Methodology
This page defines the calculation method used by Planetary Harmonics and explains how observed planetary orbits are compared with a predefined Fibonacci-based orbital scale.
The purpose of the model is to investigate whether planetary and exoplanet orbital distances show a measurable relationship with Fibonacci-number spacing. The method is designed to be transparent, reproducible and testable using published astronomical data.
The methodology does not require custom values to be created for individual planets. It uses a fixed Fibonacci Index Table and compares observed semi-major axis values against that table.
1. Semi-major axis
The semi-major axis is the standard astronomical measure used here for a planet's average orbital distance. In an elliptical orbit, it is half the longest diameter of the ellipse.
For this project, the observed semi-major axis is the value taken from a published astronomical source, normally expressed in astronomical units (AU).
2. Fibonacci index N
Each planet or exoplanet is compared against a Fibonacci-based index value, called N.
The smaller values below 1 allow close-in planets to be tested using the same method as planets with larger orbital distances.
3. Fibonacci Index Table
The table below is the fixed index used by the Orbit Calculator. Each value of N produces a corresponding ideal semi-major axis by cubing N and then taking the fourth root.
| N | N³ | Ideal semi-major axis AU (fourth root of N³) |
|---|---|---|
| 0.005 | 0.000000125 | 0.0188 |
| 0.008 | 0.000000512 | 0.0267 |
| 0.013 | 0.000002197 | 0.0385 |
| 0.021 | 0.000009261 | 0.0552 |
| 0.034 | 0.000039304 | 0.0792 |
| 0.055 | 0.000166375 | 0.1136 |
| 0.089 | 0.000704969 | 0.1629 |
| 0.144 | 0.002985984 | 0.2338 |
| 0.233 | 0.012649337 | 0.3354 |
| 0.377 | 0.053582633 | 0.4811 |
| 0.610 | 0.226981 | 0.6902 |
| 1 | 1.00 | 1.0000 |
| 2 | 8.00 | 1.6818 |
| 3 | 27.00 | 2.2795 |
| 5 | 125.00 | 3.3437 |
| 8 | 512.00 | 4.7568 |
| 13 | 2,197.00 | 6.8463 |
| 21 | 9,261.00 | 9.8099 |
| 34 | 39,304.00 | 14.0802 |
| 55 | 166,375.00 | 20.1963 |
| 89 | 704,969.00 | 28.9763 |
| 144 | 2,985,984.00 | 41.5692 |
| 233 | 12,649,337.00 | 59.6372 |
| 377 | 53,582,633.00 | 85.5571 |
| 610 | 226,981,000.00 | 122.7432 |
| 987 | 961,504,803.00 | 176.0913 |
| 1597 | 4,073,003,173.00 | 252.6264 |
| 2584 | 17,253,512,704.00 | 362.4260 |
| 4181 | 73,087,061,741.00 | 519.9483 |
| 6765 | 309,601,747,125.00 | 746.0382 |
Values are rounded for display. The calculator searches this fixed table rather than creating a custom value for each planet.
4. How does "Nearest Fibonacci Match" work?
The Orbit Calculator does not generate new values or create a custom fit for individual planets.
Instead, it searches a predefined Fibonacci Index Table. Each Fibonacci index corresponds to a fixed ideal semi-major axis calculated from:
When an observed semi-major axis is entered, the calculator compares it against every entry in the table and identifies the Fibonacci index whose ideal semi-major axis is closest to the observed value.
The selected result is therefore the nearest match from a fixed list of predefined values.
This process is deterministic and can be independently verified using the Fibonacci Index Table shown above.
5. Ideal semi-major axis
For each Fibonacci index N, the ideal semi-major axis is calculated as:
In plain English, this means: cube the Fibonacci index N, then take the fourth root of the result.
6. Proximity percentage
The observed semi-major axis is compared with the calculated ideal value using a proximity percentage:
A value of 100% would mean the observed semi-major axis is exactly equal to the calculated ideal semi-major axis. Values below 100% are closer to the star than the ideal value; values above 100% are farther out.
7. Pass/fail criterion
A result is classified as a pass when the proximity value falls within the range 80% to 120%.
| Proximity range | Classification |
|---|---|
| 80% to 120% | PASS |
| Below 80% or above 120% | FAIL |
8. Worked example: Jupiter
Jupiter provides a useful example because its nearest Fibonacci match is N = 8.
| Item | Value |
|---|---|
| Planet | Jupiter |
| Nearest Fibonacci index N | 8 |
| N³ | 512 |
| Ideal semi-major axis | 4.757 AU |
| Observed semi-major axis | 5.204 AU |
| Proximity | 109.40% |
| Status | PASS |
The Jupiter values here match the Solar System results table used elsewhere on this site.
9. Availability of exoplanet data
At the time of writing (2026), more than 6,000 confirmed exoplanets have been discovered.
Many of these planets have published orbital parameters, including semi-major axis measurements, making them suitable candidates for investigation using the Planetary Harmonics methodology.
As new exoplanets continue to be discovered and characterised, the methodology can be applied to additional planetary systems without modification.
The use of publicly available observational data allows independent verification of results and enables ongoing testing as astronomical catalogues expand.
10. Potential predictive applications
The current results mainly test the model against planets that are already known. This is a retrodictive test: the model is being compared with existing observations.
A possible future use is predictive. If a planetary system contains known planets occupying some Fibonacci-index positions but leaves gaps at other positions, the model can be used to identify candidate orbital distances where additional planets may exist.
Whether such candidate positions correspond to actual planets remains an observational question.
A cautious workflow for this type of investigation would be:
- Identify the orbital plane and known planets in a star system.
- Assign each known planet to its nearest Fibonacci match.
- Look for unoccupied Fibonacci-index positions between or beyond known planets.
- Calculate the corresponding candidate orbital distances.
- Compare those positions with future observations or published discoveries.
Summary
The methodology compares observed planetary distances with a fixed Fibonacci-based orbital scale. The calculator searches a predefined table, identifies the nearest Fibonacci match, calculates the proximity percentage, and applies the 80% to 120% pass/fail criterion.