The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: techfreak125 on December 20, 2018, 04:45:40 AM
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If the Earth is flat, why is the shadow length I measured at a latitude of 40 degrees 23 arcminutes at 1:40 PM on 12/8/2018 53 inches instead of the 33 inches that the flat earth model predicts? I used a piece of plywood 22 11/16 inches long. By measuring the length of a shadow cast by a stick, we can take the arctangent of the length of the stick divided by the length of the shadow to determine the sun's angular elevation above the horizon. This formula can also be used to determine the predicted shadow length for each model by dividing the length of the stick by the tangent of the model's predicted angular elevation. By dividing the height of the sun by the horizontal distance to it, the arctangent of the result can be used to determine the flat earth model's predicted angular elevation of the sun. I have taken the value for the sun's height from the wiki (3000 mi/4800 km). The sun's angular altitude on a round earth can be found by finding the arcsine of the addition of the product of the sine of the observer's latitude and the sine of the sun's declination to the product of the cosine of the observer's latitude, the cosine of the declination of the sun, and the cosine of the hour angle. I have factored in the declination of the sun and the obliquity of the ecliptic to ensure the most accurate predictions for both models. The flat earth model predicts an angle of 37.578 degrees. The round earth model predicts an angle of 23.210 degrees. Why does the flat earth model have an error of 32.1% from reality? How does the flat earth model explain the deviation of the sun's angular elevation from its predictions? θsr is the round earth prediction and θsf is the flat earth prediction in the following desmos link. https://www.desmos.com/calculator/sepoxbrqfz
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Is anybody going to answer me? Does anybody even have an answer?
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First, RET is not "reality". The sun isn't consistent with RET. That is imagination. To explain observation, RET incorporates massive refraction that allows the sun to stay up longer than it should, when it should be below the horizon.
(https://kosherjava.com/wp-content/uploads/refractionSunset.png)
Per a Flat Earth the two sun models are via Perspective and the Electromagnetic Accelerator Theory.
Per perspective, in order to use Euclid's model, you would need to show that the perspective lines recede and approach each other for infinity without touching. Perspective empiricists hold that the roots of perspective theory should be based on what is observed and experienced, not an ancient hypothetical model of a perfect universe.
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Pay no attention to that little man behind the curtain!
You were doing things the correct way. Any kind of actual measurements involving the sun or even better the star Polaris is a flat earth buster. The Zetetic way is to do an experiment yourself and do some calculations. Those calculations will allow you to arrive at a reasonable conclusion. As long as that conclusion is that the earth is flat all is well on this site. If the reasonable conclusion is that the earth is round then you will have opened up a nasty can of worms if you mention that on here.
Keep doing what you have been doing. Math doesn't lie, people do. The flat earth theory just can't explain the real world results you get, and you can never demonstrate to their satisfaction what the actual facts mean.
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you can never demonstrate to their satisfaction what the actual facts mean.
I believe that I fixed that for you. You guys have rarely demonstrated your claims.
The OP appears to be claiming that Euclid's perfect universe taught in school is unimpeachable and that the perspective lines would recede and approach each other for all infinity. To the OP, I would encourage demonstration of this hypothesis before incorporating it into a work involving perspective analysis.
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First, RET is not "reality".
I never said either model was 'reality'. I simply said that the angles predicted by the flat earth model do not mesh with observation.
Per a Flat Earth the two sun models are via Perspective and the Electromagnetic Accelerator Theory.
Let's imagine that we put an observer in a long corridor that is tangent with the flat earth. Let's fix light bulbs to the ceiling every 100 meters. According to the FE's definition of perspective, a horizon would form close to the observer and the light bulbs farther than the horizon would begin to sink below the horizon. Now let's hang our observer by their feet to the ceiling and turn the camera 180 degrees. Where does the horizon form? On the floor? On the ceiling? Now let's strap our observer to the wall. Where does the horizon form now? Now let's position our observer between two infinitely tall buildings. Which building gets a horizon? If the law of perspective explains horizons and the law perspective works in all directions, why do horizons only form on the ground?
