[rabinoz]

The Wiki gives the sun height as the same as the distance from the equator to latitude 45° North at "approximately 3,000 miles" in

Sun's Distance - Zetetic Cosmogony
Thomas Winship, author of Zetetic Cosmogony, provides a calculation demonstrating that the sun can be computed to be relatively close to the earth's surface if one assumes that the earth is flat --

On March 21-22 the sun is directly overhead at the equator and appears 45 degrees above the horizon at 45 degrees north and south latitude. As the angle of sun above the earth at the equator is 90 degrees while it is 45 degrees at 45 degrees north or south latitude, it follows that the angle at the sun between the vertical from the horizon and the line from the observers at 45 degrees north and south must also be 45 degrees. The result is two right angled triangles with legs of equal length. The distance between the equator and the points at 45 degrees north or south is approximately 3,000 miles. Ergo, the sun would be an equal distance above the equator.

This is illustrated in this diagram from Modern Mechanics - Oct, 1931:

Voliva's Flat Earth Sun Distance.

This is also shown in the Wiki under Distance to the Sun under the section Sun's Distance - Modern Mechanics.

But this calculates the height from only ONE location, Latitude 45°. In would seem that we would get a more accurate result by taking measurements from a number of different latitudes and averaging the result.

In Finding your Latitude and Longitude the Wiki says:

Latitude
To locate your latitude on the Flat Earth, it's important to know the following fact: The degrees of the Earth's Latitude are based upon the angle of the sun in the sky at noon equinox.
That's why 0˚ N/S sits on the equator where the sun is directly overhead, and why 90˚ N/S sits at the poles where the sun is at a right angle to the observer. At 45 North or South from the equator, the sun will sit at an angle 45˚ in the sky. The angle of the sun past zenith is our latitude.
Knowing that as you recede North or South from the equator at equinox, the sun will descend at a pace of one degree per 69.5 miles, we can even derive our distance from the equator based upon the position of the sun in the sky.

So this quote from the Wiki tells how far we would be from the equator and what the sun's angle would be at any latitude.

This enables us calculate the sun's height from
h = d x tan(Θ), where "d" is the distance from the equator, d = 69.5 x Θ,
and the sun's elevation Θ = (90° - Latitude),  as illustrated in:

The sun's height, calculated using this method for a number of latitudes is shown in the following table:

Latitude	Sun Elevation, Θ	Distance from Equator, d	Sun Height, h
7.2° N	82.8°	500 miles	3,961 miles
15° N	75°	1,043 miles	3,891 miles
45° N	45°	3,128 miles	3,128 miles
75° N	15°	5,213 miles	1,397 miles
85° N	5°	5,908 miles	517 miles

Here we see that at a latitude of 45° N (3,128 miles from the equator) the sun's height comes out to be 3,128 miles, more or less as expected.
But, at all other latitudes we get quite different results ranging from 3,961 miles at 7.2° N from the equator to only 517 miles at 85° N.

All of the figures used have come from the Wiki, and the calculation is based on the method from the Wiki.

So can someone explain why these calculations (using the method from the Wiki) give such different figures for the sun's height?

I know the same point has been raise numerous times, but has never been given a reasonable answer.

[brainsandgravy]

The Wiki gives the sun height as the same as the distance from the equator to latitude 45° North at "approximately 3,000 miles" in

Sun's Distance - Zetetic Cosmogony
Thomas Winship, author of Zetetic Cosmogony, provides a calculation demonstrating that the sun can be computed to be relatively close to the earth's surface if one assumes that the earth is flat --

On March 21-22 the sun is directly overhead at the equator and appears 45 degrees above the horizon at 45 degrees north and south latitude. As the angle of sun above the earth at the equator is 90 degrees while it is 45 degrees at 45 degrees north or south latitude, it follows that the angle at the sun between the vertical from the horizon and the line from the observers at 45 degrees north and south must also be 45 degrees. The result is two right angled triangles with legs of equal length. The distance between the equator and the points at 45 degrees north or south is approximately 3,000 miles. Ergo, the sun would be an equal distance above the equator.

This is illustrated in this diagram from Modern Mechanics - Oct, 1931:

Voliva's Flat Earth Sun Distance.

This is also shown in the Wiki under Distance to the Sun under the section Sun's Distance - Modern Mechanics.

