Offline somerled

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Re: Latitude and longitude - please enlighten me
« Reply #40 on: June 22, 2020, 04:40:11 PM »
  "I think it's because latitude/longitude have just become forever associated with the globe and that's what's causing the problem for those who don't believe in the globe."

You've answered your own question there. Plane measurements associated with a globe through spherical calculations . That's the objection.
 
From your OP.

 "Fundamentally (if you live in the northern hemisphere), your latitude is easily determined. It's simply the altitude of Polaris from your location. It's not an absolute value in miles, km or light years, because to determine that you'd need to know how far away Polaris is and in times past, that wasn't possible to determine. What we do instead is measure the angle from the horizon to the star, because that's easily done and doesn't require you to know any distances."

Point 1 . You assume Polaris is known to be a vast distance and point 2 - you assume that in past times the distance to Polaris wasn't possible to measure .

See Brahe's model for the distance to the stars for one example and I'm sure triangulation of distance has been around for a long time .

Point 3. We do not measure elevation of Polaris from the horizon - we measure elevation from the horizontal plane 

If you make a post containing assumptions you are confusing the issue.



Re: Latitude and longitude - please enlighten me
« Reply #41 on: June 22, 2020, 10:11:46 PM »
  "I think it's because latitude/longitude have just become forever associated with the globe and that's what's causing the problem for those who don't believe in the globe."

You've answered your own question there. Plane measurements associated with a globe through spherical calculations . That's the objection.


Well I've taken a guess at what the objections might be, but I want to know if that's what FErs actually object to, or is it something else?


From your OP.

 "Fundamentally (if you live in the northern hemisphere), your latitude is easily determined. It's simply the altitude of Polaris from your location. It's not an absolute value in miles, km or light years, because to determine that you'd need to know how far away Polaris is and in times past, that wasn't possible to determine. What we do instead is measure the angle from the horizon to the star, because that's easily done and doesn't require you to know any distances."

Point 1 . You assume Polaris is known to be a vast distance and point 2 - you assume that in past times the distance to Polaris wasn't possible to measure .


No, we've been here before and this has been addressed already..

Good description of how we can measure lat and long in the northern part of the world.

However you state the globe theory preconceived assumption that Polaris is at an extreme distance thus its light rays are basically parallel leading to the conclusion that any change in measured angle of elevation to the star is a product of the curvature of this globe .

No I've not stated anything about the distance to Polaris (extreme or otherwise), other than simply saying that in times past, the distance was not known, but we can however use an angular measurement instead, which works independently of distance. For instance I can measure the angular height of a tree at the bottom of my garden from my current position. It doesn't tell me anything about the actual height of the tree or how far away it is or for that matter, what shape the earth is.

Equally, it doesn't matter whether the light rays from Polaris are parallel or not, just that whenever you measure the angular elevation of Polaris from the same position, you are always going to get the same value and if you move north or south of that position, you will get a different value, which will increase as you move north and decrease as you move south.

To which you replied...

Sorry Robin , I misread your OP about distance to Polaris .


See Brahe's model for the distance to the stars for one example and I'm sure triangulation of distance has been around for a long time .

Point 3. We do not measure elevation of Polaris from the horizon - we measure elevation from the horizontal plane 

If you make a post containing assumptions you are confusing the issue.

I'm no sailor and I've never used a sextant, however my understanding of how these are normally used when in open water is that you adjust two images until they overlap. One of the images is the celestial object, sun, moon, planet or star and the other is the horizon. Determining the horizontal plane on a rolling ship is not easy. I'm not going to bother arguing about this though, it's detail, it doesn't fundamentally change the methodology, it would just lead to very slightly different results. If I'm wrong, then I'm wrong and quite happy to concede the point. To me it's a fairly unimportant detail to the overall process.

So just to reiterate. I don't assume the distance to Polaris is known to be a vast distance. The distance is utterly irrelevant if all you are doing is measuring its angular height above a datum (horizon or horizontal plane, I don't really care). I don't care if the light rays are parallel either. That won't stop you measuring an angle. Yes, I do assume that in ancient times we had no way to determine the distance to a star. I believe Tycho Brahe proposed measuring stellar parallax, but didn't have equipment capable of doing so. But again, whether they could or couldn't measure stellar distances is completely irrelevant to a method which uses angles, not distances, so I'll happily ditch that assumption and say in times past, people may or may not have been able to measure stellar distances, but since we're using angles, it makes no difference whether they did or whether they didn't.

