FET versus basic trigonometry

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Zogg

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FET versus basic trigonometry
« on: October 15, 2011, 04:10:52 PM »
If you assume FET is true and apply basic (10th grade) trigonometry to the distance and elevation of the sun, you come to results that seem to contradict everyday's observation. My computations start from the following assumptions:

1) Earth is flat
2) The equator has a radius of about 6000 miles
3) The sun rotates at a height of 3,000 miles above sea level.
4) At equinox, the sun cycles over the equator, and the illuminated area touches the pole. (Its radius is hence about 6000 miles)
5) The sun is a sphere (sorry, McIntyre) with a radius of 16 miles

So, let's consider an observer at dusk  - the moment when he is at the border of the illuminated zone. (We RE'er call this "sunset", but I'm not sure whether the sun is supposed to set in FET.) The observer is thus 6000 miles away from the center of the illuminated disk, and the sun is 3000 miles above this center. Let's draw a picture :


1st Question: What is the (angular) elevation of the sun above the horizon ?
A simple trigonometric calculation (red triangle) tells us that the sun is actually 26° above the horizon - that's more than a quarter of all the way up to zenith ! This does not really correspond to what I'm seeing each evening.

2nd Question: What's the sun's angular size at this moment ?
Pythagoras tells us that the distance to the sun is about 6700 miles. When we apply a computation similar to the one above to the green triangle, we get a half-angle of 0.137°, hence an angular size of 0.274°. To compare, the thumb on a stretched arm has roughly an angular size of 2°, as everybody can easily compute - that's more than seven times as much ! Again, the result does not correspond to everyday's observation.

Note that the same consideration holds for the moon which is supposed to rotate at the same altitude and is easier to observe without a blackened glass. Besides, it's easy to observe details on the moon's surface, so the size of the moon cannot be explained away with a "glow effect".

(Note also that a similar consideration holds if the sun is a disk - only that under this angle it would appear as an ellipse, which does - again- contradict observation.)


Logic dictates that if my assumptions lead to results which clearly contradict observation, the assumptions are false.
 
Now I'm really curious what couter-arguments you FE'er might find.

(Edit: Modified spelling errors ("It's" instead of "Its"; "0,137°" instead of "0.137°", centred image.)
« Last Edit: October 15, 2011, 09:44:54 PM by Zogg »

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Tom Bishop

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Re: FET versus basic trigonometry
« Reply #1 on: October 15, 2011, 04:34:01 PM »
If you had read Earth Not a Globe you would see where Samuel Birley Rowbotham demonstrates that the traditional rules of perspective are false.

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Tom Bishop

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Re: FET versus basic trigonometry
« Reply #3 on: October 15, 2011, 04:38:00 PM »
Why shouldn't they apply?
“The Earth looks flat, therefore it is” FEers wisdom.

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Thork

Re: FET versus basic trigonometry
« Reply #4 on: October 15, 2011, 04:39:44 PM »
Nice diagram in the OP. Sadly the sun is on the other side of the disk from me right now and it is bedtime, but I would say you are over simplifying the solution. You haven't accounted for atmospheric refraction for example, but I'm sure Tom will guide you through. I just wanted to say nice diagram. :)

Good night.

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Zogg

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Re: FET versus basic trigonometry
« Reply #5 on: October 15, 2011, 04:42:06 PM »
@Tom Bishop : Rowbotham writes about angles "less than a minute of a degree". Since when is 26° (or 0.274° for that matter) less than a minute of a degree ?

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markjo

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Re: FET versus basic trigonometry
« Reply #6 on: October 15, 2011, 04:42:13 PM »
If you had read Earth Not a Globe you would see where Samuel Birley Rowbotham demonstrates that the traditional rules of perspective are false.

If you had read Earth Not a Globe, you would see where Samuel Birley Rowbotham demonstrates that the sun is less than 700 miles above the flat earth.
Science is what happens when preconception meets verification.
Quote from: Robosteve
Besides, perhaps FET is a conspiracy too.
Quote from: bullhorn
It is just the way it is, you understanding it doesn't concern me.