But this calculates the height from only ONE location, Latitude 45°. In would seem that we would get a more accurate result by taking measurements from a number of different latitudes and averaging the result.

In Finding your Latitude and Longitude the Wiki says:

Latitude
To locate your latitude on the Flat Earth, it's important to know the following fact: The degrees of the Earth's Latitude are based upon the angle of the sun in the sky at noon equinox.
That's why 0˚ N/S sits on the equator where the sun is directly overhead, and why 90˚ N/S sits at the poles where the sun is at a right angle to the observer. At 45 North or South from the equator, the sun will sit at an angle 45˚ in the sky. The angle of the sun past zenith is our latitude.
Knowing that as you recede North or South from the equator at equinox, the sun will descend at a pace of one degree per 69.5 miles, we can even derive our distance from the equator based upon the position of the sun in the sky.

So this quote from the Wiki tells how far we would be from the equator and what the sun's angle would be at any latitude.

This enables us calculate the sun's height from
h = d x tan(Θ), where "d" is the distance from the equator, d = 69.5 x Θ,
and the sun's elevation Θ = (90° - Latitude),  as illustrated in:

The sun's height, calculated using this method for a number of latitudes is shown in the following table:

Latitude	Sun Elevation, Θ	Distance from Equator, d	Sun Height, h
7.2° N	82.8°	500 miles	3,961 miles
15° N	75°	1,043 miles	3,891 miles
45° N	45°	3,128 miles	3,128 miles
75° N	15°	5,213 miles	1,397 miles
85° N	5°	5,908 miles	517 miles

Here we see that at a latitude of 45° N (3,128 miles from the equator) the sun's height comes out to be 3,128 miles, more or less as expected.
But, at all other latitudes we get quite different results ranging from 3,961 miles at 7.2° N from the equator to only 517 miles at 85° N.

All of the figures used have come from the Wiki, and the calculation is based on the method from the Wiki.

So can someone explain why these calculations (using the method from the Wiki) give such different figures for the sun's height?

I know the same point has been raise numerous times, but has never been given a reasonable answer.

The only answer I got on this forum on a similar question was:

Why are you trying to use unverified ancient geometry/trigonometry as a proof of anything?

The Ancient Greeks did not verify that circles actually exist, and they did not verify that perspective lines actually stretch into infinity as they theorized.

You see, you're assuming that greek trigonometry is valid. You think that it works. But on a flat earth, it doesn't. Geometry is false on the flat earth.

[Rounder]

You see, you're assuming that greek trigonometry is valid. You think that it works. But on a flat earth, it doesn't. Geometry is false on the flat earth.

Why then did Rowbotham use the same technique? 

[brainsandgravy]

You see, you're assuming that greek trigonometry is valid. You think that it works. But on a flat earth, it doesn't. Geometry is false on the flat earth.

Why then did Rowbotham use the same technique?

That's a good question. I assume it's because geometry is valid when it supports the flat earth, but when it doesn't, then it's conveniently rendered "unverified".

[rabinoz]

You see, you're assuming that greek trigonometry is valid. You think that it works. But on a flat earth, it doesn't. Geometry is false on the flat earth.

Why then did Rowbotham use the same technique?

That's a good question. I assume it's because geometry is valid when it supports the flat earth, but when it doesn't, then it's conveniently rendered "unverified".

Now you're getting the message!

[Tom Bishop]

The sun's height, calculated using this method for a number of latitudes is shown in the following table:

Are those real world observations, or hypothetical ones?

[TotesNotReptilian]

The sun's height, calculated using this method for a number of latitudes is shown in the following table:

Are those real world observations, or hypothetical ones?

He is using angles of the sun from the horizon for various latitudes at noon on the equinoxes. These angles are well known, and easily observable. This is an easy to use website that you can get this data from. Do you have reason to believe that any of this data is wrong? If so, feel free to present it...

The only thing that is reasonably controversial from a flat-earther's perspective is the distance from the equator that he gives (since flat-earthers can't agree on an actual map). Do you have reason to believe that the distances from the equator are wrong? If so, feel free to present it...

[rabinoz]

The sun's height, calculated using this method for a number of latitudes is shown in the following table:

Are those real world observations, or hypothetical ones?

As real as Voliva's were!

