The impossibilities of Flat Earth - intellectual debate

Quote from: Jadyyn on December 15, 2015, 02:46:30 PM

When measuring the drop horizontally across the picture, I am not sure what latitude has to do with anything. Please explain why latitude is important.

See this sphere. The circumference at the equator (our definition; the middle of the sphere) is the largest. That makes the curvature the smallest and thus drop from horizontal tangent smallest.

Gradually towards the poles (so with increasing latitude) the circles (2D horizontal slices of the sphere) get smaller and smaller.

On Earth the equator has a circumference of 40,075 km
@ 30 degrees latitude it is the cosine of 30 of that; 86.6 %, so 34,750 km; 5325 km less circle here...

The curvature increases with a smaller circumference, so does the drop.

If you really want to prove it to yourself, cut an orange in slices and measure the circumference of them.

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Anywhere, facing any direction, the horizon is based on the same 39,940.65 km distance.

It would be incorrect to take the longitude value for latitude for 2 reasons:
1 - the circumference of latitudes is not the same as that of equator and less that of a longitude
2 - the Earth is not fully a sphere; see the differences between r(polar) and r(equator) Teutarch provided. This makes there's a slight shortening on the top, which makes the longitude "circles" actually a tad elliptical.

That longitude and latitude are different on Earth thus causes a slightly different drop when looking E-W (along latitude) versus N-S (along longitude) when the distances are equal. In New Orleans that difference is about 2 meters, in Oslo that would be much more and a little bit north or south from the equator (Singapore and Guayaquil more or less without looking at a map) the difference is zero (at the latitude where the circumference = 39,940.65, so at about 4.7 degrees North and South.

As the latitude progresses (see the image), this difference is of course increasing.

At 43 degrees (Genova), the circumference is just under 30,000 km.
But when standing in Quito (equator), the circumference is 40,000 km.
25 % difference.
In New Orleans @ 30 deg latitude, it's 13.4 % difference.

In Oslo and Ushuaia (55 deg N/S) the circumference is just under 24,000 km; 57% of the equator...

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This is how they explain it. The atmosphere acts like a magnifying glass (though they cannot explain what creates that effect), which makes the Sun always the same size.

 

A "magnifying glass" that makes things "always the same size"? Made by The Mad Hatter?

I heard a Flat Earther say "@ around 5000 km/3000 miles" so used that number. But it's even worse then?

I don't get what you are saying here at all. But it sounds ridiculous.

Yeah, this "dome". Domes are not common in nature, so the only dome would be over the Earth.  And what about meteors? Yesterday the Geminids were observable from Earth; meteor showers; extraterrestial material burning up due to the friction of the atmosphere (I guess they didn't have one of those magical NASA 'heat shields'...), did anyone observe them crashing on the dome? Or do they come from within it and do we need to worry about the cohesive strength of it? Is it falling apart?

That's shocking. My questions are simple and straightforward. That I would be the first one to ask this question since 1800 is beyond comprehension.

No worries, you did great.

Quote from: Gaia_Redonda on December 15, 2015, 03:15:02 PM

Quote from: Jadyyn on December 15, 2015, 02:46:30 PM

When measuring the drop horizontally across the picture, I am not sure what latitude has to do with anything. Please explain why latitude is important.

See this sphere. The circumference at the equator (our definition; the middle of the sphere) is the largest. That makes the curvature the smallest and thus drop from horizontal tangent smallest.

Gradually towards the poles (so with increasing latitude) the circles (2D horizontal slices of the sphere) get smaller and smaller.

On Earth the equator has a circumference of 40,075 km
@ 30 degrees latitude it is the cosine of 30 of that; 86.6 %, so 34,750 km; 5325 km less circle here...

The curvature increases with a smaller circumference, so does the drop.

If you really want to prove it to yourself, cut an orange in slices and measure the circumference of them.

Quote

Anywhere, facing any direction, the horizon is based on the same 39,940.65 km distance.

It would be incorrect to take the longitude value for latitude for 2 reasons:
1 - the circumference of latitudes is not the same as that of equator and less that of a longitude
2 - the Earth is not fully a sphere; see the differences between r(polar) and r(equator) Teutarch provided. This makes there's a slight shortening on the top, which makes the longitude "circles" actually a tad elliptical.

That longitude and latitude are different on Earth thus causes a slightly different drop when looking E-W (along latitude) versus N-S (along longitude) when the distances are equal. In New Orleans that difference is about 2 meters, in Oslo that would be much more and a little bit north or south from the equator (Singapore and Guayaquil more or less without looking at a map) the difference is zero (at the latitude where the circumference = 39,940.65, so at about 4.7 degrees North and South.

