RE: due east photography

[Robert Kellogg]

Be careful about the shortest path.  Of course you and the earth know 
that a geodesic arc is the shortest path, cutting nearly a great circle 
along the point from A to B.  But map distortions give you a different 
"view" and when you draw a straight line on a mercator, you have a rhumb 
line.  Maps are either angle preserving or area preserving ... but not 
both.  So depending on the type map you use, you will get different (and 
of course, erroneous) distances and angles.  Hence  if we go straight 
east (and maintain straight east) we follow a small circle.  On a real 
globe, it is NOT the shortest path.


Bob
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

RE: due east photos

[R. Hooijenga]

I wonder how anyone can think that the placement of an arbritrarily chosen
coordinate net on the globe will change the actual direction from A to B.

 

Suppose there were no coordinate system, and all we had was the globe and
points A and B on it.

No doubt, all would agree on what would constitute the direction from A to
B: it would be what a piece of string would do when pulled taut between the
points. Or the way in which a car would have to be driven over the surface
when only going 'straight ahead'.

To be sure, one could take the other way round; but this would still concern
the same great circle.

 

Now, add two more points; for the sake of argument, let these be called N
and S and be opposite each other on the globe.

Draw a family of lines from N to S, spread out all around the globe. We
could call them 'meridians', if we like.

Does the existence of these meridians miraculously change the position of
the taut string, or does it make the car suddenly drive differently?

 

One may certainly construct a curve from A to B which intersects all the
meridians at equal angles. But the position of such a curve on the globe
would be entirely dependent on the chosen locations for N and S. 

 

It seems humorous to me that anyone could think that the direction to Mecca
should correspond to (the start of) such an arbitrary curve, - especially
when one considers that Mercator projection did not exist at the time this
rule was postulated.

 

Rudolf

 

Van: sundial [mailto:sundial-boun...@uni-koeln.de] Namens Brent
Verzonden: donderdag 24 september 2015 22:12
Aan: sundial@uni-koeln.de
Onderwerp: Re: due east photos

 

I think you can face Mecca from 4 directions:

1. along great circle shortest direction
2. along great circle longest direction
3. along constant compass method shortest direction
4. along constant compass method longest direction

I wonder if it says in Koran to face Mecca in shortest direction?

brent



 

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east photos

[Brent]

Apparently Muslims have a similar problem when determining which way to 
pray towards Mecca (Qibla).

This non-scientific website gives  a choice of 2 different directions:

https://threesixty360.wordpress.com/2008/09/01/which-direction-is-mecca/

There is more confusion found in the comments at the bottom of that website.

brent



On 9/17/2015 2:05 AM, Richard Mallett wrote:

On 17/09/2015 09:31, Fabio nonvedolora wrote:

well said Jack,
flat Earth and similar are unlikely :-)
globe
Fabio
Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Ita
45° 34' 10'' N, 9° 10' 9'' E, GMT+1 (DST +2)


The comedian Michael Bentine used to have a show called 'It's a Square 
World' on BBC TV when I was young :-)


--
--
Richard Mallett
Eaton Bray, Dunstable
South Beds. UK


---
https://lists.uni-koeln.de/mailman/listinfo/sundial



---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east photos

[Bill Gottesman]

Well, if you are going to allow compass directions, then that opens the
door to all loxodromes.  There are an infnite number of loxodromes that
connect two points on a sphere, if you allow loxodrome paths that travel
more than once around the globe!  This gives an infinite number of compass
directions to Mecca.

-Bill

On Thu, Sep 24, 2015 at 4:11 PM, Brent  wrote:

> I think you can face Mecca from 4 directions:
>
> 1. along great circle shortest direction
> 2. along great circle longest direction
> 3. along constant compass method shortest direction
> 4. along constant compass method longest direction
>
> I wonder if it says in Koran to face Mecca in shortest direction?
>
> brent
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east photos

[Brent]

"an infinite number of compass directions to Mecca"

allahu akbar!



.

On 9/24/2015 2:39 PM, Bill Gottesman wrote:
Well, if you are going to allow compass directions, then that opens 
the door to all loxodromes.  There are an infnite number of loxodromes 
that connect two points on a sphere, if you allow loxodrome paths that 
travel more than once around the globe!  This gives an infinite number 
of compass directions to Mecca.


-Bill

On Thu, Sep 24, 2015 at 4:11 PM, Brent > wrote:


I think you can face Mecca from 4 directions:

1. along great circle shortest direction
2. along great circle longest direction
3. along constant compass method shortest direction
4. along constant compass method longest direction

I wonder if it says in Koran to face Mecca in shortest direction?

brent



---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east photos

[Brent]

I think you can face Mecca from 4 directions:

1. along great circle shortest direction
2. along great circle longest direction
3. along constant compass method shortest direction
4. along constant compass method longest direction

I wonder if it says in Koran to face Mecca in shortest direction?

brent


On 9/24/2015 12:20 PM, Brent wrote:
Apparently Muslims have a similar problem when determining which way 
to pray towards Mecca (Qibla).

