The Constancy of the Angular size of the Sun

We get repeatedly told that the sun is a ball about 50 km (or 31 miles) in diameter and about 5,000 km (or 3,100 miles) above the surface of the earth.
This makes the angular size of the sun about 0.57° when viewed from directly underneath and this is about the size we observe.

When the sun is not directly overhead, however, it must be at a greater distance from the observer as in this diagram.
For any given sun elevation angle ("Elev" on the diagram),
We know the height (on the Flat Earth model) is always 5,000 km, so we can easily calculate the sun's angular size from any location.

Now there are plenty of websites that give us data about the sunrise, sunset and sun's position in the sky at any location and any time.

Since the actual size of the sun must remain constant, as the distance changes the angular size (the apparent size to us) must change, and can be calculated as angular size = (sun size/sun distance,

Now on Youtube there is a video made by a the Flat Earther, Matrix Decode with very good photos of the sun through a filter (an arc welder's glass) showing the sun at a number of times of day from 9:30 AM to 7:00 PM on 9/March/2016 in Malaga, Spain.

The following screen shots from his video does an excellent job of proving that the sun size does not change!

Do I need to say more? Our kind Flat Earther, Matrix Decode, has said it all!


In the following table, I have given the angular size of the sun based on the information I could get on the camera used. The actual size is not very important, though, it is the constancy that matters here.

Then to compare with the Flat Earth model I have given the elevation angle for each time, from which the distance to the sun is calculated. Most of these distances look "preposterous", maybe some Flat Earther can explain them!

Then from these distances, I have calculated the angular size the sun should appear on the Flat Earth. The Wiki explains this away as

Magnification of the Sun at Sunset
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 atmosphere.

But these photos were taken through a filter to remove the glare, and most are quite sharp. In any case for "magnification effect caused by the intense rays of light passing through the strata of the atmosphere" to keep the size so close if very hard to accept.

Now, I don't know what you are going to about the "ridiculous" distances of 19,484 km and especially 91,281 km, but if the sun is at the given elevation and 5,000 km above the earth, that's where is has to be - you work it out!

On the Flat Earth with the sun at around 5,000 km altitude, the distance to the sun varies a huge amount from when it is overhead to when it sets, so the angular size (our apparent size) must change by a large amount.

If I have made some logical or arithmetic mistakes, I would be glad to hear it.

Surprising how the angular size seems to decrease around noon hours though only by one degree, probably due to something unrelated to size or position (maybe the size of the sun in the image or zoom?) while in the flat earth theory it would peak. Wow.

Surprising how the angular size seems to decrease around noon hours though only by one degree, probably due to something unrelated to size or position (maybe the size of the sun in the image or zoom?) while in the flat earth theory it would peak. Wow.

Refraction tends to slightly stretch things vertically near the horizon. Hence, it is at its smallest around noon.

Surprising how the angular size seems to decrease around noon hours though only by one degree, probably due to something unrelated to size or position (maybe the size of the sun in the image or zoom?) while in the flat earth theory it would peak. Wow.

No, that was by 0.01° and I would put it simply measurement error, mine. I could have put it all the working, showing how I estimated the field of view, etc.

What I did not show, but probably should have, is that the sunset one (at 7:30 PM) had a significantly smaller height, but the same width as the others.

Maybe refraction is real!

Quote from: MrDebunk on August 24, 2016, 09:26:01 PM

Surprising how the angular size seems to decrease around noon hours though only by one degree, probably due to something unrelated to size or position (maybe the size of the sun in the image or zoom?) while in the flat earth theory it would peak. Wow.

No, that was by 0.01° and I would put it simply measurement error, mine. I could have put it all the working, showing how I estimated the field of view, etc.

What I did not show, but probably should have, is that the sunset one (at 7:30 PM) had a significantly smaller height, but the same width as the others.

Maybe refraction is real!

Ugh. Yeah, refraction usually causes it to be shorter at the horizon rather than taller. My bad. Although it can go either way, depending on the weather conditions.

Regardless, this is probably my favorite proof that the earth is round. It is just so blatantly obvious, and there is absolutely no plausible explanation for it on a flat earth.

