# Atmospheric sunlight refraction arguments on the Eratosthenes triangulation method

#### Sandor Szekely

##### Banned
Banned
DarkStar presented his measurement using the Eratosthenes triangulation method to prove the globe earth model curvature is right.

http://flatearthinsanity.blogspot.com/2016/07/simple-proof-for-convexity-of-earth.html

Here is the heart of the proof.

Simply pick a line of longitude (along which everyone will experience high noon at the same time, doesn't have to be one perfect line of latitude but each person should measure at high noon on the same day) and measure the length of the sun's shadow at several points of latitude from directly under the sun to as far North as you can (must have at least one measurement that is above 75°). [I give a few more details in my post, must be plumb, etc]

That's all you have to do.

You can review my mathematics in more detail but IF we lived on a Flat Earth then, as you moved perpendicular to the sun's path, you would find the lengths of shadows to be proportional to the distance from the subsolar point. On a convexly curved Earth they would get longer as a power curve (which is what we observe), and on a concave Earth they would vary logarithmically.

This is a trivially true observation geometrically and the mathematics are very simple as well. And it doesn't matter what the altitude of the sun actually is! That would affect the ACTUAL values of course, but not the fact that the Gaussian curvature DEFINES the shape of this measurement.

And the cool thing is that twice a year kids around the world perform this measurement so we have years and years of data collected by kids.

http://ciese.org/curriculum/noonday/gallery/

They usually just calculate the circumference but 'hidden' in this data is a very simple, undeniable, geometric truth - the Earth is convexly curved.
Content from External Source
My argument on the Eratosthenes triangulation method is that the sunlight is NOT a straight line but a curve due to atmospheric rerfraction, therefore there is no triangle in this case.

The sun is NOT where we see it! Due to atmospheric refraction the observers see an APPARENT SUN in different position - only the one with the sun at 90 degrees overhead sees the REAL SUN.

The sun light is coming into more dense, hot and humid air with more pressure and CO2
therefore the sun light is bent downwards to earth

Please watch this video from 2:48

So the SUN is NOT where we see it - that means that the sunlight is NOT STRAIGHT!

Therefore the triangulation method is WRONG because the "c" side of the triangle is NOT a straight line - ergo there is NO triangle here.

We are looking for the REAL SUN angle to calculate with the triangulation method, but we have to define the amount of bend on the sunlight.

Compare DarkStar's results of the sun triangulation: looks like the power curve is the same as the Atmospheric refraction curve chart

SO if the sunlight triangulation measurements represent the atmospheric refraction power curve, then where is the curvature?

and here is video in the attachment - I don't know the source - that demonstrates the apparent and real sun differences on the globe earth model

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GREAT work DarkStar! I love people DOING experiments to PROVE a theory

I would like to suggest to start a NEW topic on the ATMOSPHERIC REFRACTION arguments on the Eratosthenes triangulation with the sun!

Mick, I may be off topic here than pls delete this, or if you think this is worth a new topic than maybe You could make one based on my claims here:

The sun is NOT where we see it! Due to atmospheric refraction the observers see an APPARENT SUN in different position - only the one with the sun 90 degrees overhead sees the REAL SUN.

The sun light is coming into more dense, hot and humid air with more pressure and CO2
therefore the sun light is bent downwards to earth

Please watch this video from 2:48

So the SUN is NOT where we see it - that means that the sunlight is NOT STRAIGHT!

Therefore the triangulation method is WRONG because the "c" side of the triangle is NOT a straight line - ergo there is NO triangle here.

This is EXACTLY what we are working on with my partner Zack!

We are looking for the REAL SUN to calculate with using triangulation, but for than we have to define the bent that the sunlight suffered.