This non-scientific website gives  a choice of 2 different directions:

https://threesixty360.wordpress.com/2008/09/01/which-direction-is-mecca/

There is more confusion found in the comments at the bottom of that 
website.


brent



On 9/17/2015 2:05 AM, Richard Mallett wrote:

On 17/09/2015 09:31, Fabio nonvedolora wrote:

well said Jack,
flat Earth and similar are unlikely :-)
globe
Fabio
Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Ita
45° 34' 10'' N, 9° 10' 9'' E, GMT+1 (DST +2)


The comedian Michael Bentine used to have a show called 'It's a 
Square World' on BBC TV when I was young :-)


--
--
Richard Mallett
Eaton Bray, Dunstable
South Beds. UK


---
https://lists.uni-koeln.de/mailman/listinfo/sundial





---
https://lists.uni-koeln.de/mailman/listinfo/sundial



---
https://lists.uni-koeln.de/mailman/listinfo/sundial

RE: due east photos

[Jack Aubert]

Why not?  Richard Feynman argued that that a quantum mechanical particle can
take an infinite number of paths between two points to explain the wave
function.  Or something like that.  I don’t actually understand that stuff
myself. Maybe the direction to Mecca should be a wave function.  

 

https://www.quora.com/What-is-Richard-Feynmans-sum-over-paths-approach-to-qu
antum-mechanics

 

Jack

 

From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Brent
Sent: Thursday, September 24, 2015 5:58 PM
To: Bill Gottesman
Cc: Sundials List
Subject: Re: due east photos

 

"an infinite number of compass directions to Mecca"

allahu akbar!



.

On 9/24/2015 2:39 PM, Bill Gottesman wrote:

Well, if you are going to allow compass directions, then that opens the door
to all loxodromes.  There are an infnite number of loxodromes that connect
two points on a sphere, if you allow loxodrome paths that travel more than
once around the globe!  This gives an infinite number of compass directions
to Mecca. 

 

-Bill

 

On Thu, Sep 24, 2015 at 4:11 PM, Brent <bren...@verizon.net> wrote:

I think you can face Mecca from 4 directions:

1. along great circle shortest direction
2. along great circle longest direction
3. along constant compass method shortest direction
4. along constant compass method longest direction

I wonder if it says in Koran to face Mecca in shortest direction?

brent 

 



-- 
This message has been scanned for viruses and 
dangerous content by  <http://www.mailscanner.info/> MailScanner, and is 
believed to be clean. 


-- 
This message has been scanned for viruses and
dangerous content by MailScanner, and is
believed to be clean.

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east photos

[Fabio nonvedolora]

well said Jack,

flat Earth and similar are unlikely :-)



Fabio

Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Italy
45° 34' 10'' N, 9° 10' 9'' E, GMT+1 (DST +2)

From: Jack Aubert 
Sent: Thursday, September 17, 2015 12:21 AM
To: 'Brent' ; 'sundial' 
Subject: RE: due east photos

Maybe it helps to bear in mind that while all triangles on a plane surfaces 
contain 180 degrees, this is not true on a sphere.  You cannot make a triangle 
on a plane surface that has two 90 degree angles because the sides will never 
meet.

 

On a sphere, however, a triangle can easily have two 90 degree angles.  If one 
side is congruent with the equator then the two sides will meet at the pole.  
The angle a the pole depends on the length of the equatorial side.  A triangle 
with three 90 degree angles will take up one eighth of the sphere’s surface.

 

East, west, north and south are spherical directions, not straight line on a 
plane surface. 

 

Jack Aubert

 

From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Brent
Sent: Tuesday, September 15, 2015 9:47 PM
To: sundial
Subject: due east photos

 

I am having an off list discussion with Dave but I have a photo that you may 
find informative.

I resized them for the list so I hope you can see the latitude lines.

what you are seeing is my globe oriented on north south axis and correct angle 
for latitude.

I have a ruler close to my location with the zero on a latitude line

I am pointing the ruler due east, where the sun will rise on the equinox as it 
peaks over my horizon.

As we look straight down you see a deviation from the latitude line of about 1" 
at 4" on the ruler.

Just rough scale 4" = 4,000 miles so 1" equals 1,000 miles = 25% deviation.

My horizon is about 50 miles from here so when I look at the sunrise on the 
equinox my latitude is 
actually about 12.5 miles north of that point on the horizon.

So it's not an insignificant difference.

brent

-- 
This message has been scanned for viruses and 
dangerous content by MailScanner, and is 
believed to be clean. 


-- 
This message has been scanned for viruses and 
dangerous content by MailScanner, and is 
believed to be clean. 



