[Sceptom]

Hi,

I'm not sure this question has been asked before, I browsed some pages on this forum and didn't find it.

My question is related to the length of the day on a flat earth. I've seen on the wiki, "How do you explain day/night cycles and seasons?", the sun makes a small circle during Summer in the northern hemiplane, and a large circle during winter in the same hemiplane.

But there are at least two problems with that:

1. the length of a day is not the same during summer or winter. The total distance the sun has to make is different in a small and a large circle. So that means that a day that lasts (in total) 24 hours in the northern summer, lasts longer during the northern winter.
Or maybe you believe that the sun goes faster as the circle gets bigger, so that any time a full day is 24h? This could be an explanation, but then you have to explain why the sun runs at different speeds...

2. But even then, regardless of the speed of the sun, the southern summer does not seem to be as it should be. Take Australia for example: the sun makes a large circle, and when it hovers Australia, the distance covered is quite small compared to the rest of the circle. This implies that the day is much shorter than the night. But we actually observe that in the summer, it's the opposite: the night is shorter than the day.

Obviously, I got something wrong with the animation in the wiki.
How is it explained with the flat earth theory?

Thanks.

[Thork]

Nope, you are right, the sun speed changes. I actually have an excel calculator that works out the speed of the sun on any given day. (I'm a geek and enjoy making such things.) Unfortunately I can't upload a file to a forum post. But you have all the information you need to do it.

Assume the diameter of the earth is 40,008km and the distance from the North pole to the equator is 10,002km and the sun is moving between 23°26′14.4″ S and 23°26′14.4″ North of the equator. The Summer and winter Solstices provide your two limits.
*Note: The Earth rotates once in about 24 hours with respect to the sun and once every 23 hours 56 minutes and 4 seconds with respect to the stars in round earth theory so you need to use the full 24 hours for speed, we want the sun speed. (we explain the difference between the two with celestial gearing, or the prime mover ... first theorised by Aristotle and later elaborated on by Thomas Aquinas in his cosmological arguments, as a "first cause" of existence.)

Below is the diagram of how the sun moves over the earth relative to the seasons


Below Wilbur Voliva shows how the sun orbits directly above the earth 3000 miles up.


Below is the Flammarion woodcut depicting a man lifting the curtain of the sky to see the gears that drive the heavens.

[Sceptom]

Thanks for your answer. I indeed assumed that the Sun would change speed as the circle gets wider. If the circle is 2 times larger during northern winter, then the sun has to run twice as fast.

Is there any explanation for this change of speed?

Unfortunately, your answer does not address the second part of my question, the one for which I really couldn't find an explanation myself.

[Thork]

No, it doesn't run twice as fast. It would have to run 2*pi times as fast if the circle was 2 times larger. Its also not twice as far, but you can play with the maths.

I already explained the change of speed, celestial gears. All of the heavenly bodies ... planets, stars, comets, sun, moon etc are driven by an invisible gearing system first discovered by Aristotle and documented in his book Metaphysics.

The second part of your query is already answered because the sun goes faster when directly over the southern hemisphere.

[Pete Svarrior]

No, it doesn't run twice as fast. It would have to run 2*pi times as fast if the circle was 2 times larger.

That's incorrect, no matter how you interpret "2 times larger".

If we're talking about radii: The circumference of a circle is , where r is the radius. If the radius doubles, so does the circumference.
If we're talking about areas: The area of a circle is . If the area doubles, the radius increases by a factor of , and consequently so does the circumference.

Consequently, depending on interpretation, the sun will either run twice as fast, or times as fast.

You could also more intuitively think of his in terms of angular and linear speeds. The angular speed doesn't change (the sun still makes a full circle in 24 hours), but since the radius changes, the linear speed scales with it linearly. See: http://www.efm.leeds.ac.uk/CIVE/CIVE1140/section01/index.html

[Thork]

Indeed, I assumed a radius of 1 and forgot to include it when replying.

And I guess the op is asking about speed over the earth linearly. Its a fun little challenge to work out based on the day today. :-)

[Sceptom]

yes indeed, if the radius doubles, so does the circumference, which is what I was talking about.
Actually, we can talk about the angular speed of the sun, which should remain constant all year, so that any time of the year, one complete revolution is 24h. [EDIT: pizaaplanet got there before me, but indeed angular speed is more relevant here]

But anyway, the question is not anymore on the first part of the question (how and why the sun speed changes) but on the second part which is still unanswered. It doesn't change anything that the sun goes faster in the southern hemisphere during (southern) summer. The problem is still there.
On the animation in the wiki, the sun gives daylight in a (roughly) 60° arc if you stand right below the sun's path. So anyone in Australia (for instance) will get daylight when the sun covers 60° of a complete revolution. But a complete revolution is 360°. So night should be 5 times longer than the day in Australia during summer... which is not what we observe.