Compare YOUR results of the sun triangulation like a power curve with the Atmospheric refraction

It's the same!
SO the measurements represent the atmospheric refraction power curve, then where is the curvature?

and here is video in the attachment - I don't know the source - that demonstrates the apparent and real sun differences on the globe earth model

I have watched the video, and I'm unconvinced. I'd give way to anyone with more expertise in optics or astronomy, of course. But a quick look at the Wikipedia page on twinkling confirmed what I suspected;

Large astronomical objects closer to Earth, like the Moon and other planets, encompass many points in space and can be resolved as objects with observable diameters. With multiple observed points of light traversing the atmosphere, their light's deviations average out and the viewer perceives less variation in light coming from them.[12][13]
Content from External Source
https://en.m.wikipedia.org/wiki/Twinkling

This is from one of the original sources cited in Wikipedia, always the best way to use it;

Our atmosphere is very turbulent, with streams and eddies forming, churning around and dispersing all the time. These disturbances act like lenses and prisms that shift the incoming light from a star from side to side by minute amounts several times a second. For large objects like the moon, these deviations average out. (Through a telescope with high magnification, however, we see shimmering images.) Stars, in contrast, are so far away that they effectively act as point sources, and the light we see flickers in intensity as the incoming beams bend rapidly from side to side.
Content from External Source

http://www.scientificamerican.com/article/why-do-stars-twinkle/

Do you have any evidence that the refraction is great enough to account for such differences in shadow length?

Look at the vertical axis of this chart you posted. Even when the sun is 10 degrees above the horizon the amount of refraction is less than 0.1 degrees!

Do you have any evidence that the refraction is great enough to account for such differences in shadow length?

Look at the vertical axis of this chart you posted. Even when the sun is 10 degrees above the horizon the amount of refraction is less than 0.1 degrees!

My claim is that the sunlight is NOT straight, therefore the Eratosthenes triangulation method is wrong. We need to take into consideration other effects like atmospheric refraction before we can conclude that the earth is a globe because we can triangulate the shadows in different places and come to this result.

The result or observation of a phenomena DOES NOT define a theory!

Have you seen the attached video "atmospheric refraction"? that explains it well

For crude instruments like a short stick used to measure the length of a shadow at local apparent noon, refraction is insignificant. At an elevation of 30° the error in the length of a shadow of a one meter tall stick will be 2 millimeters if you ignore refraction.

Here's the refraction formula from the Nautical Almanac:

For crude instruments like a short stick used to measure the length of a shadow at local apparent noon, refraction is insignificant. At an elevation of 30° the error in the length of a shadow of a one meter tall stick will be 2 millimeters if you ignore refraction.

Here's the refraction formula from the Nautical Almanac:

"At an elevation of 30° the error in the length of a shadow of a one meter tall stick will be 2 millimeters if you ignore refraction."

1. as you say here the error rate of the stick measurement is about 0.2%
2. you have to distinguish well between umbra / pneumbra shadow that is not possible with visual measurements
3. the deviation of the apparent sun from the real sun is a power curve upon sun angle value
4. there are other factors that we can't exclude like light retardation and some we might even not even know of yet
5. I CAN NOT ignore atmospheric refraction!
are we talking about a definite proof on the GE model or not?

1. as you say here the error rate of the stick measurement is about 0.2%
2. you have to distinguish well between umbra / pneumbra shadow that is not possible with visual measurements
3. the deviation of the apparent sun from the real sun is a power curve upon sun angle value
4. there are other factors that we can't exclude like light retardation and some we might even not even know of yet
5. I CAN NOT ignore atmospheric refraction!
are we talking about a definite proof on the GE model or not?

1. And? What accuracy do you want? If you want an accuracy greater than what can obtained by the shadow cast by a stick then go buy a sextant.
2. You just included an illustration that shows exactly how it is possible!
3. Why do you keep bringing that up as if it is some mystical confounding factor? I just showed you a formula to correct for refraction that is used by navigators the world over.
4. Navigators have known for a very long time that there aren't any additional factors. Unless you want to claim the entire science of celestial navigation has been wrong for centuries and no one, including me who navigated ships and submarines for 20 years, caught it.
5. Im saying you don't have to ignore it. (typo fixed)

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1. And? What accuracy do you want? If you want an accuracy greater than what can obtained by the shadow cast by a stick then go buy a sextant.
2. You just included an illustration that shows exactly how it is possible!
3. Why do you keep bringing that up as if it is some mystical confounding factor? I just showed you a formula to correct for refraction that is used by navigators the world over.
4. Navigators have known for a very long time that there aren't any additional factors. Unless you want to claim the entire science of celestial navigation has been wrong for centuries and no one, including me who navigated ships and submarines for 20 years, caught it.
5. Im saying you have to ignore it.