---
https://lists.uni-koeln.de/mailman/listinfo/sundial

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east photos

[Richard Mallett]

On 17/09/2015 09:31, Fabio nonvedolora wrote:

well said Jack,
flat Earth and similar are unlikely :-)
globe
Fabio
Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Ita
45° 34' 10'' N, 9° 10' 9'' E, GMT+1 (DST +2)


The comedian Michael Bentine used to have a show called 'It's a Square 
World' on BBC TV when I was young :-)


--
--
Richard Mallett
Eaton Bray, Dunstable
South Beds. UK

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Michael Ossipoff]

Brent--

On Tue, Sep 15, 2015 at 7:47 PM, Brent  wrote:

> Michael;
>
> Ok, let's make it easier.
>
> On any day I want to stand in my backyard and look due east.
> I don't want to travel anywhere.
>
> Do I look at where the sun will rise on the equinox or do I look slightly
> to the left of that? (northern hemisphere)
>

You look at where the sun will rise on the equinox..

 (but don't do it when the sun rises, because even if the rising or setting
sun doesn't look very bright, due to mist or low altitude, the un-seen and
un-felt infrared or UV could still do retinal-damage).

>
> If you tell me to look slightly to the left of where the sun will rise on
> the equinox it would mean two things:
>


> 1. the sun doesn't rise due east on the equinox
> 2. the east west line is not straight but curved
>

The equinox sun rises due east. But the east-west line is curved. But the
curved-ness of the east-west line only matters if you want to travel on it.
If you're, instead, just looking east, then, wherever you are, the
direction you're looking is a straight line (a great circle).

So, though you're looking due east, toward where the sun will rise, any
places on the Earth that are in that line-of-sight will be slightly south
of the parallel of latitude that you're on--even though they're due east
from you. Their *direction* is due east. The *route* to them will soon have
you going south of east instead of due east.

So: Say the edge of a distant telephone-pole is due-east from you. Starting
out toward it, you're starting out traveling due eastward. But, after
you've proceeded even a little way, continuing in that same straight line
toward the telephone-pole edge, you'll soon be traveling in a direction
that's south of due east.

Michael Ossipoff

>
> Thank you all for your replies.
> brent
>
>
> On 9/15/2015 4:00 PM, Michael Ossipoff wrote:
>
> Hi Brent--
>
> The paradox involves what you mean by "travel due east'.
>
> If you travel due east, and keep on traveling due east at every point of
> your journey, then you will indeed follow a parallel of latitude.
>
> If you were to drive your car in that fashion, always going due east,
> along a parallel of latitude, then your car's wheels and steering-wheel
> would have to be adjusted for a (slight) left-turn.  ...as, for example, if
> you wanted to drive east along the U.S-Canadian border.
>
> But there's another thing that you could mean by traveling due east:
>
> But, if you set out due east, and then travel in a straight line, without
> letting your car's wheels curve your car left or right at all, then you're
> not following a parallel, and, you'd indeed end up going farther and
> farther south from your original latitude.
>
> As others have pointed out, a straight line on the Earth is also called a
> "great circle".
>
> So, the paradox was just the result of two different meanings of "travel
> due-east".
>
> Michael Ossipoff
>
> On Tue, Sep 15, 2015 at 10:10 AM, Brent  wrote:
>
>> I'm confused maybe.
>>
>> I live in the northern hemishpere and anticipating the equinox on the
>> 23rd.
>>
>> Supposedly the sun will rise due east.
>>
>> So if due east is a right angle from north south and I traveled due east
>> I would not follow my line of latitude.
>> I would get further and further south of my latitude the further I
>> traveled.
>>
>> So either the lines of latitude are not east west lines or due east is
>> not a straight line but curved.
>> I suspect lines of latitude are not east west lines?
>> They would work fine if the earth was not tilted, but it is.
>>
>> Wouldn't it make sense to coordinate the globe so lines of latitude (or
>> call them something else) are straight and a right angle
>> from north south?
>>
>> brent
>>
>>
>>
>> ---
>> https://lists.uni-koeln.de/mailman/listinfo/sundial
>>
>>
>>
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Michael Ossipoff]

Hi Brent--

The paradox involves what you mean by "travel due east'.

If you travel due east, and keep on traveling due east at every point of
your journey, then you will indeed follow a parallel of latitude.

If you were to drive your car in that fashion, always going due east, along
a parallel of latitude, then your car's wheels and steering-wheel would
have to be adjusted for a (slight) left-turn.  ...as, for example, if you
wanted to drive east along the U.S-Canadian border.

But there's another thing that you could mean by traveling due east:

But, if you set out due east, and then travel in a straight line, without
letting your car's wheels curve your car left or right at all, then you're
not following a parallel, and, you'd indeed end up going farther and
farther south from your original latitude.

As others have pointed out, a straight line on the Earth is also called a
"great circle".

So, the paradox was just the result of two different meanings of "travel
due-east".

Michael Ossipoff

On Tue, Sep 15, 2015 at 10:10 AM, Brent  wrote:

> I'm confused maybe.
>
> I live in the northern hemishpere and anticipating the equinox on the 23rd.
>
> Supposedly the sun will rise due east.
>
> So if due east is a right angle from north south and I traveled due east I
> would not follow my line of latitude.
> I would get further and further south of my latitude the further I
> traveled.
>
> So either the lines of latitude are not east west lines or due east is not
> a straight line but curved.
> I suspect lines of latitude are not east west lines?
> They would work fine if the earth was not tilted, but it is.
>
> Wouldn't it make sense to coordinate the globe so lines of latitude (or
> call them something else) are straight and a right angle
> from north south?
>
> brent
>
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Brent]

Michael;

Ok, let's make it easier.

