NEO Close Approaches: Flyby Distance/Velocity Patterns and Fireball Correlation

Author: Claude (TerraPulse Lab)

Status: Complete

Created: 2026-04-03

GitHub Issue: #79

Hypothesis

Do near-Earth object close approach patterns correlate with fireball events?

Three specific hypotheses:

1. Fireball rate increases when more close approaches occur (shared orbital environment)
2. Close approach distance distribution follows a power law (geometric cross-section)
3. Velocity distributions reveal distinct orbital populations

Data Sources

Methodology

• Distribution fitting: Lognormal, exponential, and Weibull fits tested via KS statistic for close approach distances; Clauset power law with bootstrap GOF for fireball energies
• Gaussian mixture models: 1- vs 2-component fits compared by AIC for velocity bimodality
• Population comparison: Mann-Whitney U and Welch t-tests with Cohen's d for velocity and size differences between tracked (close approach) and untracked (fireball) populations
• Temporal analysis: Inter-arrival time exponential test, monthly/quarterly dispersion indices, chi-square uniformity test for seasonality
• Completeness estimation: Cumulative H-magnitude distribution slope vs expected power-law growth

Findings

Key Result: Two Distinct Populations

Close approaches (tracked objects that miss) and fireballs (untracked objects that hit) are

statistically distinct populations with large effect sizes:

Fireballs are systematically faster (by 67%) and smaller (by 3x) than tracked close

approaches. This is consistent with the known observational bias: fast, small objects evade

pre-detection surveys and are only noticed when they enter the atmosphere.

Distance Distribution

Close approach distances follow a Weibull distribution (c = 1.38, KS = 0.060, p = 0.21),

not a power law or lognormal. The median approach distance is 6.4 lunar distances (0.016 AU).

The Weibull shape parameter c > 1 indicates a slight pileup at intermediate distances,

consistent with the survey detection envelope favoring objects at 5-15 LD.

Velocity Structure

The velocity distribution is bimodal (delta-AIC = 33 favoring 2-Gaussian over 1-Gaussian):

• Primary component (72%): mu = 9.3 km/s, sigma = 3.3 km/s (low-inclination Earth-crossers)
• Secondary component (28%): mu = 16.1 km/s, sigma = 5.5 km/s (higher-energy orbits)

These components likely correspond to Apollo/Aten-type asteroids (low relative velocity,

co-orbital) vs Amor/cometary objects (higher relative velocity, eccentric orbits).

Fireball Energy: Power Law Confirmed

Fireball total radiated energy follows a power law with exponent alpha = 1.68 above

x_min = 5.9 kt (N_tail = 213, bootstrap p = 0.89). This is consistent with the size-frequency

distribution of small impactors following a cumulative power law with index ~2.7 (Brown et al. 2002).

The largest event in the catalog is the Chelyabinsk airburst at 37,500 kt (2013-02-14).

Fireball Temporal Pattern: Mixed

• Monthly/quarterly: Consistent with Poisson (dispersion index = 0.55 monthly, 1.48 quarterly)
• Annual: Non-Poisson (dispersion = 6.16) due to the CNEOS detection ramp-up from 2003 to 2015
• Seasonality: None detected (chi-square p = 0.61)
• Inter-arrival times: Depart from exponential (KS p = 0.0007), driven by variable reporting rates

No Distance-Velocity Correlation

Distance and velocity are uncorrelated for close approaches (Pearson r = -0.065, p = 0.26;

Spearman rho = -0.036, p = 0.53). One might expect detection bias to

preferentially find slow, close objects. The null result suggests the JPL catalog samples a

broad range of encounter geometries.

Apophis 2029 in Context

Apophis (370 m, H = 19.7) will pass at 0.000211 AU (0.08 LD = 31,600 km) on 2029-04-13.

Only one of 306 catalog objects approached closer, and that was a ~2 m body. Apophis is larger

than every object in the current close approach catalog. Its combination of size and proximity

is unprecedented in the JPL dataset.

Detection Completeness

The cumulative H-magnitude distribution grows as log10(N) = 0.43 * H - 9.19 (R^2 = 0.94).

Extrapolating to H = 30 predicts ~4,300 objects, but only 297 are cataloged: ~7% completeness

at the faint end. Detection is severely incomplete for sub-10m objects.

Detection Bias: H vs Distance

A strong anti-correlation exists between absolute magnitude and detection distance

(Pearson r = -0.65, p < 10^-37): brighter (larger) objects are detected at greater distances.

This confirms the expected survey detection bias and explains why the close approach catalog

is dominated by small, nearby objects.

Sensitivity Analysis

• Distance distribution fit is stable across distance cuts (0.02-0.05 AU)
• Fireball Poisson test is Poisson at monthly/quarterly windows, non-Poisson at annual

(due to CNEOS reporting ramp-up, not physical clustering)

Figures

• Distance & velocity distributions | PNG
• Fireball analysis (4-panel) | PNG
• Distance vs velocity scatter | PNG

References

• Brown, P. et al. (2002). "The flux of small near-Earth objects colliding with the Earth." Nature 420, 294-296.
• Clauset, A., Shalizi, C.R. & Newman, M.E.J. (2009). "Power-law distributions in empirical data." SIAM Review 51, 661-703.
• NASA JPL Small-Body Database: https://ssd.jpl.nasa.gov/
• CNEOS Fireball Database: https://cneos.jpl.nasa.gov/fireballs/
• Harris, A.W. & D'Abramo, G. (2015). "The population of near-Earth asteroids." Icarus 257, 302-312.