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Offline Tumeni

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Re: Latitude and longitude - please enlighten me
« Reply #42 on: June 23, 2020, 05:22:08 PM »
What happened in the 1600s? Quoting from Bryson's abbreviated account;

".. one revelation became almost immediately controversial.

This was the suggestion that the Earth is not quite round. According to Newton’s theory, the centrifugal force of the Earth’s spin should result in a slight flattening at the poles and a bulging at the equator, which would make the planet slightly oblate. That meant that the length of a degree of meridian wouldn’t be the same in Italy as it was in Scotland. Specifically, the length would shorten as you moved away from the poles. This was not good news for those people whose measurements of the planet were based on the assumption that it was a perfect sphere, which was everyone.

For half a century people had been trying to work out the size of the Earth, mostly by making very exacting measurements. One of the first such attempts was by an English mathematician named Richard Norwood. As a young man Norwood had travelled to Bermuda with a diving bell modelled on Halley’s device, intending to make a fortune scooping pearls from the seabed. The scheme failed because there were no pearls and anyway Norwood’s bell didn’t work, but Norwood was not one to waste an experience. In the early seventeenth century Bermuda was well known among ships’ captains for being hard to locate. The problem was that the ocean was big, Bermuda small and the navigational tools for dealing with this disparity hopelessly inadequate. There wasn’t even yet an agreed length for a nautical mile. Over the breadth of an ocean the smallest miscalculations would become magnified so that ships often missed Bermuda-sized targets by dismayingly large margins. Norwood, whose first love was trigonometry and thus angles, decided to bring a little mathematical rigour to navigation, and to that end he determined to calculate the length of a degree.

Starting with his back against the Tower of London, Norwood spent two devoted years marching 208 miles north to York, repeatedly stretching and measuring a length of chain as he went, all the while making the most meticulous adjustments for the rise and fall of the land and the meanderings of the road. The final step was to measure the angle of the sun at York at the same time of day and on the same day of the year as he had made his first measurement in London. From this, he reasoned he could determine the length of one degree of the Earth’s meridian and thus calculate the distance around the whole. It was an almost ludicrously ambitious undertaking—a mistake of the slightest fraction of a degree would throw the whole thing out by miles—but in fact, as Norwood proudly declaimed, he was accurate to “within a scantling”—or, more precisely, to within about six hundred yards. In metric terms, his figure worked out at 110.72 kilometres per degree of arc.

In 1637, Norwood’s masterwork of navigation, The Seaman’s Practice, was published and found an immediate following. It went through seventeen editions and was still in print twenty-five years after his death. "

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How is a Nautical Mile defined on FE?
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Re: Latitude and longitude - please enlighten me
« Reply #43 on: June 24, 2020, 01:41:43 AM »
Somerled,
sorry to come in to this discussion rather late. I just like to make sure that I understand your position in response the OP's original question :
a) you support the idea that a latitude/longitude coordinate system allows us to uniquely identify each and every point on earth. And we could use the elevation angle of polaris to clearly identify the latitude and the time difference w.r.t Greenwich (position of sun in the sky) as a measure of longitude.

b) if we look up on the internet latitude and longitude for a particular place on earth people living there would confirm these numbers by measuring the elevation angle of polaris and time difference to Greenwich. Well, at least you and I could do that as well as others on this thread making small allowances for our measurement errors.

Thank you for your response

Offline edby

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Re: Latitude and longitude - please enlighten me
« Reply #44 on: June 28, 2020, 03:56:33 PM »
Coming to this rather late. As people have noted, there are two separate questions. (i) Is it possible to make celestial observations that uniquely identify our position on the earth, (ii) can we use these observations to infer the distance between two different positions.

Regarding the first, Polaris can be used, but is not necessary. The standard method is to observe the time when the altitude of the sun as at its highest (zenith), which requires knowing the time at any place in the world. (Knowing the time was a famous problem of longitude).

This tells us the longitude. Then determine (using a sextant) the altitude of the sun at zenith. This tells us the latitude. The method works equally well in the Southern hemisphere.

Latitude and longitude make no assumptions about the shape of the land. Flat Earth believers could use the method. 

Question (ii) is whether, knowing the latitude and longitude of two different points, we could mathematically determine the distance between the points. FE navigators could work this out also, if they used the standard model used by RE navigators. They could just say “well it’s a model, and it works, we don’t really know why”.