On any day I want to stand in my backyard and look due east.
I don't want to travel anywhere.

Do I look at where the sun will rise on the equinox or do I look 
slightly to the left of that? (northern hemisphere)


If you tell me to look slightly to the left of where the sun will rise 
on the equinox it would mean two things:

1. the sun doesn't rise due east on the equinox
2. the east west line is not straight but curved

Thank you all for your replies.
brent

On 9/15/2015 4:00 PM, Michael Ossipoff wrote:

Hi Brent--

The paradox involves what you mean by "travel due east'.

If you travel due east, and keep on traveling due east at every point 
of your journey, then you will indeed follow a parallel of latitude.


If you were to drive your car in that fashion, always going due east, 
along a parallel of latitude, then your car's wheels and 
steering-wheel would have to be adjusted for a (slight) left-turn.  
...as, for example, if you wanted to drive east along the U.S-Canadian 
border.


But there's another thing that you could mean by traveling due east:

But, if you set out due east, and then travel in a straight line, 
without letting your car's wheels curve your car left or right at all, 
then you're not following a parallel, and, you'd indeed end up going 
farther and farther south from your original latitude.


As others have pointed out, a straight line on the Earth is also 
called a "great circle".


So, the paradox was just the result of two different meanings of 
"travel due-east".


Michael Ossipoff

On Tue, Sep 15, 2015 at 10:10 AM, Brent > wrote:


I'm confused maybe.

I live in the northern hemishpere and anticipating the equinox on
the 23rd.

Supposedly the sun will rise due east.

So if due east is a right angle from north south and I traveled
due east I would not follow my line of latitude.
I would get further and further south of my latitude the further I
traveled.

So either the lines of latitude are not east west lines or due
east is not a straight line but curved.
I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of
latitude (or call them something else) are straight and a right angle
from north south?

brent



---
https://lists.uni-koeln.de/mailman/listinfo/sundial





---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[koolish]

> Mark Gingrich wrote:

> Indeed.  And here's a curious bit of related trivia: If you
> start due east from *any* latitude and travel a great circle
> route -- i.e. "straight" -- a distance of one quarter of the
> Earth's circumference, you *always* end up on the equator.
>
> This also works from the North and South Pole, if you allow
> the convenient fiction that all directions are considered east
> from the poles.
>

It's easy to see why this works.

Put your finger on any spot on the globe.

Rotate the globe so that point is directly
in front of you.

Draw or imagine the great circle that goes through
that point and the point directly opposite on the earth
in the other hemisphere.

Now you see that the tangent to this great circle
is horizontal at the point of interest, i.e. due east
and west. And you can see that it is 1/4 of a circle to
the equator.


---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east photos

[koolish]

At any point on the earth, there is one great circle that
is tangent to your latitude circle. That means that at that
infinitesimally small point, both circles point in the same
direction, i.e due east, but only at that point.

Also note that the plane that cuts the earth at any
latitude is perpendicular to the north-south axis of
the sphere but is not perpendicular to the surface.
The plane that cuts a great circle is perpendicular
to the surface. So if you walk along a latitude circle,
you are not standing in the plane of the circle but
are tilted by the angle of your latitude.




> I am having an off list discussion with Dave but I have a photo that you
> may find informative.
>
> I resized them for the list so I hope you can see the latitude lines.
>
> what you are seeing is my globe oriented on north south axis and correct
> angle for latitude.
>
> I have a ruler close to my location with the zero on a latitude line
>
> I am pointing the ruler due east, where the sun will rise on the equinox
> as it peaks over my horizon.
>
> As we look straight down you see a deviation from the latitude line of
> about 1" at 4" on the ruler.
>
> Just rough scale 4" = 4,000 miles so 1" equals 1,000 miles = 25%
> deviation.
>
> My horizon is about 50 miles from here so when I look at the sunrise on
> the equinox my latitude is
> actually about 12.5 miles north of that point on the horizon.
>
> So it's not an insignificant difference.
>
> brent
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>


---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Steve Lelievre]

On 15/09/2015 10:34, Brent wrote:
I think we all agree the sun rises (appears to rise) due east on the 
equinox.


If the earth stops and the sun stops and I start walking towards the 
sun (on the surface of the earth)

I believe I would be walking a straight line - due east.



Ok, it's sunrise at the Equinox but the sun and earth are sudddenly 
frozen in place, and we consider East to be where the sunrise is.


If we move in a way that keeps the sun due East, we must be moving along 
the line of places where it is currently sunrise. That is, you're moving 
approximately northwards or southwards. On the other hand, If we move 15 
degrees to a different longitude but keeping the same latitude, we're 
moving to a place where the sun has already risen and thus is south of 
East. Isn't walking towards the sun is between the two cases? We're 
starting off going along the line of latitude but gradually veering 
towards the south.


