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https://en.wikipedia.org/wiki/Equation_of_time

Modern science says the earth changes speed to account for peculiarities of the analemma.    According to WIKI, the earth changes speed.



Wikipedia:
During a year the equation of time varies as shown on the graph; its change from one year to the next is slight. Apparent time, and the sundial, can be ahead (fast) by as much as 16 min 33 s (around 3 November), or behind (slow) by as much as 14 min 6 s (around 12 February). The equation of time has zeros near 15 April, 13 June, 1 September and 25 December. Ignoring very slow changes in the Earth's orbit and rotation, these events are repeated at the same times every tropical year. However, due to the non-integer number of days in a year, these dates can vary by a day or so from year to year.^[4][5]

So, when I first started looking into flat earth, I didn't think it likely that I would come around to accepting it.

But the evidence seems to be stacking up strongly in favor of flat earth.

1 ) cities, mountains, other objects that are clearly visible (and obviously not just refraction or "mirage") from distances at which globe earth math would make it impossible

2 ) strong evidence of NASA (and SpaceX) fakery

3 ) sun spots on the top of clouds when sun is allegedly 93 million miles away

4 ) lots of independent (not NASA controlled) footage from high enough where curvature should be visible ... and yet it's not, and where the horizon remains at eye level

5 ) flight plans that don't make any sense except for against a flat earth map

6 ) prohibition of free Antarctic exploration

7 ) moonlight being cooler than surrounding area

8 ) surveyors and engineers ignoring earth curvature

9) NASA images of globe earth are clearly (and admittedly CGI) ... with differing shapes of continents, cut-and-paste repeated cloud patterns, no satellites visible

10) fake Mars rover pictures, obvious green-screened and otherwise faked "astronaut" footage

11) Piccard's pre-NASA statement that the earth looks like a circular disc with upturned edges

12) sun changing size in the sky when it's allegedly 93 million miles away

[this is just off the top of my head, as I'm sure there's more]

On the globe earth side, I see ...

1) the Antarctica problem ... long periods of sunlight where there should be less sunlight according to a flat earth model

2) alleged flights over Antarctica

So the Antarctica problems remains the final obstacle to my being able to completely embrace flat earth.

So, flat earthers, what do you say about the Antarctica issue?  If the circuмference of the Antarctica is so big, why is there so much sunlight during "Southern Hemisphere" summer?  Is light bouncing off the dome or something?

So since I know you're actually intellectually serious about this, unlike some, I will attempt to address some of these.
1. I've talked about this one several times on this forum, and done the math on at least 2 images that I can remember. In every case I've looked at, the math works out with the expected curvature of the earth. The issue with a lot of these is that they say things like "this camera is about X feet above sea level, therefore that cliff about Y miles away should be invisible." Then if you redo the math with X+5 feet and Y+1 miles or something similar, it's completely expected for it to be visible (see here for an example of that on this forum). As I've offered before, post one that you think shouldn't work on a round earth and I'll do the math.
2, 9, and 10. Not proof either way. I have no issue believing that some NASA images could be faked, but there are explanations for that which don't affect the shape of the earth.
3. Never looked into this. 

4. See #1 kind of, but this one is more complicated. The field of regard and angle of the camera make a very significant different in what you see at the horizon. These are really finicky, but I could be convinced otheriwise.

5. This is simply not true. Also your #2 in the "against" section.
6. Other possible explanations, but sure. 
7. I've addressed on this forum (see here).
8. This is a fairly vague statement, and can be addressed various ways depending on what you mean. On small scales, curvature is negligible, so yes for probably 99% of applications it's ignored. I can't think of a significant application where it comes up off the top of my head, though they surely exist. 
11-12. The human eye is a notoriously fickle instrument. 


Lastly, I am curious what you make of this picture and others like it. I have never seen a flat-earther provide a valid explanation for how that is possible on a flat earth. If one could be provided, I'd actually change my mind on this topic, but I have never seen it, and I don't believe it's possible based on simple geometry.

So since I know you're actually intellectually serious about this, unlike some, I will attempt to address some of these.
1. I've talked about this one several times on this forum, and done the math on at least 2 images that I can remember. In every case I've looked at, the math works out with the expected curvature of the earth. The issue with a lot of these is that they say things like "this camera is about X feet above sea level, therefore that cliff about Y miles away should be invisible." Then if you redo the math with X+5 feet and Y+1 miles or something similar, it's completely expected for it to be visible (see here for an example of that on this forum). As I've offered before, post one that you think shouldn't work on a round earth and I'll do the math.
2, 9, and 10. Not proof either way. I have no issue believing that some NASA images could be faked, but there are explanations for that which don't affect the shape of the earth.
3. Never looked into this.

4. See #1 kind of, but this one is more complicated. The field of regard and angle of the camera make a very significant different in what you see at the horizon. These are really finicky, but I could be convinced otheriwise.

5. This is simply not true. Also your #2 in the "against" section.
6. Other possible explanations, but sure.
7. I've addressed on this forum (see here).
8. This is a fairly vague statement, and can be addressed various ways depending on what you mean. On small scales, curvature is negligible, so yes for probably 99% of applications it's ignored. I can't think of a significant application where it comes up off the top of my head, though they surely exist.
11-12. The human eye is a notoriously fickle instrument.


Lastly, I am curious what you make of this picture and others like it. I have never seen a flat-earther provide a valid explanation for how that is possible on a flat earth. If one could be provided, I'd actually change my mind on this topic, but I have never seen it, and I don't believe it's possible based on simple geometry.

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Since it's only YouTube videos that you guys seem to comprehend, maybe you ought to look at this one.
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Turn the sound off unless you like retarded NewAge synthesized tubular bells. Minute 2 is the relevant part, the rest is silly.
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Anyone can see this same thing by patiently watching the sun set near the latitude of Florida.
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That would be like Southern California, the Gulf states (like southern Texas), Mexico, Cuba, Guatemala or Belize in the Western hemisphere.
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The sun goes down very steeply into the western sky, and to think it then makes a right turn to the north (like flat-earthers keep claiming) is sheer nonsense.
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The sphericity of the earth is everywhere we look all around us.
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