As the latitude progresses (see the image), this difference is of course increasing.

At 43 degrees (Genova), the circumference is just under 30,000 km.
But when standing in Quito (equator), the circumference is 40,000 km.
25 % difference.
In New Orleans @ 30 deg latitude, it's 13.4 % difference.

In Oslo and Ushuaia (55 deg N/S) the circumference is just under 24,000 km; 57% of the equator...

Pick a point. 'Turn' the earth so that it is at the top. Calculate.  Answer is approx the same wherever you are.

Those aren't the accepted figures that everyone else uses to calculate horizons and drops Gaia

- this is a well used calculation for many applications, one of which is determining the distance a lighthouse is visible. your figures should roughly match http://www.sailtrain.co.uk/navigation/rising.htm which shows a drop of 10 meters over 8 nm and 75 meters over 20nm - which just happens to be 37km

Remember that on a globe the shortest distance between two point on the same lattitude is not a straight line, it's a great circle

- and if you take a slice that goes through the equator (which you should because that thats the direct sightline) lattitude does not come into the equation.

Also remember that whichever way you are looking, if you slice in that direction the slice always goes through the center - the formula for the cirumference of a sphere is the same as for a circle and is equal to 3.1416 times the Diameter. anything else is not the circumference of the sphere.

There is one simple point I have not seen mentioned.
Thanks to Napoleon the definition of the metre was originally one ten millionth of the distance from the equator to the North Pole along the line of longitude through Paris.
And the (British) nautical mile (now accepted as 6080 ft) was defined as one sixtieth of one degree at the equator.
I don't see how anyone could argue that these are very much in error.
So presumably we can accept that on the Flat Earth map the radius of the equator is close to 10,000 km, or 6214 miles,
hence the Flat Earth Equatorial circumference has to be 2xπx6214 miles or 39,042 miles.
We know, however that the earth has an equatorial circumference of very close to 360x60 = 21,600 nm or 24,873 miles.

Maybe some kind proponent of the Flat Earth map could explain this readily proven discrepancy!

Quote from: Teutarch on December 16, 2015, 02:00:45 AM

I don't know what you mean by "accepted figures", accepted by whom?

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- this is a well used calculation for many applications, one of which is determining the distance a lighthouse is visible. your figures should roughly match http://www.sailtrain.co.uk/navigation/rising.htm which shows a drop of 10 meters over 8 nm and 75 meters over 20nm - which just happens to be 37km

1 - this is about light and visibility. That is not curvature alone; also atmospheric effects play a role. The strength of the eye, etc. No this is purely visibility and when you can actually see the light above the horizon - you can see the bloom(beam) of the light before but that cannot be used to calculate a distance from it
2 - the test has been done at latitude 46.5. There the E-W great circle (the latitude) is much smaller than in New Orleans But they were looking south not east - west and anyway it doesnt matter where you are or what direction you are looking at. take slice through an orange thats equal and the circumference will be roughly the same anywhere - (assuming its not a pear)
3 - how can these numbers ever be correct if we're talking curvature only?What?
a - equator = 8 inch per mile (1602 m) = 0.2032/1.602 = 12.7 cm/kmfine for the first mile but you cant just add them you should recalculate each mile
b - 46.5 degrees lat N = 10 m / 8 nautical miles (1852 m) = 5.4 meters/km and75 m/20 nm = 2.02 m/km?what

It is impossible that the drop (the mathematical; no visual effects involved) is different over 8 nautical miles than over 20. It should be the same; a circle has constant curvature. I immediately believe it's different as we're talking light houses, but that is then a visual effect, not a geometrical one. It's not impossible and I measured it with my circle and proved that it more than doubles - those distance tables have been used all last century to help with navigation of ships at sea. Or google horizon calculator, no one else on line takes into account of lattitude and if they did it would only be effective when looking east wetst

Under certain climatic conditions (thermal inversion layers), it is possible to see fata morganas.

Bringing visual into the equation unnecessarily complicates things.but we're talking about visual horizons

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Remember that on a globe the shortest distance between two point on the same lattitude is not a straight line, it's a great circle

What I've been saying the whole time; we only can look along the curve of the circle/sphere ("s" in the drawing).No, thats not the shortest route, the shortest route between two points at the same lattitude does not follow the line of latitude between them except on the equator

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- and if you take a slice that goes through the equator (which you should because that thats the direct sightline) lattitude does not come into the equation.

I position the pictures therefore:
X = E-W is along the latitude great circle (varies with latitude)There is no such thing as
Y = N-S is along the longitude great circle (always the same, wherever on Earth)

In any 3D view (from left to right across New Orleans and from lake to city towards New Orleans) you always have both circles to take into account. The difference between these two circles around the equator can be neglected, so one could say "drop of 8"/mile in every direction".

