If you use a sextant or a transit to triangulate with the sun and several different stars at a particular time of the year, and then triangulate with the same stars and the sun 90 days later, and then triangulate the triangulations, together, the distance of the sun from the earth can be ascertained to be about 90 million miles. You can use the calc to find the rough diameter of the sun to be +/- 800,000 miles.
Your margin of error is about ~89,999,666 miles if you factor refraction (WARNING: DO NOT USE REFRACTION TABLES FROM NASA!) into the equation. You're also assuming the Earth is a sphere, the fact you made an assumption limits the validity of your evidence; petitio principii, or at least a variant thereof.
Try measuring the Sun's size directly with the sextant (32 minutes in diameter) and you'll get much more accurate results.
Okay. Thanks. Didn't realize you didn't want to use anything regarding sight, or photo-sensitivity for determining the shape of the earth.
How does triangulation suggest that the earth is a sphere? (Note that we are using photo-sensitivity assumptions again.) Simply using the same time of day for making geometric trig measurements doesn't need a sphere in any of it. All we are doing is determining the distance to the sun, and then the diameter of the sun off that distance.
For example - and I forget your figures, etc. - if the sun is 3000 miles in diameter, and is directly overhead for you, and is well within the 18,000 miles to the top of the dome from earth... somebody who is thousands of miles away from you should see a smaller sun. But he doesn't. The sun is always the same size to everybody no matter where he looks at it from. This suggests that the sun is much larger and more distant that you seem to think. The idea that refraction makes it look bigger than it is from further away, doesn't have its base in science or simple observation. In fact, it's the opposite.
Since we can't use photo-sensitivity - sight or telescopes, or probably radar since it has to do with the electromagnetic spectrum - why would you think that the earth is flat, and that the sun is only less than 18,000 miles away? If your error is in the range of 90 million miles factoring in refraction, why would you think it is any better at close range?
Math and many science experiments show that the refractive index is not any 90 million miles off. If it were, Sagnac, Michelson Morley, and Airy wouldn't have any bearing on anything, one way or another. Yet you quote these guys and refer to them all the time. Or is it that you think that they were wrong this way but not that?