If perspective accounts for the setting of the sun, how does the flat earth model explain the above thought experiment?
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Of course no demonstrations are possible when you don't know beforehand what the demonstration requires. Please set a detailed standard for what you define as a 'demonstration'.
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First, RET is not "reality". The sun isn't consistent with RET. That is imagination. To explain observation, RET incorporates massive refraction that allows the sun to stay up longer than it should, when it should be below the horizon.
(https://kosherjava.com/wp-content/uploads/refractionSunset.png)
Tom, that "massive refraction" comes to all of about 1/2 degree (one sun diameter).
Per a Flat Earth, you would need to look into perspective and the Electromagnetic Accelerator Theory.
Pray tell, what combination of perspective and/or EAT would explain both the vertical and horizontal bending of light to make the circular movement of the FE sun match the observed movements of the sun?
You do realize that the vertical position of the FE sun is not the only component of the sun's movement that doesn't match observations, don't you?
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Tom, that "massive refraction" comes to all of about 1/2 degree (one sun diameter).
You are incorrect. Refraction is used to explain anything that is not otherwise explained, and patches up any and all holes in the Round Earth model. Moon and sun in the sky at the same time during a Lunar Eclipse? Refraction!
https://www.youtube.com/watch?v=jIyw6xuEJxk
Take a look at this Selenelion, for example. The moon is in front of the camera, the sun is rising behind the camera, and the earth is below. Firstly, during a lunar eclipse the moon should be well below the horizon line when the sun is rising up from the horizon. This is an impossibility in the Round Earth model.
Secondly, in the video the shadow of the earth is obscuring the moon from the top down rather than the bottom up, contrary to what would be expected when the earth is passing between the moon and sun. The sun's light should be peeking over the earth's horizon and hitting the moon from the top down.
That moon is apparently below the horizon "via refraction". As is the sun. The shadow is on the wrong side.
(https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcT4hsXogampeWACjzvV9Ea7Sk32vTSI7QzK1OlG0RE4E9Vr3RqI)
The dark part should be on the bottom, going up.
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If you go out and get yourself a nice sextant you will find a section in the setup where you crank in the effects of atmospheric bending. Celestial navigators have known about this for a 100 years. That bending really isn't too much. Usually one half degree was about the most that I would ever use. The only time it was necessary is when the observed body was very near the horizon.
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More wacky Round Earth refraction:
http://privat.bahnhof.se/wb042294Texter/Thurayya/prayertimes/prayertimes-references/quoted/young_sunset-science.pdf
Indeed, much larger variations than these have been observed
occasionally, particularly at high latitudes, beginning
with the famous observations of the Dutch explorers led by
Willem Barents, in 1597. They observed the first sunrise in
spring 2 weeks earlier than expected
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Tom, that "massive refraction" comes to all of about 1/2 degree (one sun diameter).
You are incorrect. Refraction is used to explain anything that is not otherwise explained, and patches up any and all holes in the Round Earth model. Moon and sun in the sky at the same time during a Lunar Eclipse? Refraction!
https://www.youtube.com/watch?v=jIyw6xuEJxk
Take a look at this Selenelion, for example. The moon is in front of the camera, the sun is rising behind the camera, and the earth is below.
I'm sorry, but I didn't see the sun above the horizon in that video. This is a much better example:
https://www.youtube.com/watch?v=QUkjb4bbjpc
Firstly, during a lunar eclipse the moon should be well below the horizon line when the sun is rising up from the horizon.
Why do you say that? The sun and moon are 180 degrees apart, so that means that if you ignore refraction, the moon should be setting below the horizon at the same moment that the sun is rising above the horizon. One half degree of refraction means that both the sun and moon can be above the horizon for a few minutes.
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You better read the reference you linked to yourself. Refraction is due to the atmosphere and not the shape of the earth. You would also have measurable atmospheric refraction on a flat earth as well. The equations would have to be modified to do the calculations because they were designed assuming that the earth was a sphere.