The "squishing" of the sun at the horizon is just Rowbotham's perspective at play. I definitely agree that perspective is insufficient to account for the sunset, however, if that is your argument.

The "squishing" of the sun at the horizon is just Rowbotham's perspective at play. I definitely agree that perspective is insufficient to account for the sunset, however, if that is your argument.

I was not making any particular argument about sunsets.

I am claiming that the sun's angular size stays constant throughout the day, except for the possibility of some distortion at sunrise and sunset.

No flat earth explanations come close to being plausible.

Why? Are you talking about the distances involved? Because I'd agree that the classical numbers of Rev. Voliva and Dr. Rowbotham can't possibly be correct.

Why? Are you talking about the distances involved? Because I'd agree that the classical numbers of Rev. Voliva and Dr. Rowbotham can't possibly be correct.

Not just distances, but the fact that the distance to the sun on any flat earth model must vary greatly during the day.
Since we assume the sun's size must stay constant the angular size of the sun will vary considerably.

For example Malaga, Spain  (where the photos taken), is 4,088 km North of equator, so if the sun were over the equator due South of Malaga, the slant distance to the sun would be about 6,460 km. This would make the angular size of the sun 0.44°, compared to the 0.57° angular size of a 50 km sun 5,000 km away. The distances st 13:00 and 14:00 in the OP are a little more than this because on 9/Mar/2016 the sun was still a little South of the equator.

On the flat earth as the sun gets further away, angular the size would be expected to reduce proportionately.
The distances I showed in the OP were calculated from the sun's height  (5,000 km) and the elevation angle.
Of course, on the Flat Earth there is no way for the sun to ever get to such a low elevation.

Now, the main point I am trying to bring out is that on any "close sun" model the apparent size of the will vary, and we do not observe any  variation over a day.

So if you have a better Flat Earth model, maybe you should let us know. Till then all we can do is base our ideas on "the Wiki" and of course the Sacred Texts.

Now, the main point I am trying to bring out is that on any "close sun" model the apparent size of the will vary, and we do not observe any  variation over a day.

  Interesting... has anyone measured sun size during summer and winter? As the sun is quite farther in winter then there should also be difference in sun size, it should be noticeably smaller at winter than at summer.

Quote from: Ski on August 25, 2016, 09:04:01 PM

Why? Are you talking about the distances involved? Because I'd agree that the classical numbers of Rev. Voliva and Dr. Rowbotham can't possibly be correct.

Not just distances, but the fact that the distance to the sun on any flat earth model must vary greatly during the day.

Well that sounds like an assumption to me...

On the flat earth as the sun gets further away, angular the size would be expected to reduce proportionately.

As opposed to ..?

The distances I showed in the OP were calculated from the sun's height  (5,000 km) and the elevation angle.
Now, the main point I am trying to bring out is that on any "close sun" model the apparent size of the will vary, and we do not observe any  variation over a day.

 Are you talking about the distances involved? Because I'd agree that the classical numbers of Rev. Voliva and Dr. Rowbotham can't possibly be correct.

Quote from: rabinoz on August 25, 2016, 10:37:34 PM

Quote from: Ski on August 25, 2016, 09:04:01 PM

Why? Are you talking about the distances involved? Because I'd agree that the classical numbers of Rev. Voliva and Dr. Rowbotham can't possibly be correct.

Not just distances, but the fact that the distance to the sun on any flat earth model must vary greatly during the day.

Well that sounds like an assumption to me...

Quote

On the flat earth as the sun gets further away, angular the size would be expected to reduce proportionately.

As opposed to ..?

Quote

The distances I showed in the OP were calculated from the sun's height  (5,000 km) and the elevation angle.
Now, the main point I am trying to bring out is that on any "close sun" model the apparent size of the will vary, and we do not observe any  variation over a day.

Quote from: ski

Are you talking about the distances involved? Because I'd agree that the classical numbers of Rev. Voliva and Dr. Rowbotham can't possibly be correct.

You agree that the numbers are wrong. Well what about being less obtuse are presenting the correct model and correct distances for the movement of the sun over the flat earth.