You see the exercises on that page you linked where the bearing is included. Of course, because the great circle there in England is ~30% shorter than the equator... Bearing is included because if you know the distance (which you do when the light appears from the table) then with the bearing you can plot your position as well. Trust me I'm a skipper

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Also remember that whichever way you are looking, if you slice in that direction the slice always goes through the center - the formula for the cirumference of a sphere is the same as for a circle and is equal to 3.1416 times the Diameter. anything else is not the circumference of the sphere.

Yes and if we neglect the flattening of the Earth and take it as a perfect sphere, still any latitude great circle is smaller than the equator. Slice that orange.

It only would make the longitude great circles (now 39,750 km) equal to that of the equator (40,075 km).

But you see; when you start mixing up geometrical drop and visual values, it gets confusing; apples and pears.

A drop of 75 m / 20 nm (or 37 km) would make the islands of the Mediterranean for the most part invisible, as they are 150 km away; a drop of 303.7 meters!
Using the 10 m / 8 nm (or 14.8 km) would make the drop 101.2 m.They Are - I've been to the mediterranian in october and skipper a yacht around I stood on top of a mountain in Corfu and can tell you that italy is not visible even with perfect visibility - except if there is some sort of RARE TEMPORARY atmospheric effect thats 122km away  I was at an elevation of 1000 meters (ish)

These numbers cannot be different for geometry. For visual, sure, not geometry. That may be where the confusion comes from; that somehow there should be a squared relation and variable drops and curvatures along a circle.

The Earth is just far too big to have geometrical drops like that: Size matters not, a circle is a circle is a circle drop is a geometric progression

1/4 circumference = 90 degrees -> 1 degree of the circle is 111.32 km @ equator.

The drawings used to advocate Flat Earth are exaggerated. We are only able to see a tiny part of this giant sphere... even from the air the curvature is not visible (apparent curvature due to lens effects of windows aside). I agree but your maths is still wrong. You come with figures for drop that are smaller than they actually are.

We are too small and I am too big.

There is one simple point I have not seen mentioned.
Thanks to Napoleon the definition of the metre was originally one ten millionth of the distance from the equator to the North Pole along the line of longitude through Paris.
And the (British) nautical mile (now accepted as 6080 ft) was defined as one sixtieth of one degree at the equator.
I don't see how anyone could argue that these are very much in error.
So presumably we can accept that on the Flat Earth map the radius of the equator is close to 10,000 km, or 6214 miles,
hence the Flat Earth Equatorial circumference has to be 2xπx6214 miles or 39,042 miles.
We know, however that the earth has an equatorial circumference of very close to 360x60 = 21,600 nm or 24,873 miles.

Maybe some kind proponent of the Flat Earth map could explain this readily proven discrepancy!

I agree that if you slice off a portion of an orange that does not go through the centre the circumference and radius of that circle will differ from the orginal sphere.

Redifine this problem for yourself.

My base point was a comment by a Flat Earther that I have been using all the time "drop of 8" per mile at equator".

That must be wrong then? And causes the crazy difference between my calculations and the light house numbers which are obviously unquestionable; it's your survival.

How much do these numbers change due to weather? The foggy coasts of Britain behave different from a crystal clear polar night or the coast of dry Mauritania?

There are many, many donkeys in a drove living their lives confined within a fence line on the ranch. They share in the bounty of food and drink served to them for a lifetime.  Drinking from the trough and enjoying the groundnut hay, sorghum stover, and salt lick without ever realizing the variety of food and drink existing outside of the ranch.

There is a team of thoroughbreds who came across the drove, amused by the limited vision the donkeys possessed even though the pack seemed convinced this ranch life extended to the rest of land they inhabited.

The thoroughbreds had traveled the width and breadth of the land experiencing first-hand reality around them, enjoying fresh water from the stream and consuming the rich sources of available food offered in nature. 

Try as they may, the thoroughbreds could not convince the drove that there is something beyond what they experience on the ranch.  The drove had a reputation for obstinacy and an inability to comprehend that a treasure exists in reality...and that reality is what we call the truth. 

Their reputation, as demonstrated, exists to this day since the knowledge brought forth by the thoroughbreds continues to be disregarded.

Quote from: gotham on December 15, 2015, 02:40:13 PM

There are many, many donkeys in a drove living their lives confined within a fence line on the ranch. They share in the bounty of food and drink served to them for a lifetime.  Drinking from the trough and enjoying the groundnut hay, sorghum stover, and salt lick without ever realizing the variety of food and drink existing outside of the ranch.