My point is why did Voliva "happen" to chose 45˚ for his measurement and
you might have noticed that your Wiki contains"
Finding your Latitude and Longitude the Wiki says:

Latitude
To locate your latitude on the Flat Earth, it's important to know the following fact: The degrees of the Earth's Latitude are based upon the angle of the sun in the sky at noon equinox.
That's why 0˚ N/S sits on the equator where the sun is directly overhead, and why 90˚ N/S sits at the poles where the sun is at a right angle to the observer. At 45 North or South from the equator, the sun will sit at an angle 45˚ in the sky. The angle of the sun past zenith is our latitude.
Knowing that as you recede North or South from the equator at equinox, the sun will descend at a pace of one degree per 69.5 miles, we can even derive our distance from the equator based upon the position of the sun in the sky.

So this quote from the Wiki tells how far we would be from the equator and what the sun's angle would be at any latitude.

If I took the measurements you would only doubt them, but surely you cannot doubt your own Wiki!

So please tell us, what IS the height of the sun? 

[Rounder]

Are those real world observations, or hypothetical ones?

Rowbotham claims to have made real world observations.  Quoting directly from the flat earth bible, Earth Not A Sphere, Chapter V The True Distance of the Sun:

The distance from London Bridge to the sea-coast at Brighton, in a straight line, is 50 statute miles. On a given day, at 12 o'clock, the altitude of the sun, from near the water at London Bridge, was found to be 61 degrees of an arc; and at the same moment of time the altitude from the sea-coast at Brighton was observed to be 64 degrees of an arc, as shown in fig. 58. The base-line from L to B, 50 measured statute miles; the angle at L, 61 degrees; and the angle at B, 64 degrees. In addition to the method by calculation, the distance of the under edge of the sun may be ascertained from these elements by the method called "construction."

The diagram, fig. 58, is the above case "constructed;" that is, the base-line from L to B represents 50 statute miles; and the line L, S, is drawn at an angle of 61 degrees, and the line B, S, at an angle of 64 degrees. Both lines are produced until they bisect or cross each other at the point S. Then, with a pair of compasses, measure the length of the base-line B, L, and see how many times the same length may be found in the line L, S, or B, S. It will be found to be sixteen times, or sixteen times 50 miles, equal to 800 statute miles. Then measure in the same way the vertical line D, S, and it will be found to be 700 miles. Hence it is demonstrable that the distance of the sun over that part of the earth to which it is vertical is only 700 statute miles. By the same mode it may be ascertained that the distance from London of that part of the earth where the sun was vertical at the time (July 13th, 1870) the above observations were taken, was only 400 statute miles, as shown by dividing the base-line L, D, by the distance B, L. 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 increases 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.

[Tom Bishop]

The sun's height, calculated using this method for a number of latitudes is shown in the following table:

Are those real world observations, or hypothetical ones?

He is using angles of the sun from the horizon for various latitudes at noon on the equinoxes. These angles are well known, and easily observable. This is an easy to use website that you can get this data from. Do you have reason to believe that any of this data is wrong? If so, feel free to present it...

The only thing that is reasonably controversial from a flat-earther's perspective is the distance from the equator that he gives (since flat-earthers can't agree on an actual map). Do you have reason to believe that the distances from the equator are wrong? If so, feel free to present it...

The figures on that website do not claim to come from observations.

[Tom Bishop]

The sun's height, calculated using this method for a number of latitudes is shown in the following table:

Are those real world observations, or hypothetical ones?

As real as Voliva's were!

No one said Voliva was an unimpeachable god.

My point is why did Voliva "happen" to chose 45˚ for his measurement and
you might have noticed that your Wiki contains"
Finding your Latitude and Longitude the Wiki says:

Latitude
To locate your latitude on the Flat Earth, it's important to know the following fact: The degrees of the Earth's Latitude are based upon the angle of the sun in the sky at noon equinox.
That's why 0˚ N/S sits on the equator where the sun is directly overhead, and why 90˚ N/S sits at the poles where the sun is at a right angle to the observer. At 45 North or South from the equator, the sun will sit at an angle 45˚ in the sky. The angle of the sun past zenith is our latitude.
Knowing that as you recede North or South from the equator at equinox, the sun will descend at a pace of one degree per 69.5 miles, we can even derive our distance from the equator based upon the position of the sun in the sky.