1. I know what a sextant is - the measurement of DarkStar did not use a sextant. it has inaccuracy anyways
2. it is an illustration of a theoretical measurement model. you can't be exact on pneumbra with visual measurements
3. so you are suggesting here with the formula that the atmospheric rafraction is CONSTANT and EQUAL in any places?
4. "there aren't any additional factors" well I just named a few... how can you discard them:
5. I am NOT ignoring a variable.

are we talking scientifical here?

The sun light is coming into more dense, hot and humid air with more pressure and CO2
therefore the sun light is bent downwards to earth

That only works on a curved earth. If the earth were flat, then there would be no refraction of light from objects at the horizon, like boats.

You claim that there is refraction, hence the Earth must have a curved surface.

1. I know what a sextant is - the measurement of DarkStar did not use a sextant. it has inaccuracy anyways
2. it is an illustration of a theoretical measurement model. you can't be exact on pneumbra with visual measurements
3. so you are suggesting here with the formula that the atmospheric rafraction is CONSTANT and EQUAL in any places?
4. "there aren't any additional factors" well I just named a few... how can you discard them:
5. I am NOT ignoring a variable.

are we talking scientifical here?

1. I'll ask again: what accuracy are you looking for?
2. Why can't you be exact on penumbra measurement?
3. I gave you the standard refraction correction. Of course abnormal atmosphere conditions will cause it to vary. But why are you reluctant to use it?
4. No, you named one you invented out of thin air without any justification and then said there may be others we don't know about. Why do you discard centuries of celestial navigation science?
5. Whoops. I meant to write "you *don't* have to ignore it." I edited my previous comment to fix that.

That only works on a curved earth. If the earth were flat, then there would be no refraction of light from objects at the horizon, like boats.

You claim that there is refraction, hence the Earth must have a curved surface.

nope, refraction is the SAME on GE and FE models!
atmospheric and horizontal refraction too!

"Atmospheric refraction is the deviation of light or other electromagnetic wave from a straight line as it passes through the atmospheredue to the variation in air density as a function of height.[1] This refraction is due to the velocity of light through air decreasing (the index of refraction increases) with increased density. " WIKI

this is horizontal refraction, explained as terresterial refraction:
"Atmospheric refraction near the ground produces mirages and can make distant objects appear to shimmer or ripple, elevated or lowered, stretched or shortened with no mirage involved. "
"Terrestrial refraction usually causes terrestrial objects to appear higher than they really are, although in the afternoon when the air near the ground is heated, the rays can curve upward making objects appear lower than they really are." WIKI

So atmospheric and horizontal refractions are the same phenomenon, but have a different

Objects like boats and far away buildings OR THE WATER IN FRONT OF THEM may have lower or higher refraction at different ambient conditions.

I
I made a RED circle to show where the reflexion on water is possibly hiding the lower part of the builings:

I claim here that the refraction is NOT taken into account with the Eartosthenes triangulation method.

I claim here that the refraction is NOT taken into account with the Eartosthenes triangulation method.

What would be the resulting circumference of the Earth if Eratosthenes corrected for refraction?

1. I'll ask again: what accuracy are you looking for?
2. Why can't you be exact on penumbra measurement?
3. I gave you the standard refraction correction. Of course abnormal atmosphere conditions will cause it to vary. But why are you reluctant to use it?
4. No, you named one you invented out of thin air without any justification and then said there may be others we don't know about. Why do you discard centuries of celestial navigation science?
5. Whoops. I meant to write "you *don't* have to ignore it." I edited my previous comment to fix that.