Re: Latitude and longitude - please enlighten me
« Reply #45 on: June 30, 2020, 01:08:52 AM »
Doesn't the altitude of the sun at it highest point during a day depend on the time of the year ? Maybe at one of the equinoxes you would be a good choice ?

Would love to hear from the FE folks too.

Re: Latitude and longitude - please enlighten me
« Reply #46 on: June 30, 2020, 08:30:19 AM »
Doesn't the altitude of the sun at it highest point during a day depend on the time of the year ? Maybe at one of the equinoxes you would be a good choice ?

Yes, I think if you are in a suitable (well north of the equator) static location and you aren't in a hurry, personally I'd use the Polaris method for latitude. The sun changes its altitude during the day and throughout the year and you really don't want to look directly at it. Polaris just sits there, unmoving and you can look straight at it. If you're on the open sea, south of the equator and it's daytime, use the sun for sure.

But really whatever works for you, so long as it gives you the right answer. The key idea here is, however you choose to do it, you end up with a pair of angles which uniquely define your position and that would work, globe or flat.

Would love to hear from the FE folks too.

Yes, it's a bit pointless all us RErs discussing this because we're not going to disagree (I assume). Disappointing that we're not hearing much from them.

Offline edby

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Re: Latitude and longitude - please enlighten me
« Reply #47 on: June 30, 2020, 01:16:10 PM »
Doesn't the altitude of the sun at its highest point during a day depend on the time of the year ?

It does, and is known as the Declination. You can get that number from tables, but again it does not depend on any assumption about the shape of the earth. You can simply observe the declination each day at local noon (i.e. at zenith) and note it down, so you have a number for each day of the year.

Then take a sighting with the sextant to find the altitude of the sun at local noon. Latitude then given by the following formula:

    LAT  =  90 - ALT + DEC

Simple. Involves no assumptions about the shape of the earth, so FE and RE should agree on the latitude for any point on the earth. Likewise, if they know London (Greenwich) time, they both agree on the longitude.

Where they will profoundly disagree is on the distance implied between two points on the earth's surface. This will depend on the chosen map, about which FE will internally disagree. But assuming FE likes the AE map, and RE the globe, they will compute the distances differently, radically so the further south they get.

Re: Latitude and longitude - please enlighten me
« Reply #48 on: June 30, 2020, 02:09:10 PM »
Doesn't the altitude of the sun at its highest point during a day depend on the time of the year ?

It does, and is known as the Declination. You can get that number from tables, but again it does not depend on any assumption about the shape of the earth. You can simply observe the declination each day at local noon (i.e. at zenith) and note it down, so you have a number for each day of the year.

Then take a sighting with the sextant to find the altitude of the sun at local noon. Latitude then given by the following formula:

    LAT  =  90 - ALT + DEC

Simple. Involves no assumptions about the shape of the earth, so FE and RE should agree on the latitude for any point on the earth. Likewise, if they know London (Greenwich) time, they both agree on the longitude.

Where they will profoundly disagree is on the distance implied between two points on the earth's surface. This will depend on the chosen map, about which FE will internally disagree. But assuming FE likes the AE map, and RE the globe, they will compute the distances differently, radically so the further south they get.

I think you are probably right, FE and RE should be able to agree on the latitude (and longitude) for any point on the earth. The problem is, I've never heard a FEer actually agree to that, all I've ever heard is "can't use latitude/longitude because that's based on a globe". It's a very broad statement and I've been trying to break it down into two separate issues, i) latitude/longitude for position ii) distances based on latitude/longitude. I would love to hear a FEer say, "yes, i) is OK, but ii) is not". Then at least we know where we all stand. Just can't get an opinion on this from their side unfortunately.

Offline edby

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Re: Latitude and longitude - please enlighten me
« Reply #49 on: June 30, 2020, 04:08:19 PM »
I think you are probably right, FE and RE should be able to agree on the latitude (and longitude) for any point on the earth.

Not even 'probably'. For those who dislike the theory of declination, here is a neat video showing how to locate the southern celestial pole.

It’s the pure Zetetic method, i.e. working directly from observation rather than supporting the observations, partly or wholly, on some theory.

Re: Latitude and longitude - please enlighten me
« Reply #50 on: June 30, 2020, 04:32:23 PM »
I think you are probably right, FE and RE should be able to agree on the latitude (and longitude) for any point on the earth.

Not even 'probably'. For those who dislike the theory of declination, here is a neat video showing how to locate the southern celestial pole.