It does look like the whole flat earthers attitude is simply that the earth is flat because it looks like it, but
no-one  knows what its layout is, no map,
no-one knows any distances,
no-one knows how the sun moves or how sunsets work,
no-one knows how lunar or solar eclipses work (I know it's in the Wiki, but when we quote that, you don't seem to accept it),
no-one knows even how moon phases work, and can be seen looking the same over half the earth.

I show that the sun's angular size remains constant. The Wiki tacitly assumes that it does vary, but only "appears" to stay constant.

Magnification of the Sun at Sunset
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 atmosphere.

Whoever could write that sort of thing? And the moon does essentially the same thing - "the intense rays of light" of the moon!

Just what do you know about your own Flat Earth? If someone knows, they're not telling us.
So many times jroa tires to show us his trig prowess and calculates the sun's height using the same old method - Voliva's - big deal!

All I see is you, sandokhan, sceptimatic and many others others finding perceived holes in the globe model, yet never presenting a plausible alternative.

Quote from: rabinoz on August 25, 2016, 10:37:34 PM

Quote from: Ski on August 25, 2016, 09:04:01 PM

Why? Are you talking about the distances involved? Because I'd agree that the classical numbers of Rev. Voliva and Dr. Rowbotham can't possibly be correct.

Not just distances, but the fact that the distance to the sun on any flat earth model must vary greatly during the day.

Well that sounds like an assumption to me...

Quote

On the flat earth as the sun gets further away, angular the size would be expected to reduce proportionately.

As opposed to ..?

Quote

The distances I showed in the OP were calculated from the sun's height  (5,000 km) and the elevation angle.
Now, the main point I am trying to bring out is that on any "close sun" model the apparent size of the will vary, and we do not observe any  variation over a day.

Quote from: ski

Are you talking about the distances involved? Because I'd agree that the classical numbers of Rev. Voliva and Dr. Rowbotham can't possibly be correct.

Hardly an assumption. It is basic geometry that you simply cannot ignore. A close-sun MUST therefore be vastly different in apparent angular size on different locations on a flat earth. That is absolutely undeniable unless you wish to now overturn geometry as well.

BUT on a distance sun, the angular size would be constant... and it is.

QED

Quote from: rabinoz on August 25, 2016, 10:37:34 PM

Now, the main point I am trying to bring out is that on any "close sun" model the apparent size of the will vary, and we do not observe any  variation over a day.

  Interesting... has anyone measured sun size during summer and winter? As the sun is quite farther in winter then there should also be difference in sun size, it should be noticeably smaller at winter than at summer.

As noted, "Matrix Decode" took those photos, and the date (9/Mar/2016) is close to the March equinox.
I wouldn't regard those photos as intended to determine accurately the sun's angular size, just the constancy over one day.
The numbers I gave were calculated from the specs of what I "guessed" was the camera used (I have a similar, but much older Fuji).

They did agree well with the expected sun's angular size, but I was not aiming for any absolute accuracy, just showing that it did not change throughout the day, even till close to sunset.

I imagine the same method could be used to compare the size in early January (closest sun) with that in early July (farthest sun), but I would "calibrate" the camera by taking test photos of known sized objects at known (long) distances.

Quote from: zork on August 25, 2016, 10:41:44 PM

Quote from: rabinoz on August 25, 2016, 10:37:34 PM

Now, the main point I am trying to bring out is that on any "close sun" model the apparent size of the will vary, and we do not observe any  variation over a day.

  Interesting... has anyone measured sun size during summer and winter? As the sun is quite farther in winter then there should also be difference in sun size, it should be noticeably smaller at winter than at summer.

As noted, "Matrix Decode" took those photos, and the date (9/Mar/2016) is close to the March equinox.
I wouldn't regard those photos as intended to determine accurately the sun's angular size, just the constancy over one day.
The numbers I gave were calculated from the specs of what I "guessed" was the camera used (I have a similar, but much older Fuji).

They did agree well with the expected sun's angular size, but I was not aiming for any absolute accuracy, just showing that it did not change throughout the day, even till close to sunset.