How is it explained?

[Thork]

The animation isn't very good. It makes the spot light too small.

Rowbotham draws a better depiction although probably still a little small.


And yes, you can still get longer nights than some days, but that is what happens in winter.

[inquisitive]

Do all observations of the sun from different places and times fit in with your model and are measured distances correct?

[Thork]

Yes.

As noted in the book Huainanzi,[58] in the 2nd century BC Chinese astronomers effectively inverted Eratosthenes' calculation of the curvature of the Earth to calculate the height of the sun above the earth. By assuming the earth was flat ...

Eratosthenes used sticks in the ground and measured the shadows to work out the size of the earth.

[Sceptom]

The animation isn't very good. It makes the spot light too small.

Rowbotham draws a better depiction although probably still a little small.

In Rowbotham's graph, you still have the same problem. I've attached the picture with modifications. Let's take the green circle: it represents the daylight of the sun during southern summer at a specific spot. While the sun goes along the red arc, the blue spot gets daylight. But again, this red arc represents only a quarter of the sun's full path. So you get daylight for 6h, and the 18h left are night... during summer... which is not what we observe.

In fact, if you wanted a longer day than night (during southern summer), the spot light would be huge. So big, in fact, that the north pole would always be within the spot. Thus there would never be night in the north pole (and other northern part of the world) while it's summer in the southern hemiplane, which is not what we observe.

Plus, the only way to enlarge the spot would be to have the sun at a higher altitude. But then, it would be colder, not warmer during winter... which is not what we observe.

How can you explain that...?

[Sceptom]

I'm a bit disappointed to see much activity on other threads, but no answer so far on this question.

Could it be that it points to a fundamental flaw of FE theory?

[Thork]

Tom answered this in another thread today.

http://forum.tfes.org/index.php?topic=1258.msg56594#msg56594
I assumed you'd have read it and responded. you didn't, I guessed you were happy.

[Tom Bishop]

My mistake. I noticed that I posted it in the wrong thread. I moved it here.

In Rowbotham's graph, you still have the same problem. I've attached the picture with modifications. Let's take the green circle: it represents the daylight of the sun during southern summer at a specific spot. While the sun goes along the red arc, the blue spot gets daylight. But again, this red arc represents only a quarter of the sun's full path. So you get daylight for 6h, and the 18h left are night... during summer... which is not what we observe.

In fact, if you wanted a longer day than night (during southern summer), the spot light would be huge. So big, in fact, that the north pole would always be within the spot. Thus there would never be night in the north pole (and other northern part of the world) while it's summer in the southern hemiplane, which is not what we observe.

Plus, the only way to enlarge the spot would be to have the sun at a higher altitude. But then, it would be colder, not warmer during winter... which is not what we observe.

How can you explain that...?

The expanded explanation is that the spotlight changes shape throughout the year due to refraction and the varrying height of the sun throughout the year.

First, if no atmosphere existed, no doubt the light of the sun would diffuse over the whole earth at once, and alternations of light and darkness could not exist.

Secondly, as the earth is covered with an atmosphere of many miles in depth, the density of which gradually increases downwards to the surface, all the rays of light except those which are vertical, as they enter the upper stratum of air are arrested in their course of diffusion, and by Snell's Law bent downwards towards the earth; as this takes place in all directions round the sun--equally where density and other conditions are equal, and vice versâ--the effect is a non-uniform area of sun-light.

For a striking example of Snell's Law we simply need to put a straw into a glass of water:



As we can see, the light from behind the glass is bent downwards as it passes through the thick medium of the water. While this is an extreme example, it shows that light is malleable, able to bend and conform based on existing conditions. When the light of the sun moves from the vacuum of space into the atmosphere of the earth it is gradually compelled downwards into the surface. The refractive index of air is a bit less than water, and so the effect will me more gradual, taking place over tens of thousands of miles instead of abruptly like the above image.

This considered, lets designate some facts.