1. we have to consider the accuracy of the measurement to make definite conclusions. This is just a part of the inaccuracies adding up in this measurement.
2. You can't be accurate with VISUAL measurement. this means you can't distinguish between umbra and pneumbra with naked eye
3. there is NO standard refraction correction as the correction changes over time (not abnormal)

here 3 pictures of a timelaps video showing huge refraction in the afternoon:

9AM

13PM

18PM

and here is the original video from Jeranism:

4. so you don't like the expression "light retardation"? LOL
(light retardation means that the light is slowing down due to change in medium that it travels through and therefore it's change of speed causes a deviation from it's straight line path)

WAIT! till I am making a new post on "gravitational waves found" DEBUNKED
I had a discussion with the Hungarian leader of the scientist group who found the 1st and 2nd gravitatioal waves - I will share it with Metabunk.org soon

What would be the resulting circumference of the Earth if Eratosthenes corrected for refraction?

GOOD QUESTION!

I have no answer for that, but I know that the triangulation calculation is missing some very important factors.

I have good questions too ! easier than give a definite answer

It may turn out with the Balaton lake laser experiment as well, that Earth is a globe, but way much bigger - with way less curvature? MAYBE! LOL

But in my opinion there is something sticky with the theory if we sum up to the right value with leaving out important factors.

All you do is dismiss other people's claims without any justification. There absolutely is a standard refraction. Go on to any sailing forum and ask them how accurate the standard refraction corrections they use are.

nope, refraction is the SAME on GE and FE models!
atmospheric and horizontal refraction too!

"Atmospheric refraction is the deviation of light or other electromagnetic wave from a straight line as it passes through the atmospheredue to the variation in air density as a function of height.[1] This refraction is due to the velocity of light through air decreasing (the index of refraction increases) with increased density. " WIKI

AS A FUNCTION OF HEIGHT!

So, if your view line is parallel to the ground, and the Earth is flat, then the height does not change, hence there will be no refraction.

There would still be potential refraction looking up or down, however there would be zero refraction of a point directly opposite you at the same height, hence you would able to see it.

Since such points get obscured by the water, that proves the surface of the water is curved.

AS A FUNCTION OF HEIGHT!

So, if your view line is parallel to the ground, and the Earth is flat, then the height does not change, hence there will be no refraction.

There would still be potential refraction looking up or down, however there would be zero refraction of a point directly opposite you at the same height, hence you would able to see it.

Since such points get obscured by the water, that proves the surface of the water is curved.

I pointed out this difference:

ATMOSPHERIC refraction is a function of height, when it enters from near vacuum to the dense lower atmosphere

HORIZONTAL (terresterial) refraction is different! it is caused by change in local ambient conditions
as I wrote:
this is horizontal refraction, explained as terresterial refraction:
"Atmospheric refraction near the ground produces mirages and can make distant objects appear to shimmer or ripple,elevated or lowered, stretched or shortened with no mirage involved. "
"Terrestrial refraction usually causes terrestrial objects to appear higher than they really are, although in the afternoon when the air near the ground is heated, the rays can curve upward making objects appear lower than they really are." WIKI

this is wrong:
"So, if your view line is parallel to the ground, and the Earth is flat, then the height does not change, hence there will be no refraction."
there will be less or more horizontal terresterial refraction

In case of water surface we have to calculate with diffraction as well, when light is bent on edges.

All you do is dismiss other people's claims without any justification. There absolutely is a standard refraction. Go on to any sailing forum and ask them how accurate the standard refraction corrections they use are.

"All you do is dismiss other people's claims without any justification."

NO! I CLEARLY answered your question in detail - with photos and a video evidence of CHANGE IN REFRACTION OVER TIME in one day! look at them again

Where is the time of the day variant in your standard refraction math?