Steve







---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Brent]

Roger;

You seem to be saying there are /two/ due easts.

How can that be right? Shouldn't there only be one due east?

brent

On 9/15/2015 9:42 AM, Roger W. Sinnott wrote:


Brent,

The “small circle” route is the one that takes you on a curved path, 
always toward due east.


You could also start out going due east on a “great circle” route, and 
in that case, as you note, the path would gradually veer southward.


Both of these routes start out perpendicularly from the north-south line.

 Roger

*From:*sundial [mailto:sundial-boun...@uni-koeln.de] *On Behalf Of 
*David Patte ?

*Sent:* Tuesday, September 15, 2015 12:34 PM
*To:* sundial@uni-koeln.de
*Subject:* Re: due east

They are east-west lines, but they are not straight. They are circles.



On 2015-09-15 12:30, Brent wrote:

If I was in halifax at sunrise on the equinox and the earth
stopped rotating and I walked due east (towards the sun) across
the ocean
I would end up in Southern Spain and not on my same latitude which
is in Southern France.

So I conclude that latitude lines are not east-west lines.

Correct?

thanks;
brent



On 9/15/2015 9:01 AM, Frank Evans wrote:

Hi Brent and all,
Compass directions that are pursued make spiral curves towards
the poles, if north of east-west then towards the north pole,
if south of east-west then towards the south pole. If east or
west then they do neither but continue east-west. Try Googling
"loxodromic curve". It's what you draw on a chart. Sailors
call it a "rhumb line".
Frank 55N 1W

On 15/09/2015 15:10, Brent wrote:

I'm confused maybe.

I live in the northern hemishpere and anticipating the
equinox on the 23rd.

Supposedly the sun will rise due east.

So if due east is a right angle from north south and I
traveled due east I would not follow my line of latitude.
I would get further and further south of my latitude the
further I traveled.

So either the lines of latitude are not east west lines or
due east is not a straight line but curved.
I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of
latitude (or call them something else) are straight and a
right angle
from north south?

brent





---

https://lists.uni-koeln.de/mailman/listinfo/sundial





---

https://lists.uni-koeln.de/mailman/listinfo/sundial




--
  



---
https://lists.uni-koeln.de/mailman/listinfo/sundial



---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Mark Gingrich]

Roger Sinnott wrote:

> You could also start out going due east on a "great circle" route, and in
> that case, as you note, the path would gradually veer southward.

 
Indeed.  And here's a curious bit of related trivia: If you
start due east from *any* latitude and travel a great circle
route -- i.e. "straight" -- a distance of one quarter of the
Earth's circumference, you *always* end up on the equator.

This also works from the North and South Pole, if you allow
the convenient fiction that all directions are considered east
from the poles.


~   ~   ~   ~   ~   ~   ~   ~   ~   ~   ~   ~   ~   ~   ~   ~   ~   ~
   Mark Gingrich  gri...@rahul.net  San Leandro, California

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Brent]

I think we all agree the sun rises (appears to rise) due east on the 
equinox.


If the earth stops and the sun stops and I start walking towards the sun 
(on the surface of the earth)

I believe I would be walking a straight line - due east.
And I would not be adjusting my direction each step, I just keep 
marching towards the sun.

So would anyone argue that I am not walking due east?
And I am not walking along a latitude line.

I also understand the argument about always changing your direction as 
you move by using a compass.

So maybe there are/two /due easts.

One due east is a local due east, a compass due east, a magnetic due east.
The other due east is kind of a solar due east, the 
relationship/position between the earth and the sun.


Which has lots to do with our sundials.
So maybe we should forget about magnetic due east when discussing sundials.

ha!

brent :)


On 9/15/2015 10:12 AM, Steve Lelievre wrote:

Brent,

My 2 cents worth...

If by tilt you meant the obliquity of the ecliptic, that doesn't 
affect things.


Your question is about walking on a globe (3D), but I suspect you're 
imagining it like a flat map (2D). A map (assuming the map is a 
Mercator Projection) represents latitude as a straight line but when 
you move on the surface of the Earth you're not really following a 
line that is straight in 3D terms.


The line of latitude is a really a circle representing a sectional 
slice through the globe. To compensate for unbending a circle in 3D to 
be a straight line on a 2D map,  something else has to get distorted: 
shape. That's why on a map Greenland looks huge compared to other 
countries and is so wide at the top. On a globe it looks smaller and 
more like a rectangle than a very wide triangle. The extreme cases are 
the North and South Poles which are points on a globe but on a map get 
stretched out to be a line - they would take up the whole top or 
bottom edge of the map.