I imagine the same method could be used to compare the size in early January (closest sun) with that in early July (farthest sun), but I would "calibrate" the camera by taking test photos of known sized objects at known (long) distances.

However the difference between close and far in percentage terms is not very large and with the sun being a changing size due to its fiery nature I am not sure you will easily measure the difference.   How are you measuring the angular size of the Sun?

People were talking about Chicago mirage,
recorded video with Chicago skyline,
and behind Chicago was zoomed sunset.

It is " class="bbc_link" target="_blank" rel="noopener noreferrer">HERE.

As you can see, it doesn't change apparent size while setting.

However the difference between close and far in percentage terms is not very large

 If you are in northern hemisphere somewhere 500 km north of Tropic of Cancer then at the summer the sun is about 500 km from you. At winter when it circles near Tropic of Capricorn the sun is about 3700 km from you. Quite big difference.

Quote from: rabinoz on August 26, 2016, 12:38:36 AM

Quote from: zork on August 25, 2016, 10:41:44 PM

Quote from: rabinoz on August 25, 2016, 10:37:34 PM

Now, the main point I am trying to bring out is that on any "close sun" model the apparent size of the will vary, and we do not observe any  variation over a day.

  Interesting... has anyone measured sun size during summer and winter? As the sun is quite farther in winter then there should also be difference in sun size, it should be noticeably smaller at winter than at summer.

As noted, "Matrix Decode" took those photos, and the date (9/Mar/2016) is close to the March equinox.
I wouldn't regard those photos as intended to determine accurately the sun's angular size, just the constancy over one day.
The numbers I gave were calculated from the specs of what I "guessed" was the camera used (I have a similar, but much older Fuji).

They did agree well with the expected sun's angular size, but I was not aiming for any absolute accuracy, just showing that it did not change throughout the day, even till close to sunset.

I imagine the same method could be used to compare the size in early January (closest sun) with that in early July (farthest sun), but I would "calibrate" the camera by taking test photos of known sized objects at known (long) distances.

However the difference between close and far in percentage terms is not very large and with the sun being a changing size due to its fiery nature I am not sure you will easily measure the difference.   How are you measuring the angular size of the Sun?

I am not sure if you are referring to the angular size of the sun not varying much or the distance to the sun not varying much.

On the flat earth the distance from the observer to the sun varies tremendously on the flat earth. I have not worked it out for Malaga, but from a point on the equator at an equinox, the sun's distance should vary from
So in this case, the sun's angular size should vary from an estimated 0.57° down to 0.19°.

You ask, "How are you measuring the angular size of the Sun?"
From those pictures by measuring the sun's width and height in pixels and scaling by the estimates angular field of view of the camera. The problem with that is the without knowing the exact focal length of the lens and the effective image sensor size there will be errors. The fact that the angular size agreed with the sun's supposed angular size on the flat earth (50km/5,000km) was largely fortuitous.

When I used my camera for similar moon measurements I "calibrated" the camera by photographing a tape measure at a measured distance.

The calibration is not so very important as the intent was to show the constancy of size, not to measure the actual size accurately.

Quote from: Aliveandkicking on August 26, 2016, 05:31:44 AM

However the difference between close and far in percentage terms is not very large

 If you are in northern hemisphere somewhere 500 km north of Tropic of Cancer then at the summer the sun is about 500 km from you. At winter when it circles near Tropic of Capricorn the sun is about 3700 km from you. Quite big difference.

??

Edit:  OK we seem to be at crossed purposes.

I was saying the change in Earths orbit around the Sun is not very large between January and July

Quote from: zork on August 27, 2016, 03:24:21 AM

Quote from: Aliveandkicking on August 26, 2016, 05:31:44 AM

However the difference between close and far in percentage terms is not very large

 If you are in northern hemisphere somewhere 500 km north of Tropic of Cancer then at the summer the sun is about 500 km from you. At winter when it circles near Tropic of Capricorn the sun is about 3700 km from you. Quite big difference.

??

  I tought that you may say that. I didn't bother with calculations just took straight line on ground from observer to the sun.

