Using Google Earth to get the radius of the earth

Google Earth, Google Maps, Apple Maps, Waze, Bing Maps, Garmin, Tom Tom, and other mapping and navigation products are all accurate enough to get flat earthers to their destination.  The coordinates from GPS devices are not disputed by flat earthers as far as I have seen.  If you accept these coordinates we can use the data from these products to obtain the radius of the earth.

Equatorial radius 1

The earth has been divided into 360 degrees in the east-west direction.  These are the lines of longitude.  If we measure the distance between two points one degree apart and multiply by 360 we will get the equatorial circumference.  This can be done in software like Google Earth or other products.  If there is doubt about the accuracy of these measurements it can be tested by traveling to these locations and measuring.

This can be tested for any place on the equator.  Gabon, The Republic of the Congo, The Democratic Republic of the Congo, Uganda, Kenya, Somalia, Indonesia, Ecuador, Columbia, or Brazil.

Here is Google Earth measuring from (00° 00′ 00″, 09° 20′ 00″) on the west coast of Gabon in Africa to (00° 00′ 00″, 10° 20′ 00″).  The distance is 111,303.72 meters.  Multiplying by 360 gives 4,0069,339.2 meters for the circumference.  Knowing that c=2πr we can solve for the radius and get 6,377,233.4 meters.

 

Equatorial radius 2

If getting someone to measure the distance at the equator is too remote, you can do the same type of measurement anywhere.  Take a distance measurement from two different points on the same latitude, any angular distance is fine, longer distances will have a lower margin of error.  Multiply this distance by the appropriate amount based on the portion of the earth’s angular circumference this covers to get the circumference around that line of latitude then divide by the cosine of the latitude to get the equatorial latitude.

In this example, we take a 15 arcminute section of the -37° 45′ 00″ line of latitude.  This goes through Melbourne, Australia and suburbs.  This area is selected because people use GPS devices in this area daily for transportation.  There is no question about the accuracy of coordinates and distances within this area.

(-37° 45′ 00″, 144° 45′ 00″) to (-37° 45′ 00″, 145° 00′ 00″) is a distance of 15 arcminutes and measures to 22,037.07 meters.  Multiply by 4 to get the length of one degree: 88,148.28 meters.  Multiply by 360 to get the line of latitude circumference: 31,733,380.8 meters.  Divide by the cosine of the latitude to get the equatorial circumference:
Latitude: 37° 45′ is 37.75°
Cosine(37.75) = 0.790689573

This gives 40,133,804.5 meters for the equatorial circumference.  Knowing that c=2πr we can solve for the radius and get 6,387,493.4 meters.

Polar radius 1

We can use the same method to get the polar radius.  This is easier to verify since you can do it along any line of longitude, even near your home.  For this example, I will start from the same location on the coast of Gabon and measure south.  From (00° 00′ 00″, 09° 20′ 00″) to (-01° 00′ 00″, 09° 20′ 00″) gives a distance of 110,586.42 meters.  Multiply by 360 and we get a circumference of 39,811,111.2 meters.  Knowing that c=2πr we can solve for the radius and get 6,336,135.1 meters.

Polar radius 2

The distance between lines of latitude are well known to be 60 nautical miles.  This is originally how the distance for nautical miles was defined.  Using this knowledge we get 21,600 nautical miles for the polar circumference or 40,003,200 meters.  Knowing that c=2πr we can solve for the radius and get 6,366,707.0 meters.

 

Comparison to accepted values

Equatorial Radius

Using Google Earth which uses the same underlying data as the other mapping products gives an equatorial radius of 6,377,233.4 meters and 6,387,493.4 meters.

The accepted equatorial radius is 6,378,137 meters.  The percentage errors are 0.0141671% and 0.146695%.

Polar Radius

Google Earth gives a polar radius of 6,336,135.1 meters.  Using 60 nautical miles per line of latitude gives 6,366,707.0 meters.

The accepted polar radius is 6,356,752 meters.  The percentage errors are 0.324331% and 0.156605%.

Conclusion

The radius of the earth can be obtained using google maps.  If you don’t trust these measurements:  be honest and never use GPS based products for navigation again.