When you move on the surface of the Earth, following a true 3D 
straight line would take you off into space. You can see that by 
placing the middle of a ruler on the surface of a globe. The ends of 
the ruler are not touching the globe, are they? If the point of 
contact is at a Pole, then gradually tipping the end of the ruler down 
towards the globe's surface will always make the point of contact 
follow a line of longitude. If you start elsewhere on the globe and 
initially point your ruler East, then rolling the point of contact 
will make it cross lines of latitude as varying angles as you get 
closer to the equator.


Thus, to walk due East (i.e. perpendicular to a North-South line) on 
the Earth, after each step you have to recalculate where East is and 
make a minute adjustment in your direction. A magnetic compass does 
that for us automatically; as well, maps show East-West as linear. The 
consequence is that we're used to thinking that we're moving in a 
straight line, but really we're turning slightly after each step.


Cheers,
Steve




On 15/09/2015 07:10, Brent wrote:

I'm confused maybe.

I live in the northern hemishpere and anticipating the equinox on the 
23rd.


Supposedly the sun will rise due east.

So if due east is a right angle from north south and I traveled due 
east I would not follow my line of latitude.
I would get further and further south of my latitude the further I 
traveled.


So either the lines of latitude are not east west lines or due east 
is not a straight line but curved.

I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of latitude 
(or call them something else) are straight and a right angle

from north south?

brent




---
https://lists.uni-koeln.de/mailman/listinfo/sundial





---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Richard Mallett]

On 15/09/2015 17:42, Andrew Pettit wrote:


Hello

What fun!

Methinks that the confusion arises because the earth is not a “plane” 
but a sphere. Mercator tried to project the sphere on to the plane and 
had curved lines of latitude.


Another confusion is that there is more than one Halifax ;-)

Andrew



There was a news story a few years ago about a couple who booked a 
holiday in the wrong Sydney :-)


--
--
Richard Mallett
Eaton Bray, Dunstable
South Beds. UK

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Brent]

If I was in halifax at sunrise on the equinox and the earth stopped 
rotating and I walked due east (towards the sun) across the ocean
I would end up in Southern Spain and not on my same latitude which is in 
Southern France.


So I conclude that latitude lines are not east-west lines.

Correct?

thanks;
brent



On 9/15/2015 9:01 AM, Frank Evans wrote:

Hi Brent and all,
Compass directions that are pursued make spiral curves towards the 
poles, if north of east-west then towards the north pole, if south of 
east-west then towards the south pole. If east or west then they do 
neither but continue east-west. Try Googling "loxodromic curve". It's 
what you draw on a chart. Sailors call it a "rhumb line".

Frank 55N 1W

On 15/09/2015 15:10, Brent wrote:

I'm confused maybe.

I live in the northern hemishpere and anticipating the equinox on the 
23rd.


Supposedly the sun will rise due east.

So if due east is a right angle from north south and I traveled due 
east I would not follow my line of latitude.
I would get further and further south of my latitude the further I 
traveled.


So either the lines of latitude are not east west lines or due east 
is not a straight line but curved.

I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of latitude 
(or call them something else) are straight and a right angle

from north south?

brent




---
https://lists.uni-koeln.de/mailman/listinfo/sundial





---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[David Patte ₯]

They are east-west lines, but they are not straight. They are circles.



On 2015-09-15 12:30, Brent wrote:
If I was in halifax at sunrise on the equinox and the earth stopped 
rotating and I walked due east (towards the sun) across the ocean
I would end up in Southern Spain and not on my same latitude which is 
in Southern France.


So I conclude that latitude lines are not east-west lines.

Correct?

thanks;
brent



On 9/15/2015 9:01 AM, Frank Evans wrote:

Hi Brent and all,
Compass directions that are pursued make spiral curves towards the 
poles, if north of east-west then towards the north pole, if south of 
east-west then towards the south pole. If east or west then they do 
neither but continue east-west. Try Googling "loxodromic curve". It's 
what you draw on a chart. Sailors call it a "rhumb line".

Frank 55N 1W

On 15/09/2015 15:10, Brent wrote:

I'm confused maybe.

I live in the northern hemishpere and anticipating the equinox on 
the 23rd.


Supposedly the sun will rise due east.

So if due east is a right angle from north south and I traveled due 
east I would not follow my line of latitude.
I would get further and further south of my latitude the further I 
traveled.


So either the lines of latitude are not east west lines or due east 
is not a straight line but curved.

I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of latitude 
(or call them something else) are straight and a right angle

from north south?

brent




---
https://lists.uni-koeln.de/mailman/listinfo/sundial







---
https://lists.uni-koeln.de/mailman/listinfo/sundial




--
 

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

RE: due east

[Roger W. Sinnott]

Brent,

 

The "small circle" route is the one that takes you on a curved path, always
toward due east.

 

You could also start out going due east on a "great circle" route, and in
that case, as you note, the path would gradually veer southward.

 

Both of these routes start out perpendicularly from the north-south line.

 

 Roger

 

 

From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of David Patte
?
Sent: Tuesday, September 15, 2015 12:34 PM
To: sundial@uni-koeln.de
Subject: Re: due east

 

They are east-west lines, but they are not straight. They are circles.



