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## Flat Earth Claim

The sun is smaller on the horizon proving it's simply further away and nearby:

Wow, that's really compelling evidence, right?

## Reality

Do those look like consistent exposures to you?

They sure do NOT look consistent to me.

Here is what happens when an object is too bright for the sensor (this is the moon, I personally took these images changing ONLY the exposure to show what happens):

I've been accused of 'faking that' by zooming in - whatever, I've replicated it several ways and I'll include another example I found online - and more importantly - if you don't believe it then YOU take the pictures yourself.

Here you can see the same effect with this lamp.  Brighter light overwhelms the sensor and makes a big white blur.

Here is a series I took in an airport:

You can clearly see the 'bright spot' is significantly larger from the darker exposure.  This is PHOTOGRAPHY 101 stuff.

So I'm sorry but you'll need to do better with your photography before you can count it as evidence.

Here is an image of the Solar Disc taken from the ground -- you need THIS level of quality and detail to demonstrate your claim.

Even slightly better exposed images of the Sun show that it doesn't change size during the day.

THIS simply does not cut it.

With my analysis notes on his second image that *claims* to show the Sun getting about 200 times larger over maybe an hour.

The sun is about 32 arc minutes wide, that's about 11 suns so that's about 23 1/2 minutes.

How many thousands of miles did it travel in about 23 1/2 minutes to get THAT MUCH larger?

It is very easy to see that the sun "looks smaller" here because it is going through much more atmosphere which is substantially dimming the light allowing the camera sensor to register a more accurate view.  But it's still a fuzzy, extremely poor quality view compared to professional measurements.

## To The Math

Let's do the math now:

The formula to find the angular size of something is based on the calculation of a SLOPE.

I know Flat Earthers fear math but SURELY they can comprehend the idea of

RISE / RUN

Gives you a slope?

And the "trick" here is we're going to convert that SLOPE into an angle!

Slopes and Angles have a very simple relationship using the tan() and arctan() functions.

Slope = tan(Angle)

and

Angle = arctan(Slope)

That's some heavy magic I know.

Ok... so from our viewpoint the ANGULAR size of an object is given by:

α = 2*arctan((RISE/2) / RUN)

 Image Credit: Angular Diameter Calculator
If you are lazy you can just use the Angular Diameter Calculator but we're going to do the math here (someday that page might go away).

You'll note that they write the formula as α = 2*arctan(g/(2r)) but this is exactly the same thing.  You can also write it α = 2*arctan(g/r/2).   But the general idea is we're taking one-half of 'g' as our 'RISE', finding the slope to the middle of 'g', and then doubling that angle.  Hopefully the image makes it obvious.

You can see from this that the closer something is to you it's going to take up more of your field of vision.  If you bring it closer but make it smaller so it matches those blue lines then it will stay the SAME angular size in your field of view.

Ok... So let's see how a Sun would behave on a Flat Earth assuming the Sun is 23 miles wide and 3000 miles over the Earth.  If you believe something different then plug in your numbers instead.

For g = 23, r = 3000 - you get 0.4393° but the actual size we observer is closer to 0.53°

But now let's say that Sun is 6000 miles away.

Where g = 23, r = 6000 - you get 0.2196° which is exactly half of our previous result.  If you double the distance, you cut the angular diameter in half.

This is very very very basic observational science - and yet - this isn't anything like what Flat Earthers even claim to observe (they don't even get consistent results with each other) and I think I've shown that their methods are also extremely flawed.

So, please go gather extremely high-quality data and then do the math and see if Flat Earth Math adds up or not.  I don't see the solar diameter changing size through the day.

Meme Version: