244,830.568 / 386,701.755 km.

- Max: 603,364.852 km.

- Nominal at selected time: 3,710.267 km.

- Fractions below thresholds: 3.66% < 10,000 km; 40.12% < 100,000 km; 100.00% < 1,000,000 km.

Relative-velocity distribution at selected time:

- Minimum combination at selected time: 0.082308 m/s.

- p05 / p16: 0.547095 / 1.857212 m/s.

- Median / p84 / p95: 4.887196 / 9.988578 / 15.767729 m/s.

- Max: 24.752360 m/s.

- Nominal at selected time: 0.090495 m/s.

- Fractions below thresholds: 9.62% < 1 m/s; 84.04% < 10 m/s.

Covariance clone convergence summary: - Objective: minimize median velocity

Prefix: 2018_BM33_2003_YC111_median_100

Targets from ../ele.txt:

- 2018 BM33 = (2018 BM33)

- 2003 YC111 = 206673 (2003 YC111)

Run setup:

- Pair mode, 100 covariance clones per target plus nominal.

- 101 samples per target, 10,201 sample cross-combinations.

- Analysis epoch: JD 2461200.5.

- Objective: minimize median velocity.

- Nominal sample source: covariance.

- Integrator: REBOUND IAS15 in AU-yr-Msun, initial dt 0.3652564 day (0.001 yr), 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 2 targets; clones are massless and do not perturb the massive bodies or each other.

Window window_1:

- Window center: 7536.000000 yr before analysis epoch.

- Selected best time: 7611.996605 yr before analysis epoch.

- Selected-time JD: -319129.976812.

- Median relative velocity at selected time: 4.872823 m/s.

- Median distance at selected time: 119,286.334 km.

Distance distribution at selected time:

- Minimum combination at selected time: 3,321.845 km.

- p05 / p16: 13,576.038 / 45,314.551 km.

- Median / p84 / p95: 119,286.334 / 243,514.844 / 383,784.754 km.

- Max: 603,663.869 km.

- Nominal at selected time: 3,427.585 km.

- Fractions below thresholds: 3.55% < 10,000 km; 40.29% < 100,000 km; 100.00% < 1,000,000 km.

Relative-velocity distribution at selected time:

- Minimum combination at selected time: 0.098422 m/s.

- p05 / p16: 0.551154 / 1.850749 m/s.

- Median / p84 / p95: 4.872823 / 9.925090 / 15.636750 m/s.

- Max: 24.687983 m/s.

- Nominal at selected time: 0.104006 m/s.

- Fractions below thresholds: 9.43% < 1 m/s; 84.54% < 10 m/s.

2015 MM64 versus 2019 van Albada (1935 SX1)

This case may deserve further investigation because (2019) van Albada (1935 SX1) is a known binary asteroid with a satellite, as reported  here by Johnston’s Archive and a  photometric study by Vladimir Benishek, Petr Pravec, Russell Durkee, Marek Husarik.

Confirming a genetic relationship with 2015 MM64 would make the system particularly intriguing.

The nominal solutions show a clear convergence epoch broadly supported by the covariance clones. However, at the selected minimum-median-velocity epoch, all clone combinations remain outside van Albada’s Hill sphere and above the local escape-velocity curve. 

Thus, the case is intriguing but remains inconclusive.

 

Simulation details

Covariance clone convergence summary

Run setup:

- Pair mode, 100 covariance clones per target plus nominal.

- 101 samples per target, 10,201 sample cross-combinations.

- Analysis epoch: JD 2461200.5.

- Objective: minimize median velocity.

- Nominal sample source: covariance.

- Integrator: REBOUND IAS15 in AU-yr-Msun, initial dt 0.3652564 day (0.001 yr), 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 2 targets; clones are massless and do not perturb the massive bodies or each other.

Window window_1:

- Window center: 43768.781000 yr before analysis epoch.

- Selected best time: 43768.013514 yr before analysis epoch.

- Selected-time JD: -13525346.551110.

- Median relative velocity at selected time: 9.172443 m/s.

- Median distance at selected time: 168,300.443 km.

Distance distribution at selected time:

- Minimum combination at selected time: 10,143.336 km.

- p05 / p16: 17,042.759 / 53,341.853 km.

- Median / p84 / p95: 168,300.443 / 555,126.540 / 810,551.880 km.

- Max: 1,091,114.734 km.

- Nominal at selected time: 85,208.192 km.

- Fractions below thresholds: 0.00% < 10,000 km; 33.61% < 100,000 km; 99.01% < 1,000,000 km.

Relative-velocity distribution at selected time:

- Minimum combination at selected time: 0.693410 m/s.

- p05 / p16: 0.991334 / 2.770931 m/s.

- Median / p84 / p95: 9.172443 / 29.927771 / 43.668428 m/s.

- Max: 58.722771 m/s.

- Nominal at selected time: 4.752497 m/s.

- Fractions below thresholds: 5.10% < 1 m/s; 52.48% < 10 m/s.

Let's look at the distance and relative velocity distributions at the time when the median relative velocity was minimum:

Let's put together all pair combinations on the same density plot:

2017 VQ75 and 259711 (2003 YL54)

This is a potentially interesting couple.

100 clones + nominals, searching for the time when median relative velocity was lowest

Looking at the time when the median relative velocity was lowest, we can look at its distribution (together with asteroid distance at the same time:

Run setup:

- Pair mode, 100 covariance clones per target plus nominal.

- 101 samples per target, 10,201 sample cross-combinations.

- Analysis epoch: JD 2461000.5.

- Objective: minimize median velocity.