Come on... sailing forums... I AM talking science here

YOU seem to ignore the difinition of : "definite proof", "exact math" and "all other possibilities excluded"

I have to write again my favourite quote from deirdre
"If we have data, let's look at data. If all we have is opinions let's go with mine. -barksdale"

NO! I CLEARLY answered your question in detail - with photos and a video evidence of CHANGE IN REFRACTION OVER TIME in one day!

No, all you provided was one extreme example of abnormal refraction at the surface. Which is less reliable than asking experienced navigators on a sailing forum. Refraction at the surface is always greater than for celestial bodies at higher elevation angles. That does not negate the fact that there is a standard refraction correction that works the vast majority of the time. And there is no such thing as a "time of day variant" of refraction. You deduced there is such a ridiculous thing by watching ONE video.

"Terrestrial refraction usually causes terrestrial objects to appear higher than they really are, although in the afternoon when the air near the ground is heated, the rays can curve upward making objects appear lower than they really are." WIKI

So how would that bend a ray of light that parallel to the ground. Draw a diagram

Then explain how it does it evenly across the horizon.

It does not work on a flat earth model, as it requires a change in height, hence it CANNOT obscure something that is level with the camera.

No, all you provided was one extreme example of abnormal refraction at the surface. Which is less reliable than asking experienced navigators on a sailing forum. Refraction at the surface is always greater than for celestial bodies at higher elevation angles. That does not negate the fact that there is a standard refraction correction that works the vast majority of the time. And there is no such thing as a "time of day variant" of refraction. You deduced there is such a ridiculous thing by watching ONE video.

I understand what you are missing here:
"Refraction at the surface is always greater than for celestial bodies at higher elevation angles. That does not negate the fact that there is a standard refraction correction that works the vast majority of the time."

I explained that ATMOSPHERIC refraction and HORIZONTAL refraction (terresterial) is not the same thing.

Atmospheric refraction is constant and changes marginal to the horizontal refraction that is on the video and pictures example! I suppose that the sailors are talking about ATMOSPHERIC refraction?
We are talking about the HORIZONTAL refraction that is due to change of medium (like hot spots over water or land) on Mick's question.

We are talking about the HORIZONTAL refraction that is due to change of medium (like hot spots over water or land) on Mick's question.

That's still a function of height, and so still can not obscure something that is level with the viewer on a flat earth.

So how would that bend a ray of light that parallel to the ground. Draw a diagram

Then explain how it does it evenly across the horizon.

It does not work on a flat earth model, as it requires a change in height, hence it CANNOT obscure something that is level with the camera.

The light ray is not parallel to the ground, but a curve from one area to an other specific area that is why you see some thing that is not there or something in a different position.

"Then explain how it does it evenly across the horizon." IT CAN'T BE EVEN! That is a very important clue
as I said: a curve from one area to an other specific area
this is WHY I use a boat in the laser curvature experiment!

here well demonstreted on this picuture - I draw with RED the possible other position of the mirage we see: that is not the building but the water in front of it.
I can not draw a refraction diagramm as it has a huge number of variables and I would not go into guessing.

"It does not work on a flat earth model, as it requires a change in height, hence it CANNOT obscure something that is level with the camera"

IN GE and FE models all refraction works the same.
And I point out again:
ATMOSPHERIC refraction (that is mostly depending on the angle of the viewpoint) is caused by height.

HORIZONTAL refraction is caused by the change of the medium light travells through like turbulances or whatever.

There is always a certain amount of refraction! In some cases the amount is huge, that is what we call a mirage, super mirrage or fata morgana.

That's still a function of height, and so still can not obscure something that is level with the viewer on a flat earth.

NOPE

imagine you see a super mirrage from your car. as you move away after a distance the mirrage vanishes.

this proves as I said: a curve from one area to an other specific area.
this proves as you see something at a position where you know it can not be, therefore you can conlude that you see a kinda reflexion but not the real object.
If this mirrage is NOT the building, but the water in front of it that explaines the possibility how water blocks your vision of the lower part of the building. It is NOT the water that is blocking your view but the mirrage of the water. It is not the building that is mirraged but the water in front.

IN GE and FE models all refraction works the same.