Fact: Cold air is denser than warm air, and has therefore a greater refractive index.¹

Fact: The sun is higher over the earth in its Northern Annulus and closer to the earth during its Southern Annulus.²

During Equinox the sun is positioned over the equator, the majority of its warmth spread over the ring of the equator. The sun is at it's middle point between hemispheres. The atmosphere in this area around the equator is at its highest temperature and therefore, since warm air has less of a refractive index than cold air, light can progress further through the atmosphere without bending towards the ground. This results in the spotlight of the sun conforming to the shape of the hottest areas. The end result gives the spotlight of the sun an oval shape taking up roughly one half of the earth:



When the Sun is over the North and at its highest altitude the spotlight is small and circular. This is because the sun is far from the earth and not heating the atmosphere up very much. At this time the entire Southern Hemisphere is in its Winter, and since cold air is denser than warm air, the refractive index is higher and light cannot proceed without being redirected into the earth. Since the earth is colder, the light is restricted to a smaller circle where summer exists in the North.

When the sun is over the South and close to the earth the sun is heating up the Southern Hemisphere, giving the spotlight a wide crescent shape. The shape is a crescent because when the sun is over the South it is winter in the North and the sun's light cannot penetrate the density of the Northern Hemisphere's winter.

The shape of the spotlight defines the time it will take for the sun to set. If the spotlight is small, the sun will appear to pass over the earth quickly. If the spotlight is large, the sun will take appear to take a longer time to pass over the earth. In the above illustration the Sun's spotlight is neither small or large - but at it's median.

¹ Fourth paragraph in the Wikipedia article on Mirages
² See the Sun's Analemma which demonstrates the height of the sun over the course of the year.

[Sentient Pizza]

Tom please show a version that also displays summer sunlight distribution for the southern/outer Hemiplane, and the mathematics that allow you to predict and create these illustrations.

[Thork]

Tom please show a version that also displays summer sunlight distribution for the southern/outer Hemiplane, and the mathematics that allow you to predict and create these illustrations.

How about you produce calculations to disprove it? Do you think you can just turn up here and demand our FErs spend hours humouring your every inane and lazy request because the ones at the other site are now bored of your trolling?

Debate is a two way thing. You'll get out what you put in. If you generate content, you'll receive substantiated replies. Lazy one liners will likely see you ignored.

[Sentient Pizza]

Tom please show a version that also displays summer sunlight distribution for the southern/outer Hemiplane, and the mathematics that allow you to predict and create these illustrations.

How about you produce calculations to disprove it? Do you think you can just turn up here and demand our FErs spend hours humouring your every inane and lazy request because the ones at the other site are now bored of your trolling?

Debate is a two way thing. You'll get out what you put in. If you generate content, you'll receive substantiated replies. Lazy one liners will likely see you ignored.

Wow Thork. I'm not sure what I did to ruffle your feathers. Whatever it is I apologize.

I Have made very few posts in general and don't recall doing any trolling or having members on the other site have any issues with me.

I can produce the mathematics that show predictions for Round earth daylight. I can point you to countless websites, books, studies, and all other manner of things that you will likely not accept. That is not the intent of this thread is it? this thread is called "The length of the day on a flat earth". Tom provided a large-ish post with nothing to support his claim. I was asking for the information required to duplicate his claims so I could verify for myself. If the information was readily available somewhere else I would have looked other places first.

My apologies Thork. I thought the question I asked was on par with the level of evidence and standards this community expects.

My request to tom still stands.

[Sceptom]

Tom answered this in another thread today.

http://forum.tfes.org/index.php?topic=1258.msg56594#msg56594
I assumed you'd have read it and responded. you didn't, I guessed you were happy.

Well, your assumption was wrong.

[Sceptom]

Tom please show a version that also displays summer sunlight distribution for the southern/outer Hemiplane, and the mathematics that allow you to predict and create these illustrations.

How about you produce calculations to disprove it? Do you think you can just turn up here and demand our FErs spend hours humouring your every inane and lazy request because the ones at the other site are now bored of your trolling?

Debate is a two way thing. You'll get out what you put in. If you generate content, you'll receive substantiated replies. Lazy one liners will likely see you ignored.

I'm not sure if you know or agree with the concept of burden of proof.

[Thork]

Tom please show a version that also displays summer sunlight distribution for the southern/outer Hemiplane, and the mathematics that allow you to predict and create these illustrations.

How about you produce calculations to disprove it? Do you think you can just turn up here and demand our FErs spend hours humouring your every inane and lazy request because the ones at the other site are now bored of your trolling?

Debate is a two way thing. You'll get out what you put in. If you generate content, you'll receive substantiated replies. Lazy one liners will likely see you ignored.

I'm not sure if you know or agree with the concept of burden of proof.

And you can go about proving earth is round equally as vociferously as you demand we prove that it is flat.