It’s the pure Zetetic method, i.e. working directly from observation rather than supporting the observations, partly or wholly, on some theory.

You're right we should be able to agree. The question then becomes, will we be able to agree?

Interesting video. So much easier in the northern hemisphere.

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Online GreatATuin

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Re: Latitude and longitude - please enlighten me
« Reply #51 on: July 09, 2020, 08:12:25 PM »
I'll make a list of statements related to longitude and latitude. Hopefully each statement is simple enough to make it easy to find out possible disagreements.

* The elevation of the celestial pole is constant for any given location
* We can calculate the latitude of a location using the elevation of the celestial pole
* Solar noon is the time of the day when the Sun is at its highest in the sky, casting the shortest shadows
* At solar noon, the Sun appears due South or due North, except in the special case when it's directly overhead
* The difference between solar noon at a reference location (eg Greenwich) and solar noon at any given location is constant
* We can calculate the longitude from the difference between solar noon at Greenwich and local solar noon, 15 degrees of longitude being equivalent to 1 hour
* Any place on Earth is uniquely identified by a latitude and longitude
* Locations with the same longitude will see the Sun at its highest at the same time
* Locations with the same latitude will have the same variation of day length all through the year
* At the equinoxes, the elevation of the Sun at solar noon is 90 - current latitude (0 at the poles, 90 at the Equator)
* At any other time of the year, the elevation of the Sun at solar noon is 90 - current latitude + declination of the Sun
* The subsolar point at the June solstice is 23.5 degrees North, on the tropic of Cancer
* The subsolar point at the December solstice is 23.5 degrees South, on the tropic of Capricorn
* Latitude lines are east-west lines, called parallels
* Longitude lines are north-south lines, called meridians
* Meridians and parallels always cross at a right angle
* One degree of latitude along a meridian is approximately 111.3 km
* One degree of longitude along the Equator is approximately 111.3 km
* The borders of the state of Colorado were defined with meridians and parallels
* The eastern and western borders of Colorado are the same length, approximately 445 km
* The northern border of Colorado is significantly shorter than the southern border
* Meridians converge as you get further away from the Equator, either South or North
Nearly all flat earthers agree the earth is not a globe.

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Offline edby

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Re: Latitude and longitude - please enlighten me
« Reply #52 on: July 10, 2020, 07:42:42 AM »
I'll make a list of statements related to longitude and latitude. Hopefully each statement is simple enough to make it easy to find out possible disagreements.
* The elevation of the celestial pole is constant for any given location

Location? Did you mean latitude?

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Online GreatATuin

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Re: Latitude and longitude - please enlighten me
« Reply #53 on: July 10, 2020, 10:15:03 AM »
I'll make a list of statements related to longitude and latitude. Hopefully each statement is simple enough to make it easy to find out possible disagreements.
* The elevation of the celestial pole is constant for any given location

Location? Did you mean latitude?

There probably was a better way to phrase that. I do mean location. At a given location, the elevation of the celestial pole is constant, it doesn't change over time. This is required if you want to determine a unique, constant latitude from that measurement.
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Offline edby

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Re: Latitude and longitude - please enlighten me
« Reply #54 on: July 10, 2020, 04:55:08 PM »
I do mean location. At a given location, the elevation of the celestial pole is constant, it doesn't change over time.

That makes sense. Some comments. The statements can be divided into those which are simply definitions, and those which would have to be verified empirically. Of the latter, these could be divided into those which have no implication for the shape of the earth, and those (if any) which do.

Some of the definitions are covert. You say “At solar noon, the Sun appears due South or due North”, but you haven’t defined ‘North’ or ‘South’. Clearly magnetic poles are not meant. Perhaps you might define N and S in terms of the axis of apparent celestial rotation. As for ‘Latitude’, you could define it by the elevation of Polaris, or the Southern pole star.

Do any of these imply the shape of the earth? We have “Locations with the same longitude will see the Sun at its highest at the same time”. That implies (there is a geometrical proof) that a line of longitude is the shortest distance between any two points on that line, meaning that if the earth is flat, they must be straight. But then there is a problem with “Meridians converge as you get further away from the Equator, either South or North”.
« Last Edit: July 10, 2020, 04:56:48 PM by edby »

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Online GreatATuin

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Re: Latitude and longitude - please enlighten me
« Reply #55 on: July 10, 2020, 06:40:23 PM »
I do mean location. At a given location, the elevation of the celestial pole is constant, it doesn't change over time.

