Thanks for posting this very good thread Bobby.
I have on board my ship sextant for measuring angles pretty accurately and have been taking a series of measurements each day as we have proceeded from a position of about 20 degrees south to where we were yesterday about 20 degrees north.
The suns declination (or latitude where the sun is right overhead) at present is about 16 degrees north, so in about 10 days we have gone from a place on earth about 35 degrees south of where the sun is overhead to right underneath it, and now are north of the suns path.
The angle of the suns elevation has gone from about 55 degrees above the horizon at noon, to 90 degrees, and now has started to drop from the zenith at noon.
I have taken the suns diameter using the sextant at noon each day we have been able to (some days it was obscured by cloud) and have been able to cross check my measurements.
By taking the upper limb, and putting it onto the lower limb, and the other way round i am able to measure not only the suns diameter, but using the almanacs reading for the semi diameter of the sun, cross check my readings.
Over the last 10 days or so i have observed the suns semi diameter at Noon to be 31.8 minutes of arc consistently, even though we have travelled over about 2,000 miles closer to the suns track over the earth.
There has been NO CHANGE in the suns diameter at noon, at different apparent altitudes, when it has been crossing the meridian.
I have also taken the same measurements through the day, and have seen the same results, ie that the suns diameter does not change throughout the day, even shortly after sunrise, through noon, to before sunset.
This shows that wherever you are on earth, at whatever time of day it is, the suns diameter does not change, and simple maths will tell you that the range of differences in distance, if the sun were only 3000 miles away, the diameter would change greatly.
It does not therefore it proves the sun is a great distance away...and the earth therefore is global.