Our recent submission to the MCToon Sextant Challenge has successfully demonstrated a three-star fix algorithm based on Flat Earth geometry, with the final location of latitude 30 and longitude -50 confirming its precision. By using celestial data from an almanac and a brute-force computational approach, the algorithm accurately calculates the observer’s position based solely on the angle of elevation of stars, without requiring spherical trigonometry. This process offers a compelling proof of concept for celestial navigation on a Flat Earth.
This algorithm was written by Dr. Steven Alonzo of the Flat Earth University.
Why This Method Works Without Spherical Trigonometry
In this Flat Earth model, there’s no need for spherical trigonometry because the curvature of the Earth is not a factor. The algorithm treats the sky as a flat plane, using basic geometry to calculate angles and positions. This simplifies the process significantly, as the complex adjustments required for a spherical Earth (such as dip corrections and great circle calculations) are not needed.
Understanding the Algorithm
The core principle of this algorithm lies in how it uses the celestial sphere to determine the angle of elevation for three known stars. Here’s a step-by-step breakdown of the process:
- Almanac Data:
The first step involves consulting a celestial almanac to find the right ascension (RA) and declination (DEC) of the three stars (for example, Regulus, Arcturus, and Dubhe). These are the key coordinates used to plot the stars’ positions on the celestial sphere. - Plotting on the Celestial Sphere:
Once the RA and DEC of the stars are known, they are plotted on a celestial sphere. This sphere represents the sky as observed from the flat Earth, with the observer at the center. The right ascension specifies the star’s position along the celestial equator (analogous to longitude on Earth), while the declination measures its angular distance from the celestial equator (similar to latitude on Earth). - Angle of Elevation:
The next critical step is calculating the angle of elevation for each of these stars. The angle of elevation is the height of the star above the observer’s horizon, and it is the key measurement in celestial navigation. On a flat Earth, this angle is based on the observer’s location and the position of the star on the celestial sphere. Importantly, in this model, the distance between the observer and the substellar point (the point on Earth directly beneath the star) doesn’t affect the computation. Only the altitude angle matters here. As a result, the observer’s position is determined entirely by matching the observed star altitudes (from the horizon) with the expected angles from the celestial sphere.
The Iterative Computational Process
One of the innovative aspects of the MCToon Sextant Challenge is its use of a brute-force algorithm to iterate through possible observer locations on a flat Earth. Here’s how the computational process works:
- Latitude and Longitude Iteration:
The algorithm systematically iterates through all possible latitude and longitude coordinates on the Flat Earth map. At each location, it calculates the angle of elevation for the three stars based on their RA and DEC positions from the celestial sphere. - Matching Observed Elevations:
For each potential location, the algorithm compares the calculated angle of elevation for each star with the observed angle of elevation (measured using a sextant or another instrument). The goal is to find the latitude and longitude where the calculated and observed angles match for all three stars. - Final Location:
Through this brute-force method, the algorithm identifies the location where the star altitudes match the observer’s real-world observations. In the case of the MCToon Sextant Challenge, the final location of latitude 30 and longitude -50 was found, confirming the accuracy of the algorithm.
Precision of the Flat Earth Three-Star Fix
The brute-force computational method used in the MCToon Sextant Challenge shows that this Flat Earth algorithm can be as precise as necessary, depending on the resolution of the latitude and longitude iterations. The more computational power available, the finer the grid of possible locations, leading to higher accuracy.
In this particular case, the iterative process successfully yielded a final position of latitude 30, longitude -50, validating the effectiveness of the Flat Earth celestial navigation model. The algorithm adjusts star altitudes based on RA and DEC and then matches them with the observed altitudes, demonstrating a high level of precision.
Conclusion: A Proven Flat Earth Algorithm for Celestial Navigation
The MCToon Sextant Challenge serves as a clear demonstration that celestial navigation on a Flat Earth is entirely feasible using a three-star fix. By employing celestial data from an almanac, plotting stars on a celestial sphere, and calculating angles of elevation, the algorithm accurately determines the observer’s position without relying on spherical trigonometry.
This proof of concept shows that Flat Earth celestial navigation can achieve highly precise results, as seen in the final coordinates of latitude 30 and longitude -50. The iterative brute-force approach ensures that, with sufficient computing power, the algorithm can match observed star altitudes and deliver accurate navigational fixes, all while adhering to the Flat Earth model. This challenge not only proves the concept but also offers a valuable tool for exploring celestial navigation from a new perspective.
I have to admit, this was fun to read 🙂