Comet 1P/Halley Completes 15 Orbits in 1,151 Years

Replication package for:

Baiget Orts, C. (2026). Comet 1P/Halley Completes 15 Orbits in 1,151 Years: Commensurability with the Solar System Quasi-Period and Evidence for Jupiter–Saturn Dynamical Coupling. arXiv: [in preparation]

Companion paper (planetary cycle):

Baiget Orts, C. (2026). A 1151-Year Quasi-Commensurability of the Solar System: Empirical Detection, Statistical Characterization, and the Anomalous Exclusion of Uranus. arXiv:2604.03049

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Overview

This repository contains the complete replication code for all statistical results reported in the Halley paper. The central finding is that comet 1P/Halley's mean orbital period (76.713 yr, from 29 observed orbital periods spanning 2,225 years) satisfies:

T* / P̄ = 1151 / 76.713 = 15.004

with an angular residue of +1.43° — the smallest of any Solar System body analyzed with this method, smaller than those of all seven participating planets.

Four independent statistical tests establish that Jupiter and Saturn couple to Halley's orbital period through distinct mechanisms:

• Jupiter via phase-dependent modulation (p = 0.027–0.04, three tests)
• Saturn via distance-amplitude modulation (p = 0.007, confirmed by random-phase control p = 0.133)

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Repository structure

halley_1151_replication.py      Main replication battery (all paper results)
test_phase_locked_permutation.py Phase-locked permutation test (p=0.035)
rebound_halley.py               N-body ensemble (requires REBOUND)
rebound_stabilization.py        Long-term stabilization test (requires REBOUND)
README.md                       This file

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Requirements

Core replication (no special dependencies)

pip install numpy matplotlib scipy

N-body scripts only

pip install rebound

REBOUND will attempt to download planet positions from JPL Horizons on first run (requires internet). The scripts fall back to approximate elements if Horizons is unavailable.

Population analysis scripts

pip install requests   # for JPL SBDB download

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Quick start

Run the complete replication battery:

python3 halley_1151_replication.py

Expected runtime: ~15 minutes on a modern laptop (dominated by Monte Carlo tests with 10⁵–10⁶ iterations). All results print to stdout with the paper value noted for comparison.

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Test inventory

halley_1151_replication.py — 14 tests covering all paper sections

#	Function	Paper section	Key result
1	test_basic	§3.1	P̄ = 76.713 yr, residue +1.43°, deviation 7.4 days
2	test_comparison	Table 1	Residues for all Solar System bodies
3	test_htc_survey	§3.4, Table 2	Survey of HTCs; residues 80°–130°
4	test_bootstrap	§3.2	T*/15 inside 95% CI; residue robust
5	test_surrogates	§3.3	p = 0.036 (Gaussian), p = 0.007 (uniform)
6	test_period_scan	§3.3	T* rank 1/1901 joint, 16/1901 Halley alone
7	test_coincidence_mc	§3.3	p = 0.009 (look-elsewhere corrected)
8	test_sensitivity	§3.2	Robust to ±180 day historical uncertainties
9	test_rolling_prediction	§4.6	RMS: T*/15 = 472 d, running mean = 494 d
10	test_cancellation	§4.4	Cancellation at n=15: 9.4% of random-walk σ√15
11	test_arithmetic_landscape	Fig. 4	52 minima below 5°; Halley's convergence is dynamical
12	test_jupiter_phase_correlation	§4.2	R = 0.47, p = 0.04; R²(J+S) = 0.234
13	test_gravitational_impulse	§4.2–4.3	r_J = −0.41, p = 0.027; r_dist_S = −0.496, p = 0.007
14	test_saturn_proximity	§4.3	p_perm = 0.007, p_rphase = 0.133 (ratio 20×)

Additional scripts (extended analysis)

Script	Paper section	Key result	Runtime
test_phase_locked_permutation.py	§4.2	p = 0.035 (Jupiter, 10⁶ permutations)	~3 min
test_gravitational_impulse.py	§4.2–4.3	Full impulse analysis with plots	~5 min
test_saturn_proximity_permutation.py	§4.3	Extended Saturn tests with plots	~5 min
test_perturbation_correlation.py	§4.2, §4.4	Chirikov phases + cancellation figure	~2 min
rebound_halley.py	§4.5	N-body ensemble, r = 0.44, p = 0.001	~30 min
rebound_stabilization.py	§4.5	15,000 yr ensemble; T*/16 migration	~20 min
tstar_population.py	—	HTC population survey (JPL SBDB)	~2 min
tstar_asteroids.py	—	Asteroid belt survey (JPL SBDB)	~5 min

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Results not in the main battery

Two results in the paper come from scripts not included in the main battery, with notes on their interpretation:

Phase-locked permutation test (p = 0.035): Run test_phase_locked_permutation.py. Uses 10⁶ permutations; excluded from main battery for runtime. Replicates the third independent Jupiter test.

Synthetic-clone joint test (p = 0.012): Reported in §4.4. A subsequent analysis showed the three metrics are not fully independent (the ratio joint/product ≈ 1), so the joint p-value should be interpreted with caution. The marginal results (cancellation, R²) are the primary evidence; the joint test is supplementary.

N-body results (§4.5): Run rebound_halley.py for the 3,000-yr ensemble (r = 0.44, p = 0.001) and rebound_stabilization.py for the 15,000-yr run showing migration toward T*/16 = 71.94 yr. Requires REBOUND.

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Data

All perihelion dates are from:

Yeomans, D. K., Rahe, J., & Freitag, R. S. (1986). The History of Comet Halley. Journal of the Royal Astronomical Society of Canada, 80, 62.

Julian Day Numbers are from:

Chirikov, B. V., & Vecheslavov, V. V. (1989). Chaotic dynamics of Comet Halley. A&A, 221, 146.

The 1986 perihelion (JD 2446470.9518) is from direct observation.

Planetary periods and ephemeris positions use the DE441 ephemeris via Skyfield (Rhodes 2019) where applicable; simplified Chirikov effective periods are used in the main battery to avoid external dependencies.

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Expected output (key values)

Running halley_1151_replication.py should reproduce:

Mean period:           76.713006 yr
T*/P̄:                  15.003975
Angular residue:       +1.43°
Deviation from T*/15:  −7.4 days
Monte Carlo p-value:   ~0.009

Jupiter R (circ-lin):  0.47,  p = 0.04
Jupiter r (impulse):   −0.41, p = 0.027 (permutation, n=100,000)
Saturn dist r:         −0.496, p = 0.007 (permutation)
Saturn random-phase:   p = 0.133

Cancellation n=15:     9.4% of σ√15

Small variations in Monte Carlo results are expected due to random seed differences; p-values should agree to 2 significant figures.

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Citation

If you use this code, please cite:

@article{BaigetOrts2026halley,
  author  = {Baiget Orts, Carlos},
  title   = {Comet 1P/Halley Completes 15 Orbits in 1,151 Years:
             Commensurability with the Solar System Quasi-Period
             and Evidence for Jupiter--Saturn Dynamical Coupling},
  year    = {2026},
  note    = {arXiv: in preparation}
}

@article{BaigetOrts2026cycle,
  author  = {Baiget Orts, Carlos},
  title   = {A 1151-Year Quasi-Commensurability of the Solar System:
             Empirical Detection, Statistical Characterization,
             and the Anomalous Exclusion of Uranus},
  year    = {2026},
  journal = {arXiv:2604.03049}
}

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Contact

Carlos Baiget Orts
Independent researcher, Valencia, Spain
asinfreedom@gmail.com
ORCID: 0009-0000-6725-5188

Issues and questions welcome via GitHub Issues.