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Thork

Re: FET versus basic trigonometry
« Reply #7 on: October 15, 2011, 04:43:49 PM »
If you had read Earth Not a Globe you would see where Samuel Birley Rowbotham demonstrates that the traditional rules of perspective are false.

If you had read Earth Not a Globe, you would see where Samuel Birley Rowbotham demonstrates that the sun is less than 700 miles above the flat earth.
Voliva demonstrates with trig that it is 3000 miles
http://blog.modernmechanix.com/2006/05/19/5000-for-proving-the-earth-is-a-globe/?Qwd=./ModernMechanix/10-1931/globe&Qif=globe_3.jpg&Qiv=thumbs&Qis=XL#qdig
You pays ya money, ya takes ya choice.

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markjo

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Re: FET versus basic trigonometry
« Reply #8 on: October 15, 2011, 04:46:34 PM »
If you had read Earth Not a Globe you would see where Samuel Birley Rowbotham demonstrates that the traditional rules of perspective are false.

If you had read Earth Not a Globe, you would see where Samuel Birley Rowbotham demonstrates that the sun is less than 700 miles above the flat earth.
Voliva demonstrates with trig that it is 3000 miles
http://blog.modernmechanix.com/2006/05/19/5000-for-proving-the-earth-is-a-globe/?Qwd=./ModernMechanix/10-1931/globe&Qif=globe_3.jpg&Qiv=thumbs&Qis=XL#qdig
You pays ya money, ya takes ya choice.

So does Rowbotham. http://www.sacred-texts.com/earth/za/za23.htm#page_99
It seems that at least one of them is wrong.  If one of them was wrong about this, then what else might they be wrong about?
Science is what happens when preconception meets verification.
Quote from: Robosteve
Besides, perhaps FET is a conspiracy too.
Quote from: bullhorn
It is just the way it is, you understanding it doesn't concern me.

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Zogg

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Re: FET versus basic trigonometry
« Reply #9 on: October 15, 2011, 04:46:50 PM »
@Thork : Thanks :) As for athmospheric refraction : It bends the light downwards - as a result, the sun would appear even higher.

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Zogg

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Re: FET versus basic trigonometry
« Reply #10 on: October 15, 2011, 05:00:56 PM »
Oh, and I also created a little animation with Unity3D, to simulate how sunset / sunrise would appear with FET - this time with a disk-shaped sun. It confirms my calculations - the sun stays high above the horizon, even after "sunset".

However, it's a 3.3 Mb animated gif, so I don't know whether I should integrate it in my post. Here is the link : http://i1103.photobucket.com/albums/g461/Zoggzogg/SunAnimBig.gif

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PizzaPlanet

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Re: FET versus basic trigonometry
« Reply #11 on: October 15, 2011, 05:45:49 PM »
I'm pretty sure the sun wouldn't be visible when its light doesn't reach the observer.
hacking your precious forum as we speak 8) 8) 8)

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momentia

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Re: FET versus basic trigonometry
« Reply #12 on: October 15, 2011, 06:35:37 PM »
I'm pretty sure the sun wouldn't be visible when its light doesn't reach the observer.
Why does FE model predict this?
Please explain how the sun's angle goes to zero before someone observing a sunset is in the dark zone.
Use math as an major part of your explanation. I cannot stress enough how valuable this would be to your argument.

Thork: Even at very low angles, refraction will only result in changes of about half a degree, which is insufficient.
http://en.wikipedia.org/wiki/Atmospheric_refraction#Values
The values would be about the same on a flat earth or a round earth, and as Zogg said, would make the sun appear higher, since light going through the atmosphere gets bent slightly down, as the atmosphere is denser than space.