Actually, the observed effects illustrate that the earth is a sphere because you wouldn't have the same measured observables on a flat earth. Great catch, Tom. You just scored one for the round earth! Keep it up and you will catch up with Rowbotham.
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Tom, that "massive refraction" comes to all of about 1/2 degree (one sun diameter).
You are incorrect. Refraction is used to explain anything that is not otherwise explained, and patches up any and all holes in the Round Earth model. Moon and sun in the sky at the same time during a Lunar Eclipse? Refraction!
https://www.youtube.com/watch?v=jIyw6xuEJxk (https://www.youtube.com/watch?v=jIyw6xuEJxk)
Take a look at this Selenelion, for example. The moon is in front of the camera, the sun is rising behind the camera, and the earth is below.
I'm sorry, but I didn't see the sun above the horizon in that video. This is a much better example:
https://www.youtube.com/watch?v=QUkjb4bbjpc (https://www.youtube.com/watch?v=QUkjb4bbjpc)
Firstly, during a lunar eclipse the moon should be well below the horizon line when the sun is rising up from the horizon.
Why do you say that? The sun and moon are 180 degrees apart, so that means that if you ignore refraction, the moon should be setting below the horizon at the same moment that the sun is rising above the horizon. One half degree of refraction means that both the sun and moon can be above the horizon for a few minutes.
Refraction is occuring long before any of that under your model. In the video I posted the shadow of the earth is on the wrong side.
How does this work under your model?
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This whole argument with about the same diagrams were posted on July 06, 2014. Apparently the lesson of the eclipse of the moon wasn't learned then so what's the point in repeating it today? The flat earth people could do themselves a huge favor and look at some basic astronomy books and they would soon discover the answer to many of their questions. If you look at a book and then don't observe the same things with your own eyes then it would be reasonable to ask a few questions, but only after doing a little basic research on the internet yourself. Of course the mantra that I've observed here seems to be You can't be taught something that you don't want to learn. I'm sure that's intentional as it just generates more posts. I have to admit, I help in the 'more posts' department. I'm Bad!
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More wacky Round Earth refraction:
http://privat.bahnhof.se/wb042294Texter/Thurayya/prayertimes/prayertimes-references/quoted/young_sunset-science.pdf
Indeed, much larger variations than these have been observed
occasionally, particularly at high latitudes, beginning
with the famous observations of the Dutch explorers led by
Willem Barents, in 1597. They observed the first sunrise in
spring 2 weeks earlier than expected
Hold on there for a second. How is refraction wacky in round earth theory, but perfectly fine in flat earth theory. This from Rowbotham:
"If any allowance is to be made for refraction–which, no doubt, exists where the sun’s rays have to pass through a medium, the atmosphere, which gradually in- creases in density as it approaches the earth’s surface–it will considerably diminish the above-named distance of the sun; so that it is perfectly safe to affirm that the under edge of the sun is considerably less than 700 statute miles above the earth."
And also, the whole explanation as to why the FE sun doesn't get smaller as it moves away from the observer depends upon some atmospheric density:
"Magnification and Shrinking
Q: If the sun is disappearing to perspective, shouldn't it get smaller as it recedes?
A: The sun remains the same size as it recedes into the distance due to a known magnification effect caused by the intense rays of light passing through the strata of the atmolayer. "
Wacky indeed.
