There are two major problems with any Flat Earth model as it applies to amateur astronomy.
A) Personal. Most unfortunately, most people (probably 99%+) have not done amateur astronomy (i.e. using a telescope with an equatorial mount). This is a terrible flaw IMO. For anyone who has, much of the Flat Earth debate can be ended right there. Without this knowledge, there is a lot of hand-waving and blowing-off, because of the lack of understanding and experience, of real facts that have been experienced by 10,000's of amateur astronomers over decades.
B)
Equatorial Mount. This is one of the keys to disproving any Flat Earth model and proving a spherical Earth model. Let me explain for those of you who have not done amateur astronomy.
Distances and Movement. Basically, the closer to the Earth something is, the faster it moves relative to the "stationary" sky (i.e. galaxies).
- Galaxies. These are SOOOO FAR away that they do not appear to move at all. A stationary point of reference.
- Stars. These are very FAR away. Most appear to be stationary. There are a couple dozen stars close enough to us to move perceptively in a human life-time.
- Planets and Sun. Far away. These move across the heavens noticeably but slowly. Venus is particularly noticeable - it is the closest to the Earth and moves quickly around the Sun.
- Moon. Moves "quickly". Can be noticed night to night.
- Satellites. Move VERY quickly. Can move from one end of the horizon to the other in less than 2 hrs.
- Meteors. Woooosh.
The trick is taking pictures of these. Now-a-days, with CCD cameras, we take very short pictures (keeps atmospheric turbulence down and alignment isn't as critical) and "sandwich" them with software to get pictures. Back in the day, when pictures required many minutes or hours to photograph, alignment was critical or you got smudged stars. The good news is that most near heavenly bodies are also relatively bright and only require seconds for the photograph. So we will deal with stars and galaxies.
To take pictures, you have to track the stars in 3 ways - up/down, left/right and the rotation of the sky. If you don't compensate for the sky moving, stars move out of frame very quickly. The higher the magnification, the faster they move.
Altazimuth Mounts. Basically, these are mounts for viewing terrestrial objects (e.g. birds, buildings, etc.). For viewing the heavens, they have to have 2 sets of motors (up/down and left/right) and need to be software/hardware controlled to simulate the moving heavens. These can be quite accurate. The problem with long exposures, is that the actual telescope tube needs to rotate with the sky. That is harder to do (from a mount perspective) and would need another motor.
Equatorial Mounts. These simplify tracking the sky TREMENDOUSLY. You only need one motor, typically running at one speed (the speed the sky is rotating). Basically, you align the telescope with the axis of spin of the Earth and turn on the motor. It tracks the sky "perfectly" based on how good your alignment is. You aim at the star and take your picture. The telescope tube rotates with the sky as well.
The KEY is the alignment. On a spherical Earth, the Earth spins around its axis as defined by its N. and S. Poles. The equatorial mount needs to be aligned with that as perfectly as possible. This means that at the N. and S. Poles, the alignment would be perfectly vertical (90 deg). On the equator, it would be perfectly horizontal (0 deg).
The alignment needs to be the EXACT latitude of your location (e.g. Denver 39.7392 deg, S. Georgia Island 54.2500 deg).
This alignment matches PERFECTLY with a spherical Earth model's latitudes.
That is THE problem with ANY Flat Earth model. Since the axis of ANY Flat Earth model is always vertical everywhere, telescopes with an equatorial mount would be aligned vertically EVERYWHERE on Earth. Since we have to align telescopes based on latitude, this clearly shows the Earth is not flat but spherical.