Analysis & Export Tools
The 3D Simulation includes powerful tools for generating reports, exporting data, and validating measurements against IAU reference values.
All values are measured, not calculated from formulas. Every value produced by these analysis tools — year lengths, day lengths, precession periods, orbital parameters — is measured directly from the running 3D simulation using objective functions (e.g., detecting equinox crossings, perihelion passages, stellar reference alignments). No analytical formula is used to produce these outputs.
Measurements come first, formulas second. The analytical formulas on the Formulas page were derived from these simulation measurements — not the other way around. The 3D model produces the raw data; the analytical formulas were then derived to reproduce that data. This means the analysis tools provide an independent check on the model’s geometric framework.
Validated against 700+ historical observations. The simulation has been tested against over 700 independently recorded astronomical events spanning approximately 2000 BC to 4000 AD — including solstice and equinox dates, perihelion passages, and eclipse timings. The verification dataset contains 623 individual entries with accuracy standards that vary by epoch: ±1 day for ancient observations, ±1 hour for medieval records, and ±1 minute for modern measurements. See the verification data reference on GitHub for the full dataset.
The simulation source code is openly available on GitHub . Readers are invited to inspect how each measurement is implemented.
Location in the UI
Analysis tools are spread across two Tweakpane folders:
Reports
├── Planet Positions & Orbits (export RA/Dec, distances at specific Julian dates)
├── Solstices & Equinoxes (export solstice/equinox dates with RA and obliquity)
└── Year Length Analysis (export tropical, anomalistic, sidereal year lengths)
Tools
├── Planet Inspector (interactive 5-step orbital hierarchy modal)
├── Invariable Plane Inspector (Fibonacci d-value and phase group balance explorer)
└── Console Tests (F12)
├── Year Length (6 tests)
├── Day Length (3 tests)
└── Calibration (4 tests)Planet Inspector
An interactive 5-step modal that walks through the orbital hierarchy of any planet. Access it via Tools > Planet Inspector.
What it shows
| Step | Contents |
|---|---|
| 1 | Planet selection and overview (mass, diameter, orbital period) |
| 2 | Hierarchy breakdown — every container from scene root to planet mesh, with live rotation/position values |
| 3 | Orbital elements — eccentricity, inclination, ascending node, argument of perihelion |
| 4 | Live RA/Dec, distances (Earth→planet, Sun→planet), and anomalies |
| 5 | Position Reports — download Excel or copy data for configured test dates per planet |
The Position Report (Step 5) exports the planet’s measured positions at a set of reference dates defined in the source code (PLANET_TEST_DATES). This is useful for comparing the simulation against ephemeris data.
All values shown in the Planet Inspector are live — they update as the simulation runs. Pause the simulation first if you need stable readings.
Year Analysis Report
Generates a comprehensive Excel file with year-by-year astronomical measurements, all derived from the running 3D simulation.
Controls
| Control | Description |
|---|---|
| Mode | Range or List - how years are specified |
| Year list (CSV) | Comma-separated years (List mode) |
| Start year | First year (Range mode) |
| End year | Last year (Range mode) |
| Create file | Trigger report generation |
Output Sheets
The exported Excel file contains 5 sheets:
| Sheet | Contents |
|---|---|
| Summary | Orbital parameters, tropical/sidereal/anomalistic year comparisons with IAU references |
| Cardinal Points | Year-by-year Julian Day data for VE, SS, AE, WS |
| Anomalistic | Perihelion and aphelion dates and distances |
| Sidereal | Sidereal year crossings |
| Detailed | All measurements combined per year |
Use Cases
- Validate model accuracy against IAU J2000 values
- Analyze year length variations over time
- Study tropical vs sidereal year relationships
- Verify precession measurements
Performance note: Large year ranges can take several minutes. Progress updates appear in the console (F12).
Solstice File Export
Exports June solstice data for a range of years.
| Control | Description |
|---|---|
| Mode | Range or List |
| Start/End year | Year range (Range mode) |
| Year list (CSV) | Specific years (List mode) |
| Create file | Trigger export |
Output columns: For each year, the Excel file contains:
| Column | Description |
|---|---|
| Year | Calendar year |
| June Solstice JD | Julian Day of the measured June solstice |
| Obliquity (°) | Measured axial tilt at the solstice moment |
| Sun RA | Right Ascension of the Sun at solstice |
| Sun Dec | Declination of the Sun at solstice |
All values are measured from the 3D scene — the simulation fast-forwards to each solstice and reads the geometry.