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If the Earth is flat, why is the shadow length I measured at a latitude of 40 degrees 23 arcminutes at 1:40 PM on 12/8/2018 53 inches instead of the 33 inches that the flat earth model predicts? I used a piece of plywood 22 11/16 inches long. By measuring the length of a shadow cast by a stick, we can take the arctangent of the length of the stick divided by the length of the shadow to determine the sun's angular elevation above the horizon. This formula can also be used to determine the predicted shadow length for each model by dividing the length of the stick by the tangent of the model's predicted angular elevation. By dividing the height of the sun by the horizontal distance to it, the arctangent of the result can be used to determine the flat earth model's predicted angular elevation of the sun. I have taken the value for the sun's height from the wiki (3000 mi/4800 km). The sun's angular altitude on a round earth can be found by finding the arcsine of the addition of the product of the sine of the observer's latitude and the sine of the sun's declination to the product of the cosine of the observer's latitude, the cosine of the declination of the sun, and the cosine of the hour angle. I have factored in the declination of the sun and the obliquity of the ecliptic to ensure the most accurate predictions for both models. The flat earth model predicts an angle of 37.578 degrees. The round earth model predicts an angle of 23.210 degrees. Why does the flat earth model have an error of 32.1% from reality? How does the flat earth model explain the deviation of the sun's angular elevation from its predictions? θsr is the round earth prediction and θsf is the flat earth prediction in the following desmos link. https://www.desmos.com/calculator/sz1ugthjk4
Here's actual output from a 2016 Equinox experiment demonstrating why a globe sun model is highly accurate and the flat earth sun is wildly inaccurate according to human observation and perhaps one could say, reality:
https://www.youtube.com/watch?v=822oDc3_9AQ
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Hm. That moon video said it was "impossible". But the video seems to show that it happened - which, to my mind, indicates that it's "possible".
I think that's what they call a "misnomer".
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Such a lunar eclipse could be viewed from any location near the equator. And if any FE believers want to know how I would be more than happy to provide a detailed description. How much of their time do FE believers actually spend watching the sky from various parts of the world?
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More wacky Round Earth refraction:
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Exactly what is 'wacky; about this article Tom please? I will admit at this point I haven't read all of the article at this stage.
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Tom, that "massive refraction" comes to all of about 1/2 degree (one sun diameter).
You are incorrect. Refraction is used to explain anything that is not otherwise explained, and patches up any and all holes in the Round Earth model. Moon and sun in the sky at the same time during a Lunar Eclipse? Refraction!
https://www.youtube.com/watch?v=jIyw6xuEJxk (https://www.youtube.com/watch?v=jIyw6xuEJxk)
Take a look at this Selenelion, for example. The moon is in front of the camera, the sun is rising behind the camera, and the earth is below.
I'm sorry, but I didn't see the sun above the horizon in that video. This is a much better example:
https://www.youtube.com/watch?v=QUkjb4bbjpc (https://www.youtube.com/watch?v=QUkjb4bbjpc)
Firstly, during a lunar eclipse the moon should be well below the horizon line when the sun is rising up from the horizon.
Why do you say that? The sun and moon are 180 degrees apart, so that means that if you ignore refraction, the moon should be setting below the horizon at the same moment that the sun is rising above the horizon. One half degree of refraction means that both the sun and moon can be above the horizon for a few minutes.
Refraction is occuring long before any of that under your model.
Please elaborate. Why is that a problem? Are you sure that you aren't thinking about scattering during the pre-dawn twilight period? The atmosphere is responsible for a host of different optical effects during the course of the day. Refraction is just one of them.
https://www.atoptics.co.uk
In the video I posted the shadow of the earth is on the wrong side.
That would probably depend on whether the observer is in the northern or southern hemisphere. An observer on the other side of the equator would probably see the shadow on the "right" side.
How does this work under your model?
Since this forum is about Flat Earth Theory, the better and more on topic question would be: how does it work under your model?
