1151cycle

Empirical detection of a 1151-year multi-planet quasi-commensurability in the Solar System

Carlos Baiget Orts — asinfreedom@gmail.com — ORCID: 0009-0000-6725-5188

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Summary

This repository contains the full computational analysis for the paper. An exhaustive search over ±1,300 years identifies T* = 420,403 days (≈ 1,151 years) as the global minimum of a series-comparison similarity metric applied to daily heliocentric ecliptic longitudes of seven planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, and Neptune), computed from the DE441 ephemeris.

At this interval, the mean simultaneous angular displacement of all seven planets from their positions T* days earlier is 13.4°, with a standard deviation of 0.65° sustained over a century-long comparison window and stable across any reference epoch spanning 1,200 years.

Key results:

Result	Value
Global minimum T*	420,403 days = 1,151.001 years
Score S(T*)	14.04°
z-score (descriptive)	3.66σ below mean of 2,600 candidates
Candidates worse than T*	100%
Temporal stability (std over 1,200 yr)	0.100°
Robust from series length	1 year or more
Neptune residue at T*	−5.2° (participates)
Uranus residue at T*	−108.3° (does not participate)

The interval 1,151 years was known to Babylonian astronomers as the period after which Venus returns to the same position in the sky (de Jong 2019). This work demonstrates that the same interval is simultaneously optimal for seven planets. The sole exception is Uranus, whose large residue at T* constitutes an independent empirical signature consistent with the hypothesis that its orbital period was substantially modified by a giant impact.

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Visual demonstration

A visual animation of the phenomenon is available on YouTube: 1151 Years Later: The Sky Repeats

The animation shows planetary configurations separated by 1,151 years superimposed across several millennia, illustrating the quasi-commensurability directly.

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Repository structure

helio1151.py               Main analysis script (9 analyses)
make_figures.py               Figure generation (5 publication figures)
retrograde_sync.py            Retrograde episode synchronisation analysis
helio7_de441_cache.pkl.xz     Pre-computed position cache (LZMA compressed)
README.md                     This file

Output files (generated by running the scripts):

helio7_de441_cache.pkl.xz    Position cache, LZMA compressed
helio_results.csv             Full search — scatter plot data
helio_stats.csv               Per-planet statistics at T*
helio_panel_fast.csv          Mercury, Venus, Earth, Mars offsets (5yr daily)
helio_panel_slow.csv          Jupiter, Saturn, Neptune offsets (100yr weekly)
helio_polar.csv               Heliocentric snapshots at 5 epochs
helio_convergence.csv         Series length convergence data
retrograde_sync.csv           Per-episode retrograde shift table
retrograde_stats.csv          Retrograde synchronisation statistics

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Requirements

python >= 3.9
skyfield
numpy
matplotlib
scipy          # retrograde_sync.py only

Install dependencies:

pip install skyfield numpy matplotlib scipy

The DE441 ephemeris (de441_part-1.bsp, ~1.5 GB) is downloaded automatically by Skyfield on first run. It covers 13,201 BCE to 1,969 CE — well beyond the ±1,300 year search range used in this analysis.

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Usage

Main analysis

python helio1151_v2.py

This runs all 9 analyses in sequence:

1. Full cycle search over ±1,300 years (2,601 candidates)
2. Statistical significance of the global minimum
3. Temporal stability across 12 reference epochs
4. Per-planet breakdown at T*
5. Theoretical sidereal residues at T* (all 8 planets, including Uranus)
6. Secondary minima characterisation
7. Daily angular offset extraction (figure data)
8. Heliocentric polar snapshot data
9. Series length convergence (1–100 years)

The position cache (helio7_de441_cache.pkl.xz) is included in the repository. When the cache is present, the DE441 ephemeris (~1.5 GB) is not downloaded. The ephemeris is only needed if the cache is absent or must be rebuilt. To force a rebuild, delete the .pkl.xz file and re-run the script — it will download the ephemeris and regenerate the cache automatically.

Generate figures

python make_figures.py

Produces 5 figures as PDF and PNG:

• fig1_scatter.pdf — Score S(T) for all 2,601 candidate intervals
• fig2_histogram.pdf — Score distribution with T* isolated
• fig3_panels.pdf — Per-planet angular offset time series
• fig4_convergence.pdf — Score convergence with series length
• fig5_polar.pdf — Heliocentric snapshots at 5 independent epochs

Retrograde synchronisation

python retrograde_sync.py

Identifies all retrograde episodes in both series and measures temporal shifts for all six planets that exhibit retrograde motion as seen from Earth (Mercury, Venus, Mars, Jupiter, Saturn, Neptune). Builds a separate geocentric cache (geo_cache.pkl) on first run.

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Method

The similarity metric is defined as:

$$S(T) = \overline{\delta}(T) + \sigma_\delta(T)$$

where $\delta_i(T)$ is the mean circular angular distance between the positions of all seven planets at time $t_0 + i$ and their positions at $t_0 - T + i$, averaged over a 100-year comparison window. The mean $\overline{\delta}$ measures average positional proximity; $\sigma_\delta$ penalises temporal instability. Equal weights are used for all planets (planet-agnostic search). Uranus is excluded from the metric due to its large residue (−108.3°) but its theoretical residue is reported in full.

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Ephemeris

This analysis uses the DE441 ephemeris from the Jet Propulsion Laboratory:

• File: de441_part-1.bsp
• Coverage: 13,201 BCE – 1,969 CE
• Reference: Park et al. (2021), The Astronomical Journal, 161, 105
• Download: https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/planets/de441_part-1.bsp

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Citation

If you use this code or data, please cite the associated paper:

@article{baiget2025_1151,
  author  = {Baiget Orts, Carlos},
  title   = {A 1151-Year Quasi-Commensurability of the Solar System:
             Empirical Detection, Statistical Characterization,
             and the Anomalous Exclusion of {Uranus}},
  journal = {arXiv},
  year    = {2025},
  note    = {arXiv:2604.03049 [astro-ph.EP]}
}

License

MIT License. See LICENSE for details.