- Nominal sample source: covariance.

- Integrator: REBOUND IAS15 in AU-yr-Msun, initial dt 0.3652564 day (0.001 yr), 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 2 targets; clones are massless and do not perturb the massive bodies or each other.

Window window_1:

- Window center: 9687.860000 yr before analysis epoch.

- Selected best time: 9892.314224 yr before analysis epoch.

- Selected-time JD: -1152230.581058.

- Median relative velocity at selected time: 2.257536 m/s.

- Median distance at selected time: 44,283.075 km.

Distance distribution at selected time:

- Minimum combination at selected time: 2,700.492 km.

- p05 / p16: 4,837.868 / 12,423.673 km.

- Median / p84 / p95: 44,283.075 / 101,901.503 / 138,618.078 km.

- Max: 270,219.283 km.

- Nominal at selected time: 17,529.654 km.

- Fractions below thresholds: 12.49% < 10,000 km; 83.24% < 100,000 km; 100.00% < 1,000,000 km.

Relative-velocity distribution at selected time:

- Minimum combination at selected time: 0.057856 m/s.

- p05 / p16: 0.211032 / 0.627504 m/s.

- Median / p84 / p95: 2.257536 / 5.200980 / 7.098886 m/s.

- Max: 13.758033 m/s.

- Nominal at selected time: 0.814142 m/s.

- Fractions below thresholds: 25.23% < 1 m/s; 99.18% < 10 m/s.

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).

a compact pairwise cluster: 2014 DC113, 2019 CV15, 2003 CL11

 These three objects have very similar orbits:

•   2014 DC113
•   2019 CV15
•   267721 (2003 CL11)

Nominal backward integrations (Rebound IAS15 with big planets + Ceres/Pallas/Vesta) suggest close pairwise convergence epochs, as shown in the pairwise plots:

pair 2014 DC113 and 2019 CV15

pair 2003 CL11 and 2014 DC113

pair 2003 CL11 and 2019 CV15

To check whether these are only nominal-orbit coincidences, I also propagated 30 covariance clones plus nominal and inspected the corresponding pairwise clone boxplots:

cross_pair_dc113_cv15_31x31

cross_pair_cl11_dc113_31x31

cross_pair_cl11_cv15_31x31

For these 31 x 31 clone-pair tests, the boxplot summaries are approximately:

  Each boxplot is evaluated at the refined time, inside the corresponding

  pairwise time window, that minimizes the median distance over the 31 x 31

  clone-pair combinations.

  2014 DC113 - 2019 CV15:

    median distance 150000 km; median relative velocity 10.4 m/s

    4.1% of clone pairs below 10000 km and 1 m/s

    36.6% below 100000 km and 10 m/s

  2003 CL11 - 2014 DC113:

    median distance 89000 km; median relative velocity 6.1 m/s

    2.6% of clone pairs below 10000 km and 1 m/s

    55.5% below 100000 km and 10 m/s

  2003 CL11 - 2019 CV15:

    median distance 217000 km; median relative velocity 15.2 m/s

    1.7% of clone pairs below 10000 km and 1 m/s

    26.7% below 100000 km and 10 m/s

The clone results appear to preserve a non-negligible pairwise signal.

In particular, the 2003 CL11 - 2014 DC113 pair gives the most compact median clone convergence in this preliminary test, while 2014 DC113 - 2019 CV15 also remains interesting. 

The 2003 CL11 - 2019 CV15 pair is weaker, but not obviously irrelevant.

However, an attempt to make all three clone clouds converge simultaneously in the three time windows suggested by the pairwise plots was not successful. In that test, the three-body cluster diameter remained extremely large, as summarized in:

cross_dc113_cv15_cl11_31x31x31

In the 31 x 31 x 31 triple-clone test, the median three-body diameters in the three pairwise windows were about 33, 23, and 70 million km, respectively. No clone triple was below 1 million km in diameter, and no clone triple had maximum internal relative velocity below 10 m/s.

One possible interpretation, offered only as a working hypothesis, is not a simultaneous three-body breakup but a sequential fragmentation history. For example, an older progenitor may have split into 2003 CL11 and an intermediate progenitor, followed later by a split of that intermediate progenitor into 2014 DC113 and 2019 CV15. The pairwise clone behaviour seems at least compatible with such a scenario.

I emphasize that this is only a preliminary flag. The analysis needs independent validation before any physical conclusion can be drawn. I am sharing this mainly because the pairwise clone results suggest that the similarity may deserve closer scrutiny rather than being dismissed immediately as a purely nominal coincidence.

Best regards,

Alessandro Odasso

2026 LD1 and 2018 NC15

 U-Code for asteroid 2026 LD1 is 8 so the uncertainty is exremely high

Backward integration taking into account all big planets plus Ceres, Pallas, Vesta:

it seems that these asteroid are near the end of their synodic cycle on about 16 february 2026.

=== Update --- to avoid sampling errors, just quering JPL Horizons asking for daily resolution:

Fetching data from JPL Horizons...

==================================================
1. ANALYSIS FOR MINIMUM RELATIVE VELOCITY
==================================================
Date of occurrence:       A.D. 2026-Sep-30 00:00:00.0000
MINIMUM Relative Velocity: 0.01525 km/s
Distance at that time:    0.0023457 AU (350,912.15 km)

==================================================
2. ANALYSIS FOR MINIMUM RELATIVE DISTANCE
==================================================
Date of occurrence:       A.D. 2026-Oct-20 00:00:00.0000
MINIMUM Distance:         0.0023008 AU (344,187.88 km)
Velocity at that time:    0.01702 km/s
==================================================