I have posted essentially the same information in various forms, but no-one has ever given a reasonable
explanation as to why the sun's height is taken as about 5,000 km (a nice round number and a "bit" over 3,000 miles).
The earliest estimate for the flat earth sun's height that I know of is Rowbotham's measurement in
In this he claims
If any allowance is to be made for refraction--which, no doubt, exists where the sun's rays have to pass through a medium, the atmosphere, which gradually increases in density as it approaches the earth's surface--it will considerably diminish the above-named distance of the sun; so that it is perfectly safe to affirm that the under edge of the sun is considerably less than 700 statute miles above the earth.
So we have 700 miles (a bit over 1,100 km).
But the around 1899 we get
Thomas Winship, author of Zetetic Cosmogony. He provides a calculation demonstrating that the sun can be computed to be relatively close to the earth's surface if one assumes that the earth is flat:
On March 21-22 the sun is directly overhead at the equator and appears 45 degrees above the horizon at 45 degrees north and south latitude. As the angle of sun above the earth at the equator is 90 degrees while it is 45 degrees at 45 degrees north or south latitude, it follows that the angle at the sun between the vertical from the horizon and the line from the observers at 45 degrees north and south must also be 45 degrees. The result is two right angled triangles with legs of equal length. The distance between the equator and the points at 45 degrees north or south is approximately 3,000 miles. Ergo, the sun would be an equal distance above the equator.
This is illustrated in this diagram from
Modern Mechanics - Oct, 1931:
Voliva's Flat Earth Sun Distance. This is also shown in the Wiki under
Distance to the Sun under the section
Sun's Distance - Modern Mechanics.
Whatever happened to Rowbotham's 700 miles?
But this calculates the height from only
ONE location, Latitude 45°.
In would seem that we would get
a more accurate result by taking measurements from a
number of different latitudes and comparing the results.
So this time, I will present the sun elevations and azimuth from five locations all close to longitude 70°W.
These locations are shown on the Google Earth map on the right.
The sun azimuth and elevations have been found from: Sun Earth Tools.
If you have any doubts as the accuracy of this site, I suggest that a good test would be to check its accuracy where you live. I think if it is accurate at a lot of random locations is could be relied on for these locations.
| | Locations for Sun Height Calculations |
The following table gives the data for each location. All sun elevation was obtained from
Sun Earth Tools as close as possible to the local midday on the last equinox. The time was
UTC 20/Mar/2016 16:48.
Location
| Latitude
| Longitude
| Sun Elev
| Dist from Vaupes | Flat Sun Ht
| Lat Diff from Vaupes | Calc Circum |
Kimmirut, Canada | 62.847° | -69.869° | 27.36° | 7,034 km | 3,609 km | 63.58° | 39,828 km |
Santo Domingo | 18.486° | -69.931° | 71.72° | 2,107 km | 6,077 km | 19.22° | 39,465 km |
Vaupes, Colombia | -0.565° | -69.634° | 89.06° | 0 km | ------ | | |
Chupa District, Peru | -15.109° | -69.998° | 74.69° | 1,610 km | 6,256 km | 14.37° | 40,334 km |
Punta Arenas, Chile | -53.164° | -70.917° | 36.63° | 5,830 km | 4,388 km | 52.43° | 40,031 km |
These locations and the directions to the sun on a flat earth are shown in the left hand diagram below:
Once we have the angles from two sites the height of the sun can be calculated from:
h = d/(1/tan(A1) + 1/tan(A2)).
Sun Height on Flat Earth along 70°W Long | | Sun Height on Globe Earth along 70°W Long |
Using this method to find the height of the sun on the Flat earth gives measurements from 3609 km (for Kimmirut and Vaupes) to 6256 km (for Chupa District to Vaupes) depending on the spacing of the measurement sites.
In other words, claiming that the Flat Earth sun is at about 5,000 km altitude has no foundation whatever.
It is very telling when we note that when we plot these angles on a spherical earth the directions to the sun are all parallel.
Explain that!
Now, if instead of using these measurements to determine the Flat Earth sun height, we use them as Eratosthenes did, assuming a distant sun and use this data to calculate the circumference of the earth.
The circumference can be calculated from (distance from Vaupes) * 360°/(angle difference of sun from Vaupes)
This time, we get far better consistency.
The estimated figures for the circumference of the earth range from 39,465 km to 40,334 km.
Certainly these figures would indicate that the earth is a globe with a distant sun.
So would some kind Flat Earthers explain just what I have done wrong - if anything?