On 2015-09-15 12:30, Brent wrote:

If I was in halifax at sunrise on the equinox and the earth stopped rotating
and I walked due east (towards the sun) across the ocean
I would end up in Southern Spain and not on my same latitude which is in
Southern France.

So I conclude that latitude lines are not east-west lines.

Correct?

thanks;
brent



On 9/15/2015 9:01 AM, Frank Evans wrote:

Hi Brent and all,
Compass directions that are pursued make spiral curves towards the poles, if
north of east-west then towards the north pole, if south of east-west then
towards the south pole. If east or west then they do neither but continue
east-west. Try Googling "loxodromic curve". It's what you draw on a chart.
Sailors call it a "rhumb line".
Frank 55N 1W

On 15/09/2015 15:10, Brent wrote:

I'm confused maybe.

I live in the northern hemishpere and anticipating the equinox on the 23rd.

Supposedly the sun will rise due east.

So if due east is a right angle from north south and I traveled due east I
would not follow my line of latitude.
I would get further and further south of my latitude the further I traveled.

So either the lines of latitude are not east west lines or due east is not a
straight line but curved.
I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of latitude (or call
them something else) are straight and a right angle
from north south?

brent







---
https://lists.uni-koeln.de/mailman/listinfo/sundial
 

 







---
https://lists.uni-koeln.de/mailman/listinfo/sundial
 






-- 
 
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Ruud Hooijenga]

 
  Due east is a right angle from north-south. But the 'line' of latitude is not a great circle (except the equator, which is).
  So if you keep walking due east, you are really always curving towards the pole.Suppose you lived 1 meter from the North Pole; then you would walk along a circle of 2 meters in diameter. But you would still always walk due east, and the circle always is at right angeles to north-south.
  Rudolf
  
   Op 15 september 2015 om 16:10 schreef Brent :
   

   I'm confused maybe.  I live in the northern hemishpere and anticipating the equinox on the 23rd.  Supposedly the sun will rise due east.  So if due east is a right angle from north south and I traveled due east I would not follow my line of latitude. I would get further and further south of my latitude the further I traveled.  So either the lines of latitude are not east west lines or due east is not a straight line but curved. I suspect lines of latitude are not east west lines? They would work fine if the earth was not tilted, but it is.  Wouldn't it make sense to coordinate the globe so lines of latitude (or call them something else) are straight and a right angle from north south?  brent   
  
   
  
   ---
   https://lists.uni-koeln.de/mailman/listinfo/sundial
   
   
  
   
 

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Frank Evans]

Hi Brent and all,
Compass directions that are pursued make spiral curves towards the 
poles, if north of east-west then towards the north pole, if south of 
east-west then towards the south pole. If east or west then they do 
neither but continue east-west. Try Googling "loxodromic curve". It's 
what you draw on a chart. Sailors call it a "rhumb line".

Frank 55N 1W

On 15/09/2015 15:10, Brent wrote:

I'm confused maybe.

I live in the northern hemishpere and anticipating the equinox on the 
23rd.


Supposedly the sun will rise due east.

So if due east is a right angle from north south and I traveled due 
east I would not follow my line of latitude.
I would get further and further south of my latitude the further I 
traveled.


So either the lines of latitude are not east west lines or due east is 
not a straight line but curved.

I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of latitude 
(or call them something else) are straight and a right angle

from north south?

brent




---
https://lists.uni-koeln.de/mailman/listinfo/sundial



---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Ruud Hooijenga]

 
  Due east is a right angle from north-south. 
  
   Op 15 september 2015 om 16:10 schreef Brent :
   

   I'm confused maybe.  I live in the northern hemishpere and anticipating the equinox on the 23rd.  Supposedly the sun will rise due east.  So if due east is a right angle from north south and I traveled due east I would not follow my line of latitude. I would get further and further south of my latitude the further I traveled.  So either the lines of latitude are not east west lines or due east is not a straight line but curved. I suspect lines of latitude are not east west lines? They would work fine if the earth was not tilted, but it is.  Wouldn't it make sense to coordinate the globe so lines of latitude (or call them something else) are straight and a right angle from north south?  brent   
  
   
  
   ---
   https://lists.uni-koeln.de/mailman/listinfo/sundial
   
   
  
   
 

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

RE: due east

[Andrew Pettit]

See also

 

Martin Gardner - Mathematical Carnival - Ch. 17

 

Andrew

 

From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Brent
Sent: 15 September 2015 17:30
To: Frank Evans
Cc: sundial
Subject: Re: due east

 

If I was in halifax at sunrise on the equinox and the earth stopped rotating
and I walked due east (towards the sun) across the ocean
I would end up in Southern Spain and not on my same latitude which is in
Southern France.

So I conclude that latitude lines are not east-west lines.

Correct?

thanks;
brent



On 9/15/2015 9:01 AM, Frank Evans wrote:

Hi Brent and all,
Compass directions that are pursued make spiral curves towards the poles, if
north of east-west then towards the north pole, if south of east-west then
towards the south pole. If east or west then they do neither but continue
east-west. Try Googling "loxodromic curve". It's what you draw on a chart.
Sailors call it a "rhumb line".
Frank 55N 1W

On 15/09/2015 15:10, Brent wrote:

I'm confused maybe.

I live in the northern hemishpere and anticipating the equinox on the 23rd.

Supposedly the sun will rise due east.

So if due east is a right angle from north south and I traveled due east I
would not follow my line of latitude.
I would get further and further south of my latitude the further I traveled.

So either the lines of latitude are not east west lines or due east is not a
straight line but curved.
I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of latitude (or call
them something else) are straight and a right angle
from north south?

brent







---
https://lists.uni-koeln.de/mailman/listinfo/sundial
 

 

 

---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: due east

[Steve Lelievre]

Brent,

My 2 cents worth...

If by tilt you meant the obliquity of the ecliptic, that doesn't affect 
things.


Your question is about walking on a globe (3D), but I suspect you're 
imagining it like a flat map (2D). A map (assuming the map is a Mercator 
Projection) represents latitude as a straight line but when you move on 
the surface of the Earth you're not really following a line that is 
straight in 3D terms.


The line of latitude is a really a circle representing a sectional slice 
through the globe. To compensate for unbending a circle in 3D to be a 
straight line on a 2D map,  something else has to get distorted: shape. 
That's why on a map Greenland looks huge compared to other countries and 
is so wide at the top. On a globe it looks smaller and more like a 
rectangle than a very wide triangle. The extreme cases are the North and 
South Poles which are points on a globe but on a map get stretched out 
to be a line - they would take up the whole top or bottom edge of the map.


When you move on the surface of the Earth, following a true 3D straight 
line would take you off into space. You can see that by placing the 
middle of a ruler on the surface of a globe. The ends of the ruler are 
not touching the globe, are they? If the point of contact is at a Pole, 
then gradually tipping the end of the ruler down towards the globe's 
surface will always make the point of contact follow a line of 
longitude. If you start elsewhere on the globe and initially point your 
ruler East, then rolling the point of contact will make it cross lines 
of latitude as varying angles as you get closer to the equator.


Thus, to walk due East (i.e. perpendicular to a North-South line) on the 
Earth, after each step you have to recalculate where East is and make a 
minute adjustment in your direction. A magnetic compass does that for us 
automatically; as well, maps show East-West as linear. The consequence 
is that we're used to thinking that we're moving in a straight line, but 
really we're turning slightly after each step.


Cheers,
Steve




On 15/09/2015 07:10, Brent wrote:

I'm confused maybe.

I live in the northern hemishpere and anticipating the equinox on the 
23rd.


Supposedly the sun will rise due east.

So if due east is a right angle from north south and I traveled due 
east I would not follow my line of latitude.
I would get further and further south of my latitude the further I 
traveled.


So either the lines of latitude are not east west lines or due east is 
not a straight line but curved.

I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of latitude 
(or call them something else) are straight and a right angle

from north south?

brent




---
https://lists.uni-koeln.de/mailman/listinfo/sundial



---
https://lists.uni-koeln.de/mailman/listinfo/sundial

RE: due east

[Andrew Pettit]

Hello

 

What fun!

 

Methinks that the confusion arises because the earth is not a "plane" but a
sphere. Mercator tried to project the sphere on to the plane and had curved
lines of latitude.

 

Another confusion is that there is more than one Halifax ;-)

 

Andrew

 

From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Brent
Sent: 15 September 2015 17:30
To: Frank Evans
Cc: sundial
Subject: Re: due east

 

If I was in halifax at sunrise on the equinox and the earth stopped rotating
and I walked due east (towards the sun) across the ocean
I would end up in Southern Spain and not on my same latitude which is in
Southern France.

So I conclude that latitude lines are not east-west lines.

Correct?

thanks;
brent



On 9/15/2015 9:01 AM, Frank Evans wrote:

Hi Brent and all,
Compass directions that are pursued make spiral curves towards the poles, if
north of east-west then towards the north pole, if south of east-west then
towards the south pole. If east or west then they do neither but continue
east-west. Try Googling "loxodromic curve". It's what you draw on a chart.
Sailors call it a "rhumb line".
Frank 55N 1W

On 15/09/2015 15:10, Brent wrote:

I'm confused maybe.

I live in the northern hemishpere and anticipating the equinox on the 23rd.

Supposedly the sun will rise due east.

So if due east is a right angle from north south and I traveled due east I
would not follow my line of latitude.
I would get further and further south of my latitude the further I traveled.

So either the lines of latitude are not east west lines or due east is not a
straight line but curved.
I suspect lines of latitude are not east west lines?
They would work fine if the earth was not tilted, but it is.

Wouldn't it make sense to coordinate the globe so lines of latitude (or call
them something else) are straight and a right angle
from north south?

brent







---
https://lists.uni-koeln.de/mailman/listinfo/sundial
 

 

 

---
https://lists.uni-koeln.de/mailman/listinfo/sundial