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Flat Earth Community / Some maths regarding sun displacement in the sky
« on: August 31, 2016, 02:33:28 PM »
As it has been already mentioned in many topics, there are many inconsistencies with the Sun and the Flat Earth theory, except if accepting some unicorn magical poop responsible for huge angular deviation.
For examples, during the fall/spring equinoxes:
- if you stand on the equator, you will see the sunrise due East and the sunset due West. According to the flat Earth theory, you should see the sunset due North-East and the sunrise due North-West. For what I have read, there are yet no explanations for this 45° (!) angular deviation compared to observation in the flat earth theory.
- if you stand on the equator, at the sunrise, the sun is at the horizon level (meaning height elevation of 0°). Basic trigonometry (provided on request) shows that in the FE theory, the sun has instead an elevation height of about 28°. Here FE explains that some huge light refraction (a.k.a unicorn magical poop) is responsible for this optical illusion.
I would like to provide some maths I've made regarding height elevation and the angular speed of the sun in the sky according to FE compared with RE.
My hypotheses are the followings:
1) (RE or FE) Equator is a circle with a radius of 3958 miles
2) (FE) As the sun height elevation during sunrise is obviously 0°, and 90° at noon, and 0° at sunset (during fall/spring equinoxes, on the equator), there should be some refraction law in FE making this optical illusion possible.
I presumed a linear refraction law with the absolute elevation height of the sun, i.e. when the sun if actually at a height of 28°, it appears to be at 0° and when it is actually at 90° it appears to be at 90°. (Vertical refraction)
(If some flat earther could indicate me what is the real refraction law, I would be sooooo happy to adapt my calculation to it!)
3) (FE) I presumed also that some unicorn magical poop enable to see the sun due west where it should appears North-West, and due East where it should appears North-East. (Horizontal refraction). This horizontal refraction is obviously linear with the elevation height of the sun otherwise the sun would not appear to make a perfect line in the sky on the equator during fall/spring equinoxes.
4) (RE) I didn’t take into account the refraction with RE, therefore the length of the day during fall/spring equinox during is slightly higher than 12 hours and also has slight impact on the elevation and angular speed of the sun during the first and last hours of the day. But this does not call into question the results presented here after, especially if you compare the results near noon.
Here below are the results of the height elevation of the Sun:
- In black is the actual height elevation of the sun in FE theory
- In red is the corrected height elevation with the linear refraction law to be compliant with sunset and sunrise at 0°
- In green is the sun elevation in RE "theory" (the elevation being only due to the constant earth rotational speed
In my infinite kindness I also provide some other refraction laws I tried with flat earth theory, as I have no idea how all of this works! The idea of the other laws is to be more compliant with RE, i.e. the refraction is only significant when the sun is low on the horizon:
- In violet the observed elevation meets the real one 1 hour after sunrise (symmetrical for sunset)
- In blue, the observed elevation meets the real on 2 hours after sunrise (symmetrical for sunset)
Knowing the elevation height of the sun through the day, one can easily calculate the angular speed of the sun. Keeping the same color scheme, here are the results:
Just by looking at the angular speed of the sun around noon, on round Earth, the angular speed is equal to the angular speed of the Earth, which is 0.25°/min (this is true whatever the sun height). On flat Earth, whatever the correction I use (but again, the "real" refraction law in FE theory would be well appreciated), the angular speed of the sun should be higher (between 0.33 and 0.48 °/min).
By looking on the results at the beginning or the end of the day, the differences are much more important, and absolutely not consistent with observations.
Therefore, the Earth is not flat.
NOTA: For all flat earthers, here is an interesting property of the air (or aether I don’t really understood who is responsible for the refraction during sunset/sunrise), when talking about refraction on flat earth model, don’t forget to mention that it is (hugely) anisotropic! (45° horizontally and 28° vertically at sunrise on the equator during sunset/sunrise!)
For examples, during the fall/spring equinoxes:
- if you stand on the equator, you will see the sunrise due East and the sunset due West. According to the flat Earth theory, you should see the sunset due North-East and the sunrise due North-West. For what I have read, there are yet no explanations for this 45° (!) angular deviation compared to observation in the flat earth theory.
- if you stand on the equator, at the sunrise, the sun is at the horizon level (meaning height elevation of 0°). Basic trigonometry (provided on request) shows that in the FE theory, the sun has instead an elevation height of about 28°. Here FE explains that some huge light refraction (a.k.a unicorn magical poop) is responsible for this optical illusion.
I would like to provide some maths I've made regarding height elevation and the angular speed of the sun in the sky according to FE compared with RE.
My hypotheses are the followings:
1) (RE or FE) Equator is a circle with a radius of 3958 miles
2) (FE) As the sun height elevation during sunrise is obviously 0°, and 90° at noon, and 0° at sunset (during fall/spring equinoxes, on the equator), there should be some refraction law in FE making this optical illusion possible.
I presumed a linear refraction law with the absolute elevation height of the sun, i.e. when the sun if actually at a height of 28°, it appears to be at 0° and when it is actually at 90° it appears to be at 90°. (Vertical refraction)
(If some flat earther could indicate me what is the real refraction law, I would be sooooo happy to adapt my calculation to it!)
3) (FE) I presumed also that some unicorn magical poop enable to see the sun due west where it should appears North-West, and due East where it should appears North-East. (Horizontal refraction). This horizontal refraction is obviously linear with the elevation height of the sun otherwise the sun would not appear to make a perfect line in the sky on the equator during fall/spring equinoxes.
4) (RE) I didn’t take into account the refraction with RE, therefore the length of the day during fall/spring equinox during is slightly higher than 12 hours and also has slight impact on the elevation and angular speed of the sun during the first and last hours of the day. But this does not call into question the results presented here after, especially if you compare the results near noon.
Here below are the results of the height elevation of the Sun:
- In black is the actual height elevation of the sun in FE theory
- In red is the corrected height elevation with the linear refraction law to be compliant with sunset and sunrise at 0°
- In green is the sun elevation in RE "theory" (the elevation being only due to the constant earth rotational speed
In my infinite kindness I also provide some other refraction laws I tried with flat earth theory, as I have no idea how all of this works! The idea of the other laws is to be more compliant with RE, i.e. the refraction is only significant when the sun is low on the horizon:
- In violet the observed elevation meets the real one 1 hour after sunrise (symmetrical for sunset)
- In blue, the observed elevation meets the real on 2 hours after sunrise (symmetrical for sunset)
Knowing the elevation height of the sun through the day, one can easily calculate the angular speed of the sun. Keeping the same color scheme, here are the results:
Just by looking at the angular speed of the sun around noon, on round Earth, the angular speed is equal to the angular speed of the Earth, which is 0.25°/min (this is true whatever the sun height). On flat Earth, whatever the correction I use (but again, the "real" refraction law in FE theory would be well appreciated), the angular speed of the sun should be higher (between 0.33 and 0.48 °/min).
By looking on the results at the beginning or the end of the day, the differences are much more important, and absolutely not consistent with observations.
Therefore, the Earth is not flat.
NOTA: For all flat earthers, here is an interesting property of the air (or aether I don’t really understood who is responsible for the refraction during sunset/sunrise), when talking about refraction on flat earth model, don’t forget to mention that it is (hugely) anisotropic! (45° horizontally and 28° vertically at sunrise on the equator during sunset/sunrise!)