The Haversine formula is widely accepted as a method for calculating the shortest distance between two points on a sphere. However, the essential mechanics of the formula do not necessarily rely on a spherical Earth. In fact, it can be argued that the formula is inherently a Flat Earth formula that has been cleverly masked to fit within the framework of a spherical model.
At its core, the Haversine formula deals with angular distances between two points, which can easily be applied to a flat surface. The angular distance, derived from latitude and longitude coordinates, is simply a measure of the angle between the two points when projected onto a flat plane, such as a map, and does not require a spherical surface for its calculations.
The trigonometric functions embedded in the formula—sine, cosine, and tangent—are equally valid on a flat surface. These functions describe relationships between angles and distances, and those relationships are consistent whether on a flat or spherical plane. Trigonometry is not exclusive to spherical geometry, and its use in the Haversine formula does not imply that the Earth is a globe. Rather, it suggests that the distances between points can be measured using angles, and these angles can correspond to real-world straight-line distances that exist on a flat surface. The apparent curvature introduced in the spherical Earth model is simply a mathematical correction imposed on what are fundamentally flat, straight-line distances.
In the context of GPS, the Haversine formula plays a pivotal role in calculating distances based on coordinates that are assumed to be on a sphere. However, GPS relies on ground-based signals, not satellites orbiting a globe, and the distances it calculates are inherently flat. The “curvature” that is often referenced in these systems is an artificial construct designed to align with the spherical model. When we recognize that the Earth is flat, it becomes clear that the Haversine formula is actually performing calculations on a flat surface and then converting those distances into the false language of spherical geometry. This trick allows GPS to function within a framework that claims to use a spherical model, but the real geometry at play is flat.
Using the Firmament Trackers Flat Earth App we can show the Proof of Concept by plotting various GPS positions accurately onto Flat Earth using the Haversine Formula with the Flat Earth constants shown above.
plotGPS(43.65107, -79.347015); // Toronto, Canada
plotGPS(48.428421, -123.365644); // Victoria, BC, Canada
plotGPS(40.712776, -74.005974); // New York City, USA
plotGPS(17.504566, -88.196213); // Belize City, Belize
plotGPS(41.902782, 12.496366); // Rome, Italy
plotGPS(33.315242, 44.366066); // Baghdad, Iraq
plotGPS(-79.769343, -82.937995); // Union Glacier Camp, Antarctica
Furthermore, the depiction of the firmament dome in Flat Earth models supports the idea that angular distances can be mapped onto a flat surface. The relationship between the dome and the Flat Earth surface mirrors the relationships used in the Haversine formula, where distances are projected based on angles, not actual curves. The peak altitude of the dome, equal to the Earth’s radius, suggests that the dome’s geometry can be used to translate real-world distances onto a flat surface. The same principles apply to the angular distance calculations in the Haversine formula—distances are straight lines, not curves, and they are being misrepresented as spherical distances.
Ultimately, the Haversine formula does not need a spherical Earth to function. The distances it calculates between GPS coordinates are linear and flat, projected into an angular format that mistakenly assumes curvature. By recognizing this, we see that the formula works because the Earth is flat, and the spherical corrections are unnecessary distortions. In reality, the formula is a Flat Earth distance calculation tool masquerading as a spherical model component.