Object File Export
Exports measured planet positions from the simulation at specified Julian Days.
| Control | Description |
|---|---|
| Mode | Range or List |
| Start/End JD | Julian Day range (Range mode), with number of sample points |
| JD list (CSV) | Specific Julian Days (List mode) |
| Create file | Trigger export |
Output columns: For each Julian Day and each planet, the Excel file contains:
| Column | Description |
|---|---|
| Julian Day | The epoch |
| RA | Right Ascension (measured from 3D scene) |
| Dec | Declination (measured from 3D scene) |
| Distance (AU) | Earth-to-planet distance |
| Sun Distance (AU) | Sun-to-planet distance |
This is useful for comparing the simulation’s geocentric positions against JPL Horizons or other ephemeris services.
Console Tests (F12)
Runs detailed astronomical validation tests with output to the browser’s Developer Console.
Setup
- Open Developer Tools (F12)
- Open Tools > Console Tests (F12)
- Set the year range
- Click a test button
Available Tests
Year Length Analysis
| Test | Description |
|---|---|
| Analyze Year at June Solstice | Measures tropical year length at June solstice |
| Analyze Year at December Solstice | Measures tropical year length at December solstice |
| Analyze Year Length by Cardinal | Measures all 4 cardinal points |
| Analyze Anomalistic Year | Measures perihelion-to-perihelion interval |
| Analyze Sidereal Year | Measures Sun’s return to same stellar position |
| Analyze All Alignments | Combined measurement analysis |
Day Length Analysis
| Test | Description |
|---|---|
| Analyze Sidereal Day | Measures Earth’s rotation period relative to stars |
| Analyze Solar Day | Measures Earth’s rotation period relative to Sun |
| Analyze Stellar Day | Measures Earth’s rotation period relative to distant stars |
Parameter Verification
| Test | Description |
|---|---|
| Verify Obliquity Calibration | Tests whether earthtiltMean and earthRAAngle produce the correct obliquity at J2000 |
| Verify Perihelion Rate | Validates the measured perihelion precession rate against the expected H/16 period |
| Investigate Parameters | Sensitivity analysis — shows how small changes to model constants affect outputs |
| Find Optimal earthRAAngle | Optimization algorithm that searches for the earthRAAngle value producing the best match to observed precession rates |
Example Output
══════════════════════════════════════════════════════════════════════════
TROPICAL YEAR ANALYSIS (VERNAL EQUINOX)
══════════════════════════════════════════════════════════════════════════
Year range: 2000 to 2025
Year VE Julian Day Interval (days) IAU Ref (days) Diff (seconds)
─────────────────────────────────────────────────────────────────────────
2001 2451991.234567 365.242374 365.242374 +0.12
2002 2452356.477891 365.243324 365.242374 +82.15
SUMMARY:
Mean tropical year: 365.242374 days
IAU J2000 reference: 365.242374 days
Difference: +0.05 seconds
Status: ✓ PASS (within ±1 second tolerance)Invariable Plane Validation
This validation shows whether the simulation’s invariable plane matches the reference orientation from Souami & Souchay (2012).
Read-only displays:
| Metric | Expected value |
|---|---|
| Calculated Tilt | 1.5787° (Souami & Souchay 2012) |
| Calculated Ascending Node | ~107.58° |
| Jupiter Angular Momentum | 58–62% |
| Saturn Angular Momentum | 23–26% |
| A vs B Difference | < 0.5° |
The panel also shows the current height above or below the invariable plane (in AU) for each of the 8 major planets.
Balance Trend Tracking
Tracks the invariable plane balance over time as the simulation runs.
| Control | Description |
|---|---|
| Start Tracking | Begin recording mass-weighted balance samples each frame |
| Stop Tracking | Pause recording |
| Reset Tracking | Clear all samples (use after jumping to a new date) |
Live metrics displayed:
| Metric | Description |
|---|---|
| Years Tracked | Duration of tracking window |
| Sample Count | Number of recorded samples |
| Cumulative Sum | Running total of mass-weighted balance |
| Lifetime Avg (AU) | Should converge toward ~0 over 165+ years (one full Neptune orbit) |
| Min / Max Seen (AU) | Extremes during tracking |
The Lifetime Average is the key validation metric — if the invariable plane is correctly positioned, the mass-weighted deviations should cancel out over a full outer-planet cycle.
Invariable Plane Balance Explorer
An interactive modal for testing planetary phase group assignments and Fibonacci divisors against the Fibonacci Laws of Planetary Motion. It provides instant visual feedback on whether a given configuration satisfies the inclination balance (Law 3), eccentricity balance (Law 5), and fits within Laplace-Lagrange secular theory bounds.
Accessing the Explorer
- Click Tools > Invariable Plane Inspector
The explorer opens as a centered overlay modal.