Except that in the FE model the layers of the atmosphere are flat, whereas in the GE model they are curved.

In the FE model if you draw a line between two objects at the same height then the air inbetween is at the same height above the ground, so at the same same temperature and pressure. Hence there is no refraction at that level, so the refraction alone cannot hide the object.

In the GE model since the atmosphere is curved you can't draw a straight line though air of equal pressure, so it's possible for something to be obscure by a mirage.

imagine you see a super mirrage from your car. as you move away after a distance the mirrage vanishes.

Yes, if you are looking up or down, but if you look level, and the ground and atmosphere are flat and level, then a level target cannot be obscured.

imagine you see a super mirrage from your car. as you move away after a distance the mirrage vanishes.

I suspect you mean an inferior mirage?

Except that in the FE model the layers of the atmosphere are flat, whereas in the GE model they are curved.

In the FE model if you draw a line between two objects at the same height then the air inbetween is at the same height above the ground, so at the same same temperature and pressure. Hence there is no refraction at that level, so the refraction alone cannot hide the object.

In the GE model since the atmosphere is curved you can't draw a straight line though air of equal pressure, so it's possible for something to be obscure by a mirage.

"Except that in the FE model the layers of the atmosphere are flat, whereas in the GE model they are curved."
Yes this is correct.

"In the FE model if you draw a line between two objects at the same height then the air inbetween is at the same height above the ground, so at the same same temperature and pressure. "
NO, they are not the same temperature, humidity and pressure or density at the same height. Nor in the GE model.

"In the GE model since the atmosphere is curved you can't draw a straight line though air of equal pressure, so it's possible for something to be obscure by a mirage."
We are NOT talking about straight lines here, the light is curved: it comes from a different place than we see it. GE model height difference has a MARGINAL effect : HORIZONTAL refraction is caused by the local differences on the surface or the air above.

This is very important to understand :

this is horizontal refraction, explained as terresterial refraction:
"Atmospheric refraction near the ground produces mirages and can make distant objects appear to shimmer or ripple,elevated or lowered, stretched or shortened with no mirage involved. "
"Terrestrial refraction usually causes terrestrial objects to appear higher than they really are, although in the afternoon when the air near the ground is heated, the rays can curve upward making objects appear lower than they really are." WIKI

I suspect you mean an inferior mirage?

These are perfect examples of different HORIZONTAL refraction effects.
Both are horizontally seen and caused by ambient weather at these locations, and important to point out that they are observable from an other specific area not everywhere.

HEIGHT has nothing to do with horizontal refraction - exept that there are different weather conditions in different heights.

These are perfect examples of different HORIZONTAL refraction effects.
Both are horizontally seen and caused by ambient weather at these locations, and important to point out that they are observable from an other specific area not everywhere.

HEIGHT has nothing to do with horizontal refraction - exept that there are different weather conditions in different heights.

But what you show is clearly horizontal.

Hence it's a function of height.

Otherwise you are suggesting it's just some luckily placed blob of air that just happens to be in the right place every time someone takes a photo to demonstrate the curve of the earth.

Try to think in mode detail exactly what this change in temperature would have to be between two objects three miles apart, and 1 foot above the totally flat surface of a lake, for one not to be visible from the other.

After you think you know what is going on, answer two important questions.

Why is the temperature varying?

Why is the temperature gradient at an acute angle to the view line?

(And to expand on that a bit. If that image is caused by refraction, and the water level is flat, then the required temperature gradient would have to be basically straight, and at a very slight angle to the horizontal view line. )​

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I explained that ATMOSPHERIC refraction and HORIZONTAL refraction (terresterial) is not the same thing.

Your confusion of ideas exceeds any reasonable person's time and effort to sort out. Good luck to you.

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But what you show is clearly horizontal.

Hence it's a function of height.

Otherwise you are suggesting it's just some luckily placed blob of air that just happens to be in the right place every time someone takes a photo to demonstrate the curve of the earth.