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If the Earth is flat, why is the shadow length I measured at a latitude of 40 degrees 23 arcminutes at 1:40 PM on 12/8/2018 53 inches instead of the 33 inches that the flat earth model predicts? I used a piece of plywood 22 11/16 inches long. By measuring the length of a shadow cast by a stick, we can take the arctangent of the length of the stick divided by the length of the shadow to determine the sun's angular elevation above the horizon. This formula can also be used to determine the predicted shadow length for each model by dividing the length of the stick by the tangent of the model's predicted angular elevation. By dividing the height of the sun by the horizontal distance to it, the arctangent of the result can be used to determine the flat earth model's predicted angular elevation of the sun. I have taken the value for the sun's height from the wiki (3000 mi/4800 km). The sun's angular altitude on a round earth can be found by finding the arcsine of the addition of the product of the sine of the observer's latitude and the sine of the sun's declination to the product of the cosine of the observer's latitude, the cosine of the declination of the sun, and the cosine of the hour angle. I have factored in the declination of the sun and the obliquity of the ecliptic to ensure the most accurate predictions for both models. The flat earth model predicts an angle of 37.578 degrees. The round earth model predicts an angle of 23.210 degrees. Why does the flat earth model have an error of 32.1% from reality? How does the flat earth model explain the deviation of the sun's angular elevation from its predictions? θsr is the round earth prediction and θsf is the flat earth prediction in the following desmos link. https://www.desmos.com/calculator/sz1ugthjk4
Here's actual output from a 2016 Equinox experiment demonstrating why a globe sun model is highly accurate and the flat earth sun is wildly inaccurate according to human observation and perhaps one could say, reality:
https://www.youtube.com/watch?v=822oDc3_9AQ
I am arguing for the round earth, not the flat earth.
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First, RET is not "reality". The sun isn't consistent with RET. That is imagination. To explain observation, RET incorporates massive refraction that allows the sun to stay up longer than it should, when it should be below the horizon.
Where is your evidence for the refraction being 'massive'. Please demonstrate your claim. First, state the threshold for 'massive' in quantitative terms. How many degrees, e.g. ? Then provide evidence that the observed refraction exceeds that threshold.
True science proceeds on observation and precise measurement, not on wild claims.
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you can never demonstrate to their satisfaction what the actual facts mean.
I believe that I fixed that for you. You guys have rarely demonstrated your claims.
Please provide evidence or demonstration for your claim that RET rarely demonstrates its claims.
The OP appears to be claiming that Euclid's perfect universe taught in school are unimpeachable and that the perspective lines would recede and approach each other for all infinity. To the OP, I would encourage demonstration of this hypothesis before incorporating it into a work involving perspective analysis.
Another wild claim. Where exactly does Euclid say that "perspective lines would recede and approach each other for all infinity". Please demonstrate this claim with a citation, i.e. book title and section number. Thanks.
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There is absolutely nothing odd about the December 10, 2011 eclipse for a round Earth.
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you can never demonstrate to their satisfaction what the actual facts mean.
I believe that I fixed that for you. You guys have rarely demonstrated your claims.
Please provide evidence or demonstration for your claim that RET rarely demonstrates its claims.
Round earth claims are demonstrated daily. When I was working each and every day I could observe the position of the ship while on a long trip across one of the oceans of the earth. Multiple times of the day I would check the equipment to make sure everything was in agreement and was accurate. Math is completely agnostic. It doesn't care about anything or anyone. It's function is to DEMONSTRATE the relationship between numbers. Those numbers can be anything. In the case of a ship the numbers represented spherical position coordinates. Everything is based upon a spherical earth. If the earth isn't a sphere then the relationships would be meaningless because there would be no correlation between the calculations and our assumed position on the high seas. If that breaks down then we are lost. The fact that we always arrived on time (give or take the weather) DEMONSTRATED that the world is a sphere. For emergency purposes we also were required to carry two sextants. Usually we would have a maritime academy cadets aboard learning the 'ropes'. They were required to DEMONSTRATE proper navigation techniques. The sextant was used to observe a heavenly body, celestial tables were consulted, spherical trigonometry was employed and an estimated position was determined the old fashioned Zetetic way. If the cadet could DEMONSTRATE all this then he could be 'signed off' and another required skill practiced.
The bottom line is that MATH was doing the DEMONSTRATION not any human. If you want to say that the earth isn't a sphere then you have to impeach the math.
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Tom, that "massive refraction" comes to all of about 1/2 degree (one sun diameter).