So this quote from the Wiki tells how far we would be from the equator and what the sun's angle would be at any latitude.

If I took the measurements you would only doubt them, but surely you cannot doubt your own Wiki!

Why can't we doubt the Wiki? Those writings come from a number of sources. It's a user editable online encyclopedia.

[Tom Bishop]

Are those real world observations, or hypothetical ones?

Rowbotham claims to have made real world observations.  Quoting directly from the flat earth bible, Earth Not A Sphere, Chapter V The True Distance of the Sun:

If so, then that makes Rowbotham's evidence stronger than the litany of hypothetical observations suggested by others.

[Rama Set]

Are those real world observations, or hypothetical ones?

Rowbotham claims to have made real world observations.  Quoting directly from the flat earth bible, Earth Not A Sphere, Chapter V The True Distance of the Sun:

If so, then that makes Rowbotham's evidence stronger than the litany of hypothetical observations suggested by others.

You don't know that Rowbotham's observations were real or hypothetical.

[Tom Bishop]

Are those real world observations, or hypothetical ones?

Rowbotham claims to have made real world observations.  Quoting directly from the flat earth bible, Earth Not A Sphere, Chapter V The True Distance of the Sun:

If so, then that makes Rowbotham's evidence stronger than the litany of hypothetical observations suggested by others.

You don't know that Rowbotham's observations were real or hypothetical.

It's certainly stronger than a hypothetical proposition. To make it even stronger we need to have peer review. I would be curious to see what the journal Earth Not a Globe Review found on this subject when they did their review of the work.

[rabinoz]

Are those real world observations, or hypothetical ones?

Rowbotham claims to have made real world observations.  Quoting directly from the flat earth bible, Earth Not A Sphere, Chapter V The True Distance of the Sun:

If so, then that makes Rowbotham's evidence stronger than the litany of hypothetical observations suggested by others.

I have read that long ago, and he says:

The distance from London Bridge to the sea-coast at Brighton, in a straight line, is 50 statute miles. On a given day, at 12 o'clock, the altitude of the sun, from near the water at London Bridge, was found to be 61 degrees of an arc; and at the same moment of time the altitude from the sea-coast at Brighton was observed to be 64 degrees of an arc, as shown in fig. 58. The base-line from L to B, 50 measured statute miles; the angle at L, 61 degrees; and the angle at B, 64 degrees. In addition to the method by calculation, the distance of the under edge of the sun may be ascertained from these elements by the method called "construction." The diagram, fig. 58, is the above case "constructed;" that is, the base-line from L to B represents 50 statute miles; and the line L, S, is drawn at an angle of 61 degrees, and the line B, S, at an angle of 64 degrees. Both lines are produced until they bisect or cross each other at the point S. Then, with a pair of compasses, measure the length of the base-line B, L, and see how many times the same length may be found in the line L, S, or B, S. It will be found to be

FIG. 58.

sixteen times, or sixteen times 50 miles, equal to 800 statute miles. Then measure in the same way the vertical line D, S, and it will be found to be 700 miles. Hence it is demonstrable that the distance of the sun over that part of the earth to which it is vertical is only 700 statute miles. By the same mode it may be ascertained that the distance from London of that part of the earth where the sun was vertical at the time (July 13th, 1870) the above observations were taken, was only 400 statute miles, as shown by dividing the base-line L, D, by the distance B, L. 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 increases 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.

I do think that Samuel Birley Rowbotham conforms precisely what I claimed in my first post! Working from different baselines gives completely different answers!^[1]
As we used to add in our geometry (Euclidean I believe - though no-one said to) of many years ago: Quod Erat Demonstrandum

[1] Actually, there is more to it than that. I haven't time just now, but I'll find my earlier work and you might find his work not quite so "bad".

[brainsandgravy]

Are those real world observations, or hypothetical ones?

Rowbotham claims to have made real world observations.  Quoting directly from the flat earth bible, Earth Not A Sphere, Chapter V The True Distance of the Sun:

If so, then that makes Rowbotham's evidence stronger than the litany of hypothetical observations suggested by others.

Rowbotham states, "The foregoing remarks and illustrations are, of course, not necessary to the mathematician; but may be useful to the general reader, showing him that plane trigonometry, carried out on the earth's plane or horizontal surface, permits of operations which are simple and perfect in principle, and in practice fully reliable and satisfactory."