Cheapest way that I know to measure angular diameter of the Sun is by using
cheap welding mask (wearable one is easier to use than hand-held), calliper,
and some ruler or stick to keep calliper at known distance from your eyes.
Actualy from the dark glass of the mask.

Ruler or stick should be just a bit shorter than your arm.

If angle is Phi, calliper Sun measure is d, and calliper eye distance is D, then

Phi = arctan ( d / D )

So no answer yet. That is not suprising, since the credibility of FE is just trash.

I was once given the following answer:
the Sun maintains its angular size due to atmosphere acting like a magnifying glass. But when asked about the magnification rate, someone wrote it follows the inverse square law, which doesn't match with the math.

Also, no answer what causes the magnification and how does the magnification rate matches perfectly for arbitrary observator.

So no answer yet. That is not suprising, since the credibility of FE is just trash.

I was once given the following answer:
the Sun maintains its angular size due to atmosphere acting like a magnifying glass. But when asked about the magnification rate, someone wrote it follows the inverse square law, which doesn't match with the math.

Also, no answer what causes the magnification and how does the magnification rate matches perfectly for arbitrary observator.

It can be "explained" by increase of magnification with observing angle.
Further the Sun, shallower the angle, more magnification.

But it doesn't explain why such magnification occurs.
How is it posible. More layers multiply refraction index of the air???
And why is not magnified gap between Sun and ground too.

Quote from: Brouwer on August 27, 2016, 09:06:51 AM

So no answer yet. That is not suprising, since the credibility of FE is just trash.

I was once given the following answer:
the Sun maintains its angular size due to atmosphere acting like a magnifying glass. But when asked about the magnification rate, someone wrote it follows the inverse square law, which doesn't match with the math.

Also, no answer what causes the magnification and how does the magnification rate matches perfectly for arbitrary observator.

It can be "explained" by increase of magnification with observing angle.
Further the Sun, shallower the angle, more magnification.

But it doesn't explain why such magnification occurs.
How is it posible. More layers multiply refraction index of the air???
And why is not magnified gap between Sun and ground too.

One thing I can never grasp is that if this "magnification" occurs it seems very fortuitous that the reduced them magnified sun manages to stay exactly the same size all through the day. In reality, it's much more constant than even those photos show.

But, no Flat Earther seems willing to explain this.

Are you certain that the angular size is exactly the same all throughout the day?

Are you certain that the angular size is exactly the same all throughout the day?

It is not the same all the day, you can find the measurements above.

It's change in size does not fit the expected change with the flat earth model.

With a small change/error of less than 2% the sun stays the same size.

Quote from: jroa on September 01, 2016, 05:30:47 AM

Are you certain that the angular size is exactly the same all throughout the day?

It is not the same all the day, you can find the measurements above.

It's change in size does not fit the expected change with the flat earth model.

With a small change/error of less than 2% the sun stays the same size.

Perhaps you were simply not expecting atmoplanic lensing?

Are you certain that the angular size is exactly the same all throughout the day?

Those measurements were only from scaling off photographs. But to within that accuracy, I would say that the sun's size does not change.

But on your Flat Earth model the distance from an observer to the sun varies but a big factor. For an observer on the equator at an equinox the sun is about 5,000 km away when overhead, but about 15,000 km away, so the sun size at sunset should be only 1/3 the size at noon.

And yes, I can tell you where the numbers came from, but surely a self-proclaimed maths genius can work it out!

When will you factor in refraction and perspective? 

Quote from: User324 on September 01, 2016, 05:32:07 AM

Quote from: jroa on September 01, 2016, 05:30:47 AM

Are you certain that the angular size is exactly the same all throughout the day?

It is not the same all the day, you can find the measurements above.

It's change in size does not fit the expected change with the flat earth model.

With a small change/error of less than 2% the sun stays the same size.

Perhaps you were simply not expecting atmoplanic lensing?

Why would that lensing magnify the Sun and skip magnifying the gap below the Sun?

And why would it selectively skip flying objects, like ISS?

You hate ISS and ordered the "lensing" to not magnify it so you won't have to look at it?