Nominal Analysis - Objective: minimize nominal velocity.
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 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: 19564.000000 yr before analysis epoch.
- Selected best time: 19570.451626 yr before analysis epoch.
- Selected-time JD: -4687032.207266.
- Median relative velocity at selected time: 17.540110 m/s.
- Median distance at selected time: 320,716.143 km.
Distance distribution at selected time:
- Minimum combination at selected time: 4,942.666 km.
- p05 / p16: 33,851.918 / 104,130.595 km.
- Median / p84 / p95: 320,716.143 / 689,440.411 / 897,367.988 km.
- Max: 1,411,826.381 km.
- Nominal at selected time: 12,600.442 km.
- Fractions below thresholds: 1.14% < 10,000 km; 15.31% < 100,000 km; 97.03% < 1,000,000 km.
Relative-velocity distribution at selected time:
- Minimum combination at selected time: 0.061954 m/s.
- p05 / p16: 1.710916 / 5.568755 m/s.
- Median / p84 / p95: 17.540110 / 37.732473 / 49.184678 m/s.
- Max: 77.110485 m/s.
- Nominal at selected time: 0.315716 m/s.
- Fractions below thresholds: 3.02% < 1 m/s; 28.75% < 10 m/s.
Median Analysis - Objective: minimize median velocity.
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.
Candidate screening:
- A pair qualifies only when distance and relative velocity pass a tier at the same sampled time.
- Physical primary: 748805 (2013 XF5) (largest derived target mass).
- Hill radius: 213.761630 km (derived from primary mass and heliocentric semimajor axis).
- Escape velocity: 0.562674 m/s (derived from primary mass and radius).
- Primary diameter: 1.064167 km (derived from H and geometric albedo).
- Primary mass: 1.262e+12 kg (derived from diameter and assumed spherical bulk density).
- Fixed tiers: strict = 1 R_H and 1 v_esc; ordinary = 5 R_H and 2 v_esc; relaxed = 10 R_H and 4 v_esc.
- Found 213,306 qualifying pair-time rows from 1,386 distinct sample pairs.
- Cross-combinations share clone samples and are not statistically independent.
Window window_1:
- Window center: 19564.000000 yr before analysis epoch.
- Selected best time: 19576.771568 yr before analysis epoch.
- Selected-time JD: -4689340.606703.
- Median relative velocity at selected time: 11.270876 m/s.
- Median distance at selected time: 248,171.516 km.
Distance distribution at selected time:
- Minimum combination at selected time: 1,585.842 km.
- p05 / p16: 17,529.396 / 58,617.398 km.
- Median / p84 / p95: 248,171.516 / 533,663.025 / 678,717.034 km.
- Max: 1,083,590.527 km.
- Nominal at selected time: 47,912.957 km.
- Fractions below thresholds: 2.71% < 10,000 km; 22.30% < 100,000 km; 98.68% < 1,000,000 km.
Relative-velocity distribution at selected time:
- Minimum combination at selected time: 0.242574 m/s.
- p05 / p16: 0.835436 / 2.634319 m/s.
- Median / p84 / p95: 11.270876 / 24.186385 / 30.689984 m/s.
- Max: 48.852710 m/s.
- Nominal at selected time: 2.132417 m/s.
- Fractions below thresholds: 6.08% < 1 m/s; 44.57% < 10 m/s.
Simultaneous candidate pairs:
- Distinct qualifying sample pairs: 1,386.
- Strongest class counts: strict=0; ordinary=247; relaxed=1139.
- Leading pairs (lexicographic tier, then sampled distance and velocity):
- 0-1 samples 62-63: ordinary; representative d=1.055 R_H, v=0.5 v_esc at t=-19614.375 yr.
- 0-1 samples 62-82: ordinary; representative d=1.178 R_H, v=0.5046 v_esc at t=-19618.125 yr.
- 0-1 samples 62-94: ordinary; representative d=1.234 R_H, v=0.5025 v_esc at t=-19618.125 yr.
- 0-1 samples 94-71: ordinary; representative d=1.304 R_H, v=0.5557 v_esc at t=-19640.5 yr.
- 0-1 samples 87-82: ordinary; representative d=1.323 R_H, v=0.5572 v_esc at t=-19561.4375 yr.
- 0-1 samples 27-47: ordinary; representative d=1.395 R_H, v=0.6558 v_esc at t=-19546.625 yr.
- 0-1 samples 96-65: ordinary; representative d=1.609 R_H, v=0.574 v_esc at t=-19640.5 yr.
- 0-1 samples 52-100: ordinary; representative d=1.694 R_H, v=0.6395 v_esc at t=-19554.25 yr.
- 0-1 samples 86-18: ordinary; representative d=1.707 R_H, v=0.6011 v_esc at t=-19648 yr.
- 0-1 samples 9-22: ordinary; representative d=1.885 R_H, v=0.6305 v_esc at t=-19539.125 yr.
The dynamical analysis reveals a small but noteworthy subset of orbital solutions in which the two objects approach one another under remarkably gentle conditions. The most interesting point is therefore not so much the minimum of the median at ~19,577 years ago, but rather the existence of individual covariance realizations that produce simultaneously very slow and very close encounters.
The strongest combination is particularly intriguing:
- km;
- m/s;
- ;
- ;
- epoch ≈ 19,614 years before the reference epoch.
Thus, the relative velocity is actually about half of the estimated escape velocity, while the encounter distance misses the Hill sphere by only about 5.5%.
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