Input Values
The explorer reads orbital parameters live from the running simulation. These values are fetched directly from the simulation’s input variables, so any change you make to a planet’s properties in the simulation is immediately reflected in the explorer.
| Parameter | Source | Used in |
|---|---|---|
| Mass (m) | Simulation input (JPL DE440 mass ratios) | Law 3 and Law 5 weights |
| Semi-major axis (a) | Simulation input (AU) | Law 3 weight √(m·a(1−e²)), Law 5 weight √m·a^(3/2)·e |
| Eccentricity (e) | Simulation input (J2000) | Law 3 weight (1−e² term), Law 5 weight (e factor) |
| J2000 inclination (i) | Simulation input (to invariable plane) | Laplace-Lagrange bounds, trend verification |
| Ascending node (Ω) | Simulation input (on invariable plane) | Ecliptic trend calculation |
Try it: change Neptune’s semi-major axis in the simulation, then open the explorer — you’ll see the inclination and eccentricity balance percentages update to reflect the new value.
Explorer Controls
Three parameters per planet are adjustable directly within the explorer. Every change triggers immediate recalculation — no “Calculate” button needed.
| Control | Description |
|---|---|
| Preset dropdown | 755 pre-computed configurations that achieve ≥99.994% inclination balance (the TNO margin), grouped by Jupiter/Saturn scenario |
| Phase angle (γ) | Per planet: 203.3195° (prograde group) or 23.3195° (retrograde group), plus Laplace-Lagrange eigenmode angles and custom input |
| Fibonacci divisor (d) | Per planet: common Fibonacci values (1, 2, 3, 5, 8, 13, 21, 34, 55) or custom |
| Period (years) | Precession period of each planet’s ascending node; negative = retrograde |
Earth’s row is locked: phase = 203.3195°, d = 3. Earth’s amplitude (0.635105°) is independently calibrated from the temperature/obliquity model.
Results
The explorer displays:
| Output | Description |
|---|---|
| Inclination balance (Law 3) | Balance percentage using structural weights w = √(m · a(1−e²)) / d |
| Eccentricity balance (Law 5) | Balance percentage using eccentricity weights v = √m × a^(3/2) × e / √d |
| Per-planet table | Amplitude, mean, range, Laplace-Lagrange verification, ecliptic trend vs JPL, direction match |
| ψ formula | Confirms ψ = 2205 / (2 × 333,888) = 3.302005 × 10⁻³ |
Default Planet Configuration (Config #32)
The model’s uniquely determined mirror-symmetric configuration:
| Planet | Period (yr) | Period = | d | Fibonacci | Phase | Mirror partner |
|---|---|---|---|---|---|---|
| Mercury | 242,828 | H/(11/8) | 21 | F₈ | 203° | Uranus |
| Venus | 667,776 | 2H | 34 | F₉ | 203° | Neptune |
| Earth | 111,296 | H/3 | 3 | F₄ | 203° | Saturn |
| Mars | 77,051 | H/(13/3) | 5 | F₅ | 203° | Jupiter |
| Jupiter | 66,778 | H/5 | 5 | F₅ | 203° | Mars |
| Saturn | 41,736 | H/8 | 3 | F₄ | 23° | Earth |
| Uranus | 111,296 | H/3 | 21 | F₈ | 203° | Mercury |
| Neptune | 667,776 | 2H | 34 | F₉ | 203° | Venus |
Expected results: inclination balance 99.9998%, eccentricity balance 99.88%, Laplace-Lagrange bounds 8/8 pass, trend directions 7/7 match.
Experiments to Try
- Change Saturn to 203°: balance collapses — Saturn must be in the opposite group
- Increase Neptune’s d from 34 to 55: amplitude decreases, observe effect on balance
- Browse the 755 valid configurations: use the Preset dropdown to compare alternatives
- Find Config #32 (Scenario A): the only configuration with mirror-symmetric d-assignments
For background on the laws and their derivations, see Fibonacci Laws and Fibonacci Laws Derivation.
IAU Reference Values
The analysis tools compare measured simulation values against these IAU J2000 reference values:
| Measurement | IAU J2000 Value |
|---|---|
| Tropical Year (March Equinox) | 365.242374 days |
| Tropical Year (June Solstice) | 365.241626 days |
| Tropical Year (September Equinox) | 365.242018 days |
| Tropical Year (December Solstice) | 365.242740 days |
| Tropical Year (Mean) | 365.242189 days |
| Anomalistic Year | 365.259636 days |
| Sidereal Year | 365.256363 days |
| IAU Precession Period | 25,771.57 years |
Tips
- List Mode: Use comma-separated years for non-consecutive analysis (e.g.,
2000, 2025, 2050, 2100) - Console: Always open Developer Tools (F12) before running console tests
- Validation: Compare measured output against IAU references to verify model accuracy
- Export Format: All exports use Excel format (.xlsx)
Return to the 3D Simulation Guide or explore Mathematical Foundations for the underlying calculations.