Zogg: great animation/diagram

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The Knowledge

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Re: FET versus basic trigonometry
« Reply #13 on: October 15, 2011, 07:06:50 PM »
If you had read Earth Not a Globe you would see where Samuel Birley Rowbotham demonstrates that the traditional rules of perspective are false.

If you had read Earth Not a Globe, you would see where Samuel Birley Rowbotham demonstrates that the sun is less than 700 miles above the flat earth.
Voliva demonstrates with trig that it is 3000 miles
http://blog.modernmechanix.com/2006/05/19/5000-for-proving-the-earth-is-a-globe/?Qwd=./ModernMechanix/10-1931/globe&Qif=globe_3.jpg&Qiv=thumbs&Qis=XL#qdig
You pays ya money, ya takes ya choice.

So does Rowbotham. http://www.sacred-texts.com/earth/za/za23.htm#page_99
It seems that at least one of them is wrong.  If one of them was wrong about this, then what else might they be wrong about?

Seeing as Rowbotham's own perspective theory disagrees with his results from his beloved Bedford Level Experiment, probably everything.
Watermelon, Rhubarb Rhubarb, no one believes the Earth is Flat, Peas and Carrots,  walla.

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Nolhekh

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Re: FET versus basic trigonometry
« Reply #14 on: October 15, 2011, 08:53:07 PM »
I'm pretty sure the sun wouldn't be visible when its light doesn't reach the observer.
Irrelevent.  We're discussing sunset, not after sunset.  The point is that the sun itself never goes below 26 degrees in this model, while visible.

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Nolhekh

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Re: FET versus basic trigonometry
« Reply #15 on: October 15, 2011, 08:54:28 PM »
Nice diagram in the OP. Sadly the sun is on the other side of the disk from me right now and it is bedtime, but I would say you are over simplifying the solution. You haven't accounted for atmospheric refraction for example, but I'm sure Tom will guide you through. I just wanted to say nice diagram. :)

Good night.

Atmospheric refraction invalidates the Bedford levels, as it is already one of RET's possible explanations for the observations.

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Nolhekh

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Re: FET versus basic trigonometry
« Reply #16 on: October 15, 2011, 09:01:12 PM »
If you had read Earth Not a Globe you would see where Samuel Birley Rowbotham demonstrates that the traditional rules of perspective are false.

Invoke all the rules you like, it does not change the fact that this model was just mathematically disproven.

The existence of atmospheric refraction invalidates the bedford levels, leaving Rowbotham with no grounds to rewrite the traditional rules of perspective.  One observation made by a couple of people does not disprove mathematics, or the science conducted by thousands.
« Last Edit: October 16, 2011, 07:43:20 AM by Nolhekh »

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Zogg

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Re: FET versus basic trigonometry
« Reply #17 on: October 15, 2011, 09:15:11 PM »
According you your own theory and your own numbers, "sunset" consists in the sun vanishing about 26° above the horizon.
That makes me wonder : Has anyone of your FE'ers ever seen a sunset ?

« Last Edit: October 15, 2011, 09:29:46 PM by Zogg »

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Moon squirter

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Re: FET versus basic trigonometry
« Reply #18 on: October 16, 2011, 12:00:05 AM »
http://theflatearthsociety.net/wiki/index.php/Sinking_Ship_Effect

Tom, you say that:

man cannot perceive infinity due to human limitations, the perspective lines are modified and placed a finite distance away from the observer...

...but then go on to show Rowbotham's pictures of ships, which are not at "infinity" distance. This is incoherent.
I haven't performed it and I've never claimed to. I've have trouble being in two places at the same time.

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Moon squirter

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Re: FET versus basic trigonometry
« Reply #19 on: October 16, 2011, 12:03:04 AM »
If you had read Earth Not a Globe you would see where Samuel Birley Rowbotham demonstrates that the traditional rules of perspective are false.

Can you please provide a 2D side-on diagram of the observer and sun at sunset, showing what it happening to the light rays from the sun.
I haven't performed it and I've never claimed to. I've have trouble being in two places at the same time.