There is a team of thoroughbreds who came across the drove, amused by the limited vision the donkeys possessed even though the pack seemed convinced this ranch life extended to the rest of land they inhabited.

The thoroughbreds had traveled the width and breadth of the land experiencing first-hand reality around them, enjoying fresh water from the stream and consuming the rich sources of available food offered in nature. 

Try as they may, the thoroughbreds could not convince the drove that there is something beyond what they experience on the ranch.  The drove had a reputation for obstinacy and an inability to comprehend that a treasure exists in reality...and that reality is what we call the truth. 

Their reputation, as demonstrated, exists to this day since the knowledge brought forth by the thoroughbreds continues to be disregarded.

Reported for derailment and off-topic posting.

Hiya, and welcome to the trenches. I think the biggest problem with flat earthers is that they misrepresent the round earth and basically make straw man arguments.

Quote from: rabinoz on December 16, 2015, 04:43:23 AM

There is one simple point I have not seen mentioned.
Thanks to Napoleon the definition of the metre was originally one ten millionth of the distance from the equator to the North Pole along the line of longitude through Paris.
And the (British) nautical mile (now accepted as 6080 ft) was defined as one sixtieth of one degree at the equator.
I don't see how anyone could argue that these are very much in error.
So presumably we can accept that on the Flat Earth map the radius of the equator is close to 10,000 km, or 6214 miles,
hence the Flat Earth Equatorial circumference has to be 2xπx6214 miles or 39,042 miles.
We know, however that the earth has an equatorial circumference of very close to 360x60 = 21,600 nm or 24,873 miles.

Maybe some kind proponent of the Flat Earth map could explain this readily proven discrepancy!

What flat earth map?

What is the general belief regarding other planets?

Do we think all planets are flat?

Quote from: Andromeda Galaxy on December 17, 2015, 05:22:35 PM

What is the general belief regarding other planets?

Do we think all planets are flat?

Good question, but it seems impossible to have a flat Mercury and Venus as the phases can be observed.

Also the Sun must be spherical in the Flat Earth idea as it looks circular from wherever you are on Earth and only spheres can produce that effect.

What is the general belief regarding other planets?

Do we think all planets are flat?

Quote from: Gaia_Redonda on December 17, 2015, 05:27:57 PM

Quote from: Andromeda Galaxy on December 17, 2015, 05:22:35 PM

What is the general belief regarding other planets?

Do we think all planets are flat?

Good question, but it seems impossible to have a flat Mercury and Venus as the phases can be observed.

Also the Sun must be spherical in the Flat Earth idea as it looks circular from wherever you are on Earth and only spheres can produce that effect.

I'm often out with my telescope, yet to observe a flat planet 

I was interested to hear what flat earthers opinions were on this, is planet Earth the exception?

I would be interested to know how many science graduates believe in a flat earth?

I would be interested to know how many science graduates believe in a flat earth?

Quote from: Andromeda Galaxy on December 17, 2015, 05:49:39 PM

I would be interested to know how many science graduates believe in a flat earth?

Tell me how on earth you would graduate , if you didnt parrot what you were told you had to parrot, if you wanted to graduate.?just one example of thousands .it use to be standard practice for years ,  taught as first aid in  medical school for snake bite. To cut the wound & suck the venom out. Which is known today as total nonsence. With possible risk of poisoning to the person treating the victoms wound

Quote from: Andromeda Galaxy on December 17, 2015, 05:49:39 PM

I would be interested to know how many science graduates believe in a flat earth?

Tell me how on earth you would graduate , if you didnt parrot what you were told you had to parrot, if you wanted to graduate.?just one example of thousands .it use to be standard practice for years ,  taught as first aid in  medical school for snake bite. To cut the wound & suck the venom out. Which is known today as total nonsence. With possible risk of poisoning to the person treating the victoms wound

Quote from: charles bloomington on December 17, 2015, 06:24:43 PM

Quote from: Andromeda Galaxy on December 17, 2015, 05:49:39 PM

I would be interested to know how many science graduates believe in a flat earth?

Tell me how on earth you would graduate , if you didnt parrot what you were told you had to parrot, if you wanted to graduate.?just one example of thousands .it use to be standard practice for years ,  taught as first aid in  medical school for snake bite. To cut the wound & suck the venom out. Which is known today as total nonsence. With possible risk of poisoning to the person treating the victoms wound

Your aggressive attitude shows you're not a scientist. If there's a difference of opinion within science you don't need swear words or "parrots" to convince others; you use science itself to prove yourself or someone else wrong.

And that insights in medical sciences AND in Earth sciences do change over time is a good sign; advancement.

Only religious people want to stick to 1 story which is blind for new input and data which can change the story.