In keeping within the envelope this discussion creates, I am looking to show the math that definitively proves GE. The Polaris example of the math on the previous FE model shows how it's done.

According to GE, Polaris' distance is unsettled. 433 - 448 light-years. According to GE, Earth's distance to the sun is 93,000,000 miles.

For purpose and mechanics of this discussion, for now I label 433 LY's and 93,000,000 miles an assumption. I used these figures for my investigative calculations. The purpose being how small of an angular difference.

My calc's show only 0.000,002,09° difference. 93e6 / 2.3e15. So that does not prove nor disprove because of angular resolution. I messed with a sextant that I inherited. My opinion of this particular sextant is +/- 0.5° margin of error. I doubt you have a more precise instrument and I know I don't.

Santa Barbara, CA

34.42352697861604, -119.69657200920265

Surf City, NC

34.42961212770392, -77.55404848374764

Difference

-42.14252352545501

Because those two cities are not on the equator, the declination angles will be lower by the number of degrees latitude. I don't care to have to teach myself 3D trig. I am ignoring that error so that how the sun's elevation a.k.a. distance is determined along with the earth's circumference and radius.

If the sun's zenith is 90° over Santa Barbara, and at exactly the same time, the sun's angle of declination is 42° west of Surf City... The following calc's apply.

As depicted in SUN 1:

The declination of the sun is 90° above Santa Barbara.

The declination of the sun is X° (unknown) above Surf City.

The elevation - distance of the sun above Santa Barbara is Y (unknown).

Ground Truth:

Gobble Maps routing shows 2716 miles. I am using that as my ground truth.

As I write this, I am undecided if I want to do the Polaris flat earth exercise with this ground truth that will show a discrepancy and the 90° will not be over Santa Barbara.