Equator Length
It is safe to say that flat earthers and the rest of civilisation agree that the latitude/longitude coordinate system accurately maps locations on the Earth; after all, they make a lot of noise about celestial navigation proving the earth is flat. It's also the basis of mapping, including GPS.
Mention equator to flerfs and they will often deny its existence, or point out that it's not a real line on the face of the earth, or some other panic measure. Which is odd, because they can't deny the 0° circle of latitude as it is a feature of the celestial navigation they love so much, despite it being part of the spherical coordinate system. The equator is, of course, the 0° circle of latitude.
Asking for the length/circumference of the equator/0° circle of latitude inevitably leads to deflection and denial. There is a good reason for this; the answer leads to the falsification of the flat earth model.
Globe vs Flat Earth Models
Globe
The earth is an oblate spheroid, or a slightly squashed sphere; the circumference through the poles (40,007 km) being about 68km less than the circumference of the equator (40,075 km). The average circumference is 40,041 km. Eratosthenes (276 - 194 BCE) was the first to reliably measure the circumference, getting a value of 40,338 km.
Flat
At the time of Eratosthenes, it was commonly known that the earth was spherical and the sun was a very distant object. Flat earthers believe that the earth is flat and the sun is local, so the method used by Eratosthenes is not applicable. As the equator is a circle centred on the North Pole, its circumference must be
2 x π x r
where r, the radius, is the distance from the equator to the North Pole. Historically, the metre was defined as 1/10,000,000 of this distance, which equals 10,000 km. The modern distance is not much different to this. So according to flat earth, the circumference of the earth is
2 x π x 10,000, or 62,832 km
Comparing the Models
There is quite a difference in the two measurements of earth's circumference:
Eratosthenes = 40,338 km
Flat geometry = 62,832 km
Which is closest to the truth?
Celestial Navigation
Celestial navigation tells us that the distance along a great circle, which includes the equator, is 60 nautical miles (NM) per degree. The full circle of the equator will therefore be
60 x 360, or 21600 NM. This converts to 40,003 km.
Google Earth
The measurement tool of Google Earth, which uses the same geometric model for the earth as Google maps, can be used to find the length of the equator. It's a bit fiddly, the result I got was 40,074 km.
Avenue Equatorial, Macapá, Brazil
As its name suggests, this street runs along the equator in Brazil.
Using Google Maps, we can measure the actual length, which is 1.9 km, or 1 NM;. This is 1 minute of arc along a great circle of the earth, which as all celestial navigators know, includes the equator; the Brazilians seem to have thought this through. Anyone who disputes the measurement can look on Google Maps themselves and if they are still sceptical, could drive along it and check the odometer.
Using this, we can make another simple calculation of the length of the equator. There are
60 x 360 = 21,600
minutes of arc in a full circle. To convert this to km, multiply by the length:
21,600 x 1.9 = 41,0400 km
Putting all this together, we can compare all the results.
| Geometry | Method | Circumference (km) |
|---|---|---|
| Flat | 2 x π x r | 62,832 |
| Globe | Eratosthenes | 40,338 |
| Globe | Celestial navigation | 40,003 |
| Globe | Google Earth | 40,074 |
| Globe | Google Maps | 41,040* |
*Bear in mind that the distance Google Maps returns is only accurate to 0.1 km.
Conclusion
Flat geometry is the one clear anomaly here; the globe results are in good agreement. We must reject the notion that the earth is flat and accept that the globe is the best model.