I should also point out that we can easily prove that the stars are much farther than the few thousand miles Tom puts them at. This is stupidly easy to see with a rudimentary knowledge of the Doppler effect. https://en.wikipedia.org/wiki/Relativistic_Doppler_effect One can easily see that the red-shifted galaxies must be moving away from us at an appreciable fraction of the speed of light. Now one might say, well speed is not the same thing as position. And I would respond that galaxies moving away from us at an appreciable fraction of the speed of light take only a few seconds to move many tens of thousands of miles; so if I weren't right a second ago, now I'm right.
Of course, Tom still hasn't taken my suggestion and at the very least tried to understand basic science. This is why he doesn't understand why his parallax experiment is junk (hint: your angle measurements are taken with respect to different reference normals -- since we don't know whether they are parallel or not, you need to take them at a lot of locations).
Such proof could be "blurred" in the eyes of less educated readers.
Simple stuff explainable to everyone is better.
For example, lunar parallax can show distance to the Moon to be 380 000 km.
Sextant could be as low as $22 on eBay, and it is best affordable way to measure angles.
Cheapest models can measure angles with accuracy within 0.2 arcminute.
Find dark place without light pollution. Mark your latitude.
Wait till Moon is about 15 degrees before highest point (a bit to the left from due south).
Find star at its path, few degrees away, and measure angle to the Moon (not to the horizon).
(Hold sextant almost horizontally to align it with line connecting Moon and selected star.)
Wait EXACTLY two hours, for the Moon to move 30 degrees.
If you are at latitude of 45 degrees, it will actually be your movement by about 2350 km.
If you are at Equator, your movement will be about 3325 km.
(Or you can say sky moved for that much. In both cases it is relative movement between the two.)
Measure the angle between Moon and selected star and calculate difference.
If they are at same distance, angle will stay the same.
But if star is much farther than Moon, you will have change of the angle between them.
From latitude of 45 degrees you will have change of about 21 arcminutes (0.35 degrees).
Distance to the moon will be 2350 / tan(0.35) = 2350 / 0.006 = 384 695 km.
Ofcourse, it could be a bit more or less, because we could make an error in our readings.
If we measure 20 arcminutes we get distance to Moon of 404 000 km.
If we measure 22 arcminutes we get distance to Moon of 367 000 km.
But it would still be pretty far.
And it will show how much farther is the selected star.
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This is how to understand sextant:
NOTE: For error correction part, you have to adjust index arm to zero
including micrometer.