You are incorrect. Refraction is used to explain anything that is not otherwise explained, and patches up any and all holes in the Round Earth model. Moon and sun in the sky at the same time during a Lunar Eclipse? Refraction!
https://www.youtube.com/watch?v=jIyw6xuEJxk
Take a look at this Selenelion, for example. The moon is in front of the camera, the sun is rising behind the camera, and the earth is below. Firstly, during a lunar eclipse the moon should be well below the horizon line when the sun is rising up from the horizon. This is an impossibility in the Round Earth model.
Secondly, in the video the shadow of the earth is obscuring the moon from the top down rather than the bottom up, contrary to what would be expected when the earth is passing between the moon and sun. The sun's light should be peeking over the earth's horizon and hitting the moon from the top down.
That moon is apparently below the horizon "via refraction". As is the sun. The shadow is on the wrong side.
(https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcT4hsXogampeWACjzvV9Ea7Sk32vTSI7QzK1OlG0RE4E9Vr3RqI)
The dark part should be on the bottom, going up.
Tom, Your diagram is completely wrong as well. Realize you are looking at objects far from the Earth in 3D space. Trying to just draw a line to the source of light without recognizing the distances involved and considering which hemisphere you are in will be confusing I am sure. As far as some of the videos with a full moon and Sun in the sky at the same time; the moon looks quite full for a couple days. Combining that with a little refraction and the near full moon and sun can be in the sky easily.
Step 1 is acknowledging the Moon and Sun are far from the Earth. Explain the worldwide same phases of the moon please on a near sun/moon model.
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It says that the video was taken in New Mexico. And, that point is based on fallacy. Shadow orientations would not be changed as to make something physically impossible.
Draw a diagram. Show how this is possible.
(https://i.imgur.com/0qYkb4e.png)
Where is the sun? Is the sun at A, B or C? If there is an explanation, show us how it works. If this diagram is flawed in any manner, show the correct one. It is difficult to see how any nitpicking about scale makes this possible.
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It says that the video was taken in New Mexico. And, that point is based on fallacy. Shadow orientations would not be changed as to make something physically impossible.
Draw a diagram. Show how this is possible.
(https://i.imgur.com/0qYkb4e.png)
Where is the sun? Is the sun at A, B or C? If there is an explanation, show us how it works. If this diagram is flawed in any manner, show the correct one. It is difficult to see how any nitpicking about scale makes this possible.
Dont you think before you tackle anything as confusing as a selenelion you should explain simple daily phases of the moon in a near moon/sun system as seen worldwide?
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The sun is below B and just a bit of light is being refracted around the surface like happens each and every day at sunset. It's well known that the sun physically goes below the horizon before you can see it. Sailors have known this for a long time. The fact that the bottom of the moon is being lit by a bit of refracted light is completely expected. You can also expect that the top of the moon would be in the earth's shadow. Thank you for again for your demonstration of the global earth. Soon you will catch up with Rowbotham!
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If the Earth is flat, why is the shadow length I measured at a latitude of 40 degrees 23 arcminutes at 1:40 PM on 12/8/2018 53 inches instead of the 33 inches that the flat earth model predicts? I used a piece of plywood 22 11/16 inches long. By measuring the length of a shadow cast by a stick, we can take the arctangent of the length of the stick divided by the length of the shadow to determine the sun's angular elevation above the horizon. This formula can also be used to determine the predicted shadow length for each model by dividing the length of the stick by the tangent of the model's predicted angular elevation. By dividing the height of the sun by the horizontal distance to it, the arctangent of the result can be used to determine the flat earth model's predicted angular elevation of the sun. I have taken the value for the sun's height from the wiki (3000 mi/4800 km). The sun's angular altitude on a round earth can be found by finding the arcsine of the addition of the product of the sine of the observer's latitude and the sine of the sun's declination to the product of the cosine of the observer's latitude, the cosine of the declination of the sun, and the cosine of the hour angle. I have factored in the declination of the sun and the obliquity of the ecliptic to ensure the most accurate predictions for both models. The flat earth model predicts an angle of 37.578 degrees. The round earth model predicts an angle of 23.210 degrees. Why does the flat earth model have an error of 32.1% from reality? How does the flat earth model explain the deviation of the sun's angular elevation from its predictions? θsr is the round earth prediction and θsf is the flat earth prediction in the following desmos link. https://www.desmos.com/calculator/sz1ugthjk4
Here's actual output from a 2016 Equinox experiment demonstrating why a globe sun model is highly accurate and the flat earth sun is wildly inaccurate according to human observation and perhaps one could say, reality:
https://www.youtube.com/watch?v=822oDc3_9AQ (https://www.youtube.com/watch?v=822oDc3_9AQ)
It has been admitted by science that the Equinox claims are false. https://wiki.tfes.org/The_Equinox
The observations require magic wands of refraction, just as with everything else wrong with that model.
