Orbit Calculator
Use this calculator to compare any published planetary semi-major axis with the Planetary Harmonics Fibonacci spacing model.
Use this calculator to compare any published planetary semi-major axis with the Planetary Harmonics Fibonacci Orbital Index. Obtain a semi-major axis value from a recognised astronomical source, enter it into the calculator, and compare the result with the fixed Fibonacci Orbital Index.
Primary Astronomical Data Sources
Start with a published semi-major axis or orbital radius value in astronomical units (AU).
Source note: NASA, ESA and JAXA are identified solely as primary sources of publicly available astronomical data. Planetary Harmonics is an independent research project and is not affiliated with, sponsored by, or endorsed by these organisations.
Find a planet
Choose a confirmed planet or exoplanet.
Find its SMA
Locate its semi-major axis or orbital radius in AU.
Enter the value
Place the published value into the calculator.
Check the index
Use the calculator, or inspect the index manually.
Interactive Calculator
The calculator searches the fixed Fibonacci Orbital Index shown lower on this page.
Result
Fibonacci Orbital Index
Use the calculator above, or inspect the index manually.
The calculator searches the same fixed table shown below. This allows users to verify for themselves that the calculator is not inventing values to suit the entered planet.
| Fibonacci Index N | N³ | Ideal SMA (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 |
Transparency note: The Orbit Calculator does not generate theoretical orbital distances. It searches the fixed Fibonacci Orbital Index shown above. Users are encouraged to inspect the index manually and verify the calculator's results independently.
How Does "Nearest Fibonacci Match" Work?
The calculator does not generate new values or create a custom fit for individual planets.
It searches a predefined Fibonacci Orbital Index and identifies the entry whose calculated ideal semi-major axis is closest to the observed semi-major axis supplied by the user.
The ideal semi-major axis values are calculated from:
where N is a Fibonacci index value. The calculator simply identifies which fixed index entry produces the closest theoretical orbital distance.
Log Your Findings Here
Use this editable worksheet to record your own tests. Type directly into the table, add rows as needed, then copy the table or download your findings as a CSV file that can be opened in Excel, LibreOffice or Google Sheets.
| Planet | Source | SMA (AU) | Nearest N | Ideal SMA | Proximity % | Pass/Fail / Notes |
|---|---|---|---|---|---|---|
Privacy note: The worksheet works only in your browser. It does not send your entries to Planetary Harmonics or any outside service. Use the download button to save your own copy.
Research Note
Planetary Harmonics investigates whether a measurable relationship exists between observed orbital distances and a Fibonacci-based spacing model. It does not claim that planetary formation is caused by Fibonacci numbers.