That makes sense. Some comments. The statements can be divided into those which are simply definitions, and those which would have to be verified empirically. Of the latter, these could be divided into those which have no implication for the shape of the earth, and those (if any) which do.

Some of the definitions are covert. You say “At solar noon, the Sun appears due South or due North”, but you haven’t defined ‘North’ or ‘South’. Clearly magnetic poles are not meant. Perhaps you might define N and S in terms of the axis of apparent celestial rotation. 

Actually, it can also be used as a definition of North and South. South is were the Sun is at solar noon if you're north of the tropic of Capricorn. North is the opposite direction, West is due left if you face North. Most common definitions of North and South imply a round Earth, so I prefer not to include them. Maybe someone will come up with a different definition. The point is to see if any of these statements could be refuted.
 
Quote
As for ‘Latitude’, you could define it by the elevation of Polaris, or the Southern pole star.

As there is no southern equivalent of Polaris, I prefer the term "celestial pole": the point in the sky around which the stars seem to be spinning. The direction you have to point an equatorial mount at to cancel out the apparent movement of the stars. Also, Polaris is not exactly at the celestial pole, but it's probably close enough for our purpose.

Quote
Do any of these imply the shape of the earth? We have “Locations with the same longitude will see the Sun at its highest at the same time”. That implies (there is a geometrical proof) that a line of longitude is the shortest distance between any two points on that line, meaning that if the earth is flat, they must be straight. But then there is a problem with “Meridians converge as you get further away from the Equator, either South or North”.

That's part of the point, none of these statements alone directly implies a shape of the Earth. But all of them should be verifiable without requiring space travel or anything out of reach. And all together, I guess they're hard to fit in a flat Earth model.
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Offline edby

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Re: Latitude and longitude - please enlighten me
« Reply #56 on: July 10, 2020, 10:15:57 PM »
That's part of the point, none of these statements alone directly implies a shape of the Earth. But all of them should be verifiable without requiring space travel or anything out of reach. And all together, I guess they're hard to fit in a flat Earth model.
Convergence of longitude lines does imply a shape of the Earth, if longitude lines are the shortest distance between two points, i.e. straight. Then two straight lines enclose a space, right?

See Euclid postulate I.
« Last Edit: July 10, 2020, 10:21:13 PM by edby »

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Offline Tumeni

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Re: Latitude and longitude - please enlighten me
« Reply #57 on: July 10, 2020, 10:58:04 PM »
Convergence of longitude lines does imply a shape of the Earth, if longitude lines are the shortest distance between two points, i.e. straight. Then two straight lines enclose a space, right?

The shortest distance over the surface of any globe is the arc (S). The shortest distance between the points is the chord (C), but that cannot be travelled without mining into the globe.

Arc S will appear straight only if you view it from directly above. Else it will appear curved. But it's never physically straight

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Offline edby

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Re: Latitude and longitude - please enlighten me
« Reply #58 on: July 11, 2020, 09:04:30 AM »
Convergence of longitude lines does imply a shape of the Earth, if longitude lines are the shortest distance between two points, i.e. straight. Then two straight lines enclose a space, right?

The shortest distance over the surface of any globe is the arc (S). The shortest distance between the points is the chord (C), but that cannot be travelled without mining into the globe.

Arc S will appear straight only if you view it from directly above. Else it will appear curved. But it's never physically straight



If the earth is a globe, yes. But the question is whether any of GreatATuin's statements above imply something about the shape of the earth. If they imply that two apparently straight lines enclose a space, then the earth cannot be flat.  For FE to be true, either (1) lines of longitude are not straight or (2) lines of longitude do not converge at the Poles.

Note that (1) is true under the bipolar model, where lines of longitude converge, but for that reason are not straight. And (2) is true of the AE model, where the lines are straight but do not converge at the South Pole.

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Online GreatATuin

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Re: Latitude and longitude - please enlighten me
« Reply #59 on: July 11, 2020, 09:18:02 AM »
My statements don't actually mention "straight lines", just North-South and East-West lines. On a globe Earth, meridians are great circles that converge at the poles, parallels are rhumb lines perpendicular to the meridians. Parallels are not great circles, except in the special case of the Equator. Being circles at the surface of a sphere, they obviously are not "straight" in a 3D sense like a laser beam.

On a flat Earth, what parallels and meridians look like highly depends on the model. None of the flat Earth models I've seen are compatible with my list of statements.
Nearly all flat earthers agree the earth is not a globe.

you guys just read what you want to read