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QUOTE:
The observations require magic wands of refraction, just as with everything else wrong with that model.
Refraction is independent of any earth model. It's just another property of a fluid. That property fully applies to the flat earth model as well. You better start waving that magic wand over the flat earth model, it's sinking fast! Rowbotham would be discouraged.
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If the Earth is flat, why is the shadow length I measured at a latitude of 40 degrees 23 arcminutes at 1:40 PM on 12/8/2018 53 inches instead of the 33 inches that the flat earth model predicts? I used a piece of plywood 22 11/16 inches long. By measuring the length of a shadow cast by a stick, we can take the arctangent of the length of the stick divided by the length of the shadow to determine the sun's angular elevation above the horizon. This formula can also be used to determine the predicted shadow length for each model by dividing the length of the stick by the tangent of the model's predicted angular elevation. By dividing the height of the sun by the horizontal distance to it, the arctangent of the result can be used to determine the flat earth model's predicted angular elevation of the sun. I have taken the value for the sun's height from the wiki (3000 mi/4800 km). The sun's angular altitude on a round earth can be found by finding the arcsine of the addition of the product of the sine of the observer's latitude and the sine of the sun's declination to the product of the cosine of the observer's latitude, the cosine of the declination of the sun, and the cosine of the hour angle. I have factored in the declination of the sun and the obliquity of the ecliptic to ensure the most accurate predictions for both models. The flat earth model predicts an angle of 37.578 degrees. The round earth model predicts an angle of 23.210 degrees. Why does the flat earth model have an error of 32.1% from reality? How does the flat earth model explain the deviation of the sun's angular elevation from its predictions? θsr is the round earth prediction and θsf is the flat earth prediction in the following desmos link. https://www.desmos.com/calculator/sz1ugthjk4
Here's actual output from a 2016 Equinox experiment demonstrating why a globe sun model is highly accurate and the flat earth sun is wildly inaccurate according to human observation and perhaps one could say, reality:
https://www.youtube.com/watch?v=822oDc3_9AQ (https://www.youtube.com/watch?v=822oDc3_9AQ)
It has been admitted by science that the Equinox claims are false. https://wiki.tfes.org/The_Equinox
The observations require magic wands of refraction, just as with everything else wrong with that model.
And FE requires the 'magic wand' of perspective and the supposition that geometry magically stops working at long distances, to even get the sun to set at all.
Refraction is quantized in many places. The paper you source in that wiki article in fact uses a known refractive index based upon the wavelength of sunlight and the average atmosphere of Earth to come to the conclusion you tout on the page (it also must utilize some form of planetary model, but we'll set that aside for now.)
Can FE explain why a sun which circles the pole(s) can even appear to rise within 2 degrees of directly East?
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That moon is apparently below the horizon "via refraction". As is the sun. The shadow is on the wrong side.
(https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcT4hsXogampeWACjzvV9Ea7Sk32vTSI7QzK1OlG0RE4E9Vr3RqI)
The dark part should be on the bottom, going up.
Not correct, but then this has been rehashed before before to no apparent effect (https://forum.tfes.org/index.php?topic=1676.0).
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One of these days a FE proponent will address the obvious elephant in the room which is the same phase of the moon seen worldwide daily and a near moon chasing a near sun are impossible. This is easy stuff... if any FE model with near sun/moon cannot explain this they are dead in the water.