Why do you think Rowbotham would be endorsing "that Ancient Greek nonsense math where things are continuous and divide or stretch into infinities?" Was he not "assuming conclusions based on an Ancient Greek fantasy model where things are continuous, rather than an experience of the real world."?

[rabinoz]

Actually, there is more to it than that. I haven't time just now, but I'll find my earlier work and you might find his work not quite so "bad".

Yes, I said "you might find his work not quite so 'bad'"!

Rowbotham has Brighton to London as 50 miles and a change in the sun's elevation of 61.0° to 64.0° or 3°. A little thought would show that 50 miles could never give a 3° change in latitude of sun's elevation (not if we accept "the Wiki's" 69.5 miles per degree).

Checking these figures on Google Earth puts Brighton Pier (on the beach just west of the pier - yes, I've been there) at Lat 50.82° and London (just west of the north end of London  Bridge - can't get near the water on the south end) at Lat 51.51°, putting these locations into Sun Earth Tools for July 13th⁽¹⁾ we get the suns elevation in London as 60.33° and in Bright as 61.02°⁽²⁾.

Now, using these figures, we get the sun's height as 3030 miles - much closer to the Flat Earth accepted figure!

But, no-one has yet given any justification for picking Lat 45° N as the one spot to calculate the sun's height, simply because there is none!

• I don't think the time is given, so I am guessing about 12 noon and can't go back as far as 1870, so used 2016.
• Why so different from Rowbotham? Simply that his measurements with "an instrument with a graduated arc" were not accurate enough for such small differences. I won't criticise him too much for that, but modern reviews have been very remiss it not correcting it.

 

[TotesNotReptilian]

The sun's height, calculated using this method for a number of latitudes is shown in the following table:

Are those real world observations, or hypothetical ones?

He is using angles of the sun from the horizon for various latitudes at noon on the equinoxes. These angles are well known, and easily observable. This is an easy to use website that you can get this data from. Do you have reason to believe that any of this data is wrong? If so, feel free to present it...

The only thing that is reasonably controversial from a flat-earther's perspective is the distance from the equator that he gives (since flat-earthers can't agree on an actual map). Do you have reason to believe that the distances from the equator are wrong? If so, feel free to present it...

The figures on that website do not claim to come from observations.

Of course not. They just made a fancy way of presenting already well-known data. The position of the sun in the sky has been measured for thousands of years using sun dials. You can get this data on hundreds of different websites and libraries around the world. If this data was wrong, millions of people would notice.

You can test it yourself if you want:

Angle = arctan(height of sundial / length of shadow)

Use this website (Or one of a hundred others like it) to calculate the position of the sun for your specific location and time.

Don't claim that well-known, easily-testable, public-available data is fake unless you have personally tested it and found inconsistent results yourself.

[Rounder]

If so, then that makes Rowbotham's evidence stronger than the litany of hypothetical observations suggested by others.

Do you really want to defend his results?  He calculated the sun to be a mere 700 miles up, and the subsolar point only 400 miles away.  The Wiki, so beloved by FE proponents, has the sun over four times as high, and the nearest the subsolar point EVER gets to London is over the Tropic of Cancer, some two THOUSAND miles away, more than five times as far.

[rabinoz]

If so, then that makes Rowbotham's evidence stronger than the litany of hypothetical observations suggested by others.

Do you really want to defend his results?  He calculated the sun to be a mere 700 miles up, and the subsolar point only 400 miles away.  The Wiki, so beloved by FE proponents, has the sun over four times as high, and the nearest the subsolar point EVER gets to London is over the Tropic of Cancer, some two THOUSAND miles away, more than five times as far.

Then if you look at my previous post in The Sun's height from the method and distances in "the Wiki" « Reply #16 on: Today at 02:48:56 AM » I show that Rowbotham had a ridiculous 3° difference in solar elevation from Brighton (near the Pier) to London (near water at N end)^[1]. The difference in latitude is only 0.69° and as expected SunEarthtools gives a difference in solar elevation of (guess what!) 0.69° at midday on that date.

These figures put the sun at a height of 3030 miles. But, this does not get away from fact that the apparent sun height varies dramatically with the baseline -

and they simply will not address the problem!

[1] Rowbotham could have looked at a map - too simple!