Try to think in mode detail exactly what this change in temperature would have to be between two objects three miles apart, and 1 foot above the totally flat surface of a lake, for one not to be visible from the other.

After you think you know what is going on, answer two important questions.

Why is the temperature varying?

Why is the temperature gradient at an acute angle to the view line?

(And to expand on that a bit. If that image is caused by refraction, and the water level is flat, then the required temperature gradient would have to be basically straight, and at a very slight angle to the horizontal view line. )​

I circled here on the right side picture the SAME horizontal refraction I am pointing to:

You can not see the lower part of the car, because it is blocked by the refraction of the road and it self. The car it self is not a mirrage. A mirrage is blocking the view of the car's down part. The same as on the pictures with boats or buildings in far distance.

"Hence it's a function of height."

height may play a role in horizontal refraction, but it is caused by:

"Otherwise you are suggesting it's just some luckily placed blob of air that just happens to be in the right place every time someone takes a photo to demonstrate the curve of the earth." haha funny

but nearly true: light REFRACTION is ALWAYS PRESENT! making sometimes less sometimes more distorsion
check the video of the bay: yes it changes over time and sometimes has a huge volume

"Try to think in mode detail exactly what this change in temperature would have to be between two objects three miles apart, and 1 foot above the totally flat surface of a lake, for one not to be visible from the other."

mirrage is a kinda miracle

the picture "Rob Skiba proves the Chicago skyline..." shows how compex these distortions are.

"Why is the temperature varying?"
for example the sun shining stongly at one area and blocked by clouds in other areas. A mirrage occurs when different temperatures of layers in the air are aligned to reflect or bend the light back to a cerain area poition.

Why is the temperature gradient at an acute angle to the view line?
(And to expand on that a bit. If that image is caused by refraction, and the water level is flat, then the required temperature gradient would have to be basically straight, and at a very slight angle to the horizontal view line. )​

The light (the picture) you see in front of the ship / car / building is reflected from upwards back from above, when meeting a colder layer of air above, that is why you see them upside down. ( there are even special cases that the mirage is reversed back to upright position caused by multiple refractions)

Your confusion of ideas exceeds any reasonable person's time and effort to sort out. Good luck to you.

I am shocked to read this, and that Mick has agreed with it!

I have NO confusion on the refraction subject, please!

I am EXPLAINING the difference between the types AN QUOTING WIKI to be a credible source.

I have attached here the exact definition of the two for the reason not to mix them up, as the post is originally about ATMOSPHERIC refraction argument on triangulation method. Now we are talking about HORIZONTAL refraction know as a super mirage at it's extreme case.
We are now discussing the possibility of the horizontal or terresterial refraction that is well presented in Mick's picture of the car on the road.

there is no big height difference between the observer and the car -yet it does have a mirrage effect.

"exceeds any reasonable person's time "

let me point out that I do not force anybody to take part in the conversation it is upon "free will"

TIME is subjective, it looks like I have more time just looking at the comments lenght lol

think about the ONE HOUR at the dentist and with your loved... not the same ONE HOUR right?

TIME IS WHAT YOU THINK OF IT

So how can something at the same level be obscured? Describe the temperature gradient, and how it is angled.

Now we are talking about HORIZONTAL refraction know as a super mirage at it's extreme case.
We are now discussing the possibility of the horizontal or terresterial refraction that is well presented in Mick's picture of the car on the road.
I'm really really trying to follow along here. Can you skip the car mirage -because that is an inferior mirage, but in your first sentance you say its a superior mirage so you are confusing the bejeezus out of me. Plus the car type mirage cant be what you are talking about because all of the examples i see of that type of mirage its the top thing that's reflected downward. So this would have absolutely nothing to do with lake water (or sea water etc) miraging UP.

right?

Sandor:

The first thing you have to do is sort out your confusion about these things:

- Astronomical refraction, terrestrial refraction and variability near the horizon. (You seem to have some awareness of this.) But you are confusing terrestrial refraction with "variability near the horizon." Not the same thing at all.

