[AATW]

In the flat earth model the sun at sunset is about 6000 miles away horizontally and 3000 miles above the earth. Yes?
So how does the flat earth model explain the long shadows you see at sunset?



The FE Wiki has this diagram when explaining how the sun could be calculated to be 3000 miles high if the earth was flat:



So your own diagram agrees that shadow length depends on the physical relationship between the light source and the object which casts a shadow. No perspective is accounted for in this diagram, nor does it need to be. That is not how shadows work. Photons from a light source hit an object at a certain angle. That angle depends on the physical relationship between the object and the light source.

In the above diagram if we take 'h' to be 3000 and 'a' to be 6000. Let's say the height of the object at R1 is 1 and the length of its shadow is 'x':

The triangle formed by the object, its shadow and the ray from the sun is a similar triangle (in the mathematical sense) to
the triangle formed by the shadow+the horizontal distance to the sun, the vertical line from the ground to the sun and the ray from the sun (which is the shared hypotenuse of both triangles)

So: h/a+x = 1/x. Plugging in the numbers:
3000/6000+x = 1/x (multiply both sides by 'x')
3000x/6000+x = 1 (multiply both sides by '6000+x')
3000x = 6000+x (subtract 'x' from both sides)
2999x = 6000, so...
x = 6000/2999 - let's call that 2 for simplicity.

So the shadow is pretty much twice the height of the object. Which is what you'd expect if you think about it, the sun is twice as far away horizontally as it is high. The only way of making the shadow longer is to move it further away horizontally or move it lower in the sky. In the round earth model the sun is physically lower in the sky as the earth rotates, hence the long shadows. What is the flat earth explanation?
Perspective does not work as an explanation here, shadows depend on the PHYSICAL location of the light source and the object, not your or anyone else's perspective. Note that there are no units above, it could be 3000cm, meters, inches, yards or miles. So long as the 1, 3000 and 6000 are in the same units the unit of the shadow is the same so distance doesn't matter.

I should also say that perspective cannot make an object 3000 miles high appear to sink slowly below the horizon. Tom cites rail tracks which appear to converge



Note that "appear to" is the key phrase there. They don't really converge as this detail from the above shows:



Think about how we see things. Light bounces off an object and travels in a straight line to our eyes.
In this diagram you can see that the rays from the tracks at 'A' meet at the person who is looking at a bigger angle than the light at 'B':



So 'A' will appear to be bigger than 'B'. And there will be a distance at which the two rails can no longer be distinguished but that is only because of the limitation of the resolution of your eye.
Magnification would show that a gap still exists between the rails.
The angle of light rays will never be zero because the sleeper forms the hypotenuse and the light rays form the other two sides of an isosceles triangle. The hypotenuse remains constant so while the angle at the "apex" of the triangle becomes smaller with distance it is never 0 (apart from at infinity).

Long shadows at sunset prove that the sun is either physically low in the sky (as round earth model claims) or the light is bending somehow so it appears so.

[JohnAdams1145]

It's even more absurd. Tom Bishop and the rest who say that sunsets on the horizon are a result of perspective don't even understand what perspective is. Perspective is not a fundamental law of optics. It is just simply the result that because light rays converge on your eyeballs, objects/distances farther away look smaller.

Therefore, the idea that if the Sun gets farther away, it will somehow merge with the horizon is utter garbage. No. It will not. No other observations needed (although your long shadow proof is genius). The Sun would have to get farther off the Earth's imaginary edge for the angle to become that acute (or it would have to get close to the plane of the Earth), none of which are observed to happen. This is not to mention that part of the Sun is clearly occluded by the horizon, which wouldn't be expected as a result of perspective.

[Macarios]

It's even more absurd. Tom Bishop and the rest who say that sunsets on the horizon are a result of perspective don't even understand what perspective is. Perspective is not a fundamental law of optics. It is just simply the result that because light rays converge on your eyeballs, objects/distances farther away look smaller.

Therefore, the idea that if the Sun gets farther away, it will somehow merge with the horizon is utter garbage. No. It will not. No other observations needed (although your long shadow proof is genius). The Sun would have to get farther off the Earth's imaginary edge for the angle to become that acute (or it would have to get close to the plane of the Earth), none of which are observed to happen. This is not to mention that part of the Sun is clearly occluded by the horizon, which wouldn't be expected as a result of perspective.

Idea is garbage, but Rowbotham had to create it to have defense when they disguise his scam lectures again.
Before he assembled it he had to run away from lectures when they ask about things go behind horizon.

[AATW]

Therefore, the idea that if the Sun gets farther away, it will somehow merge with the horizon is utter garbage. No. It will not. No other observations needed (although your long shadow proof is genius). The Sun would have to get farther off the Earth's imaginary edge for the angle to become that acute (or it would have to get close to the plane of the Earth), none of which are observed to happen. This is not to mention that part of the Sun is clearly occluded by the horizon, which wouldn't be expected as a result of perspective.

I'm still laughing at his assertion that:

As per the argument of how the sun can be lower than the mountain in order to look up at it, this was discussed earlier in this thread. If we have a series of lamp posts stretching into the horizon, it is possible and raise your hand to be above a small lamp post on the horizon in the distance. The distant lamp post is now looking up at your hand.

The distant lamp post has the opposite perspective. It sees you at the horizon and it sees your hand slightly above the horizon, and therefore its photons are angled upwards at it.

How do you debate with someone who thinks like that?! 

But what is particularly satisfying about the shadow proof - and it is proof - is that their own Wiki has a diagram showing shadows of different lengths because of the sun at different positions and their diagram doesn't account for perspective. Which is correct. It doesn't need to. That's now how shadows work.

Your move, Tom...

[AATW]

Addendum, I realised later that assuming the height of the object to be 1 is a bit lazy so let's call it y:

h/a+x = y/x. Plugging in the numbers:

3000/6000+x = y/x  (multiply both sides by x)
3000x/6000+x = y (multiply both sides by 6000+x)
3000x = 6000y + xy (-xy from both sides)
(3000-y)x = 6000y (divide both sides by 3000-y)

x = 6000y / (3000-y)

So actually the shadow length ISN'T always twice the height BUT it does tend to that as y approaches 0.
And given we're working in miles, for most normal objects it is very close to zero, so our shadows would be twice our height at sunset on the flat earth model as outlined in the Wiki.