Well, the first would stand as stronger evidence for planism than globularism, but it would not conclusively rule out a sphere or toroid or turtle-shaped earth of sufficient size, no.

This is correct; it would be inconclusive, so it's not a good experiment.

The second could actually falsify globularism/turtlism fantasies or planism, so I'm sure that's why it draws no further interest.

"Could." Again, correct. It's the only one that appears to have a theoretical chance. Lets examine this one in detail in a moment.

The third falsifies Newtonianism so prevalent here abouts amongst gobularists.

Please explain why you think this experiment "falsifies Newtonianism"? It does no such thing.

The fourth might also provide evidence of planism or globularism.

Because of the limited distances involved, the differences are subtle. Since we've seen that commonly-observed complicating factors make small differences in conditions swamp the effect being tested, people to come away claiming they have evidence for either model. So this one, too, is ambiguous.

Are you asking if there is experimental* proof* of planism? No. There is no experiment providing proof of planism any more than any experiment could ever offer proof of any hypothesis. There are no proofs in science. This isn't a math problem to be derived or calculated.

Very good! You're one of the few here that recognize that!

Anyway, let's consider your second proposed experiment, measuring the sum of the interior angles of a carefully surveyed triangle.

If the earth is a flat plane, the result will always be 180°. If the earth is a sphere, the result will always be > 180°. Seems straightforward enough.

The question, however, is: How much different from than 180° would the result be, and can you realistically expect to be able to measure it?

The sum of the interior angles of a spherical triangle, T, has the range 180° < T < 900°. The value for T depends on the area contained within the triangle as a proportion to the area of the sphere, using the formula

T = 180° (1 + 4 a/A) where a is the area of the triangle and A is the area of the sphere.

The excess angle, x (amount T exceeds 180°) would be

x = T - 180°

= 180° (1 + 4 a/A) - 180°

= 180° + 720° a/A - 180°

= 720° a/A

So, let's see how large the triangle must be to produce an excess angle of 1° on a sphere 4,000 miles in radius.

Area of a sphere with radius r is

A = 4 pi r

^{2}so

A = 4 pi (4000 miles)

^{2} = 4 pi 16,000,000 mi

^{2} = 201,061,929.8 mi

^{2}Let's call it 200 million mi

^{2}.

remember,

x = 720° a/A

so

1° = 720° a/(200,000,000 mi

^{2})

solving for a,

a = 1° (200,000,000 mi

^{2}) / 720°

= 200,000,000 mi

^{2} / 720

= 277,778 mi

^{2}That's a little larger than the US state of Texas. It's also about half again as large as the Ross Ice Shelf (which is roughly triangular and pretty flat, but logistics are something of a problem).

Although, in theory, it seems sound, that experiment just doesn't seem practical if you're looking for an

obvious difference. Sorry. Good idea, though!