- Refraction in the "standard atmosphere" versus extreme and variable refraction that can be caused by layers of air with steep thermal gradients - (mirages, looming, towering, stooping and sinking.) By steep thermal gradients we mean inversion layers.

You are confusing all of these. Very badly confusing them. You're even confusing superior mirages with inferior mirages.

The best person I can refer to is Dr. Andrew Young and I'm going to quote him and give links to his site.

Refraction is caused by differences in the refractive index of air. And that is caused by differences in density in both standard-atmosphere conditions and in conditions in which there are steep thermal gradients. There can be extreme but temporary variability in refraction near the horizon.

This variability near the horizon is very surprising to the average astronomer, who has been educated to believe that refraction (in the part of the sky where astronomical measurements are usually made) can be calculated accurately from the local atmospheric temperature and pressure. This is true in the part of the sky where Oriani's Theorem holds, but it breaks down very rapidly on approaching the horizon.

In fact, it can be shown that the refraction near the horizon depends mostly on the local temperature gradient, which is much more important than the local temperature itself. For this reason, all the refraction phenomena near the horizon — mirages, dip, terrestrial refraction, etc., as well as the astronomical refraction — are very sensitive to the temperature gradient; and they all vary a great deal more than does the astronomical refraction well up in the sky. - Dr. Young
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Astronomical refraction is very predictable and not variable at altitudes above 10 or 15 degrees. All mirage effects (plus looming, towering, stooping and sinking) are a part of variability near the horizon. You have to be looking nearly parallel with the surface of the earth - and the layers of the inversion. Within a certain critical angle!

And this variability near the horizon is not synonymous with terrestrial refraction as you imply.

The observations taken in the Eratosthenes experiment were taken when the sun was at the meridian (noon). Ray bending by inversion layers would not affect the rays of the sun at noon.

The amount of astronomical refraction you show in your diagram is incorrect.

Extremely exaggerated. Appealing to the kind of extreme and variable refraction you can get near the horizon is not valid.

"To give some rough numbers: the astronomical refraction is about a minute of arc in the part of the sky midway between zenith and astronomical horizon, but is typically over 30 minutes of arc (half a degree) at the horizon." - Dr. Andrew Young.
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This exaggerated idea of how displaced the image of the sun is when it is high in the sky is simply an ad hoc excuse.

A clear definition of astronomical refraction, terrestrial refraction and variability near the horizon:
http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/astr_refr.html

I'm going to link to three more pages of his site, but you should read every page. At this point you are hopelessly confused.
http://www-rohan.sdsu.edu/~aty/mirages/mirsims/std/std.html

http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/bending.html

http://www-rohan.sdsu.edu/~aty/mirages/mirsims/loom/loom.html

I'm sure that if by chance Dr. Young saw this post he'd make corrections to what I'm saying, but I'm a lot less wrong than you are.

Astronomical and terrestrial refraction are well understood. Geodetic surveyors (map makers) and navigators (when using the sextant) have been taking it into account for hundreds of years. I'm going to also refer you to the history and practice of Snell's law.

And Dr. Young's site: http://www-rohan.sdsu.edu/~aty/explain/optics/refr.html#sinelaw

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The hollow earthers explain what we see by appealing to curved light. The surface of the earth is concave but it looks convex because light curves. But they don't have any set law. They just appeal to a vague "curvature" which is convenient for the situation without having any consistent mathematical model.

Are you are going to do the same thing? Appeal to any vague and arbitrary amount of light curvature that fits the situation?

For instance, if we see only the tallest buildings of Toronto across Lake Ontario, are you going to appeal to a just right amount of light curvature to account for it? Or for the results of your Lake Balaton experiment?

If you are going to appeal to curved light you must have a mathematical theory. It must be consistent and precise.

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If you are going to appeal to curved light you must have a mathematical theory. It must be consistent and precise.

And really there no reason why such a theory should not be testable. People have been taking observations of the sun and the stars for thousands of years and doing the math. And the models they come up with that explain their observations fit with the actual globe Earth.

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