Definition of a nautical mile
JF Mezei
1852 metres.
And then, there is the following page:
http://home.online.no/~sigurdhu/Grid_1deg.htm
Where it states that there are 21638.778 nm at the equator according to WGS84.
Is it correct to state that the traditional definition of a nautical mile "one
minute (1/60 of a degree at equator)" is , strictly speaking, no longer valid ?
If the nautical mile was fixed to 1852 metres in 1929 and since then, the
actual measurements of the earth would have changed, that would explain why
the nautical mile no longer precisely represents one minute of longitude at equator.
Is this a correct interpretation ?
In the case of a GPS, when it calculates values, does it know that there are
more than 21600nm in the earth's circumference ? I.E., if I move one degree,
will the GPS know that I have actually advanced more than 60nm ? For one
degree, the error would be about .1 nautical mile. (almost 200 metres).
xander
Nautical College it is 1/60 of a degree of a meridian and not of the
equator. Due to the fact that WGS84 reference to a geoid, it is not a
perfect mathimatical shape. WGS84 is not used for standardisation of a Nm.
Nm's are used to give the size of the equator in a WGS84 system.
I hope this helps and sorry for the maybe weird english, but that si what
you get with dutch sailors.
regards,
Xander Langschmidt
JF Mezei <jfmezei...@videotron.ca> schreef in berichtnieuws
3BF8E9D2...@videotron.ca...
Jack Yeazel
xander wrote:
> I hope this helps and sorry for the maybe weird english, but that si what
> you get with dutch sailors.
-Who probably invented the idea of the nautical mile in the first place!
--
Jack
Get general GPS information at http://joe.mehaffey.com/
Spam Remove"@hotmail.com Brian
Latitude. One minute of latitude is not a constant length, being longer near
the poles than near the equator.
Brian
"JF Mezei" <jfmezei...@videotron.ca> wrote in message
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Hans-Georg Michna
>The old definition of Nautical Mile was the average length of one minute of
>Latitude. One minute of latitude is not a constant length, being longer near
>the poles than near the equator.
Brian,
shorter near the poles, not longer.
Hans-Georg
--
No mail, please.
Spam Remove"@hotmail.com Brian
because geodetic latitude is not geocentric. I'm looking at Bowditch at
present and one degree of latitude at the poles is 11694 metres (60.310 Nm)
and at the equator is 110574 metres (59.705 Nm).
Brian
"Hans-Georg Michna" <hans-georgN...@michna.com> wrote in message
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Laurie Brown
From: http://www.howstuffworks.com/question79.htm
Question:
What is a nautical mile, and how does it differ from a normal mile and a
kilometer?
Answer:
A nautical mile is based on the circumference of the planet earth. If you were
to cut the earth in half at the equator, you could pick up one of the halves and
look at the equator as a circle. You could divide that circle into 360 degrees.
You could then divide a degree into 60 minutes. A minute of arc on the planet
earth is one nautical mile. This unit of measurement is used by all nations for
air and sea travel.
A _knot_ is a unit of measure for speed. If you are traveling at a speed of
one nautical mile per hour, you are said to be traveling at a speed of one knot.
A kilometer is also defined using the planet earth as a standard of distance. If
you were to take the earth and cut it in half along a line passing from the
North Pole through Paris, and then measure the distance of the curve running
from the North Pole to the equator on that circle, and then divide that distance
by 10,000, you would have the traditional unit for the kilometer as defined in
1791 as by the French Academy of Sciences. A nautical mile is 1,852 meters.
A nautical mile is equivilent to 1.1508 miles, or 6,076 feet, in the English
measurement system.
To travel around the earth at the equator you would have to travel 360 * 60 =
21,600 nautical miles, or 24,857 miles, or 40,003 kilometers.
JF Mezei
> From: http://www.howstuffworks.com/question79.htm
> A kilometer is also defined using the planet earth as a standard of distance. If
> you were to take the earth and cut it in half along a line passing from the
> North Pole through Paris, and then measure the distance of the curve running
> from the North Pole to the equator on that circle, and then divide that distance
> by 10,000, you would have the traditional unit for the kilometer as defined in
> 1791 as by the French Academy of Sciences. A nautical mile is 1,852 meters.
Not anymore, the current official definition is: http://www.bipm.fr/enus/3_SI/base_units.html
metre m
The metre is the length of the path travelled by light in vacuum during a time
interval of 1/299 792 458 of a second.
History of the evolution of the definition of the metre at:
http://www.bipm.fr/enus/3_SI/metre_hist.html
another history at:
http://physics.nist.gov/cuu/Units/meter.html
Can't find the link, but I read that the nautical mile was "accepted" in 1929
and equated to 1852 metres. There was also another link that described how the
metre was calculated (they manually measured the distance between one city in
france and one in spain, and I *guess* by measuring angle of sun/stars at both
points, they could determine the distance in degrees between the two cities.
> To travel around the earth at the equator you would have to travel 360 * 60 =
> 21,600 nautical miles, or 24,857 miles, or 40,003 kilometers.
According to http://home.online.no/~sigurdhu/Grid_1deg.htm
The distance at equator would be: 21,638.778 nm
Graper
> 1852 metres.
>
> And then, there is the following page:
> http://home.online.no/~sigurdhu/Grid_1deg.htm
>
> Where it states that there are 21638.778 nm at the equator according to WGS84.
>
> Is it correct to state that the traditional definition of a nautical mile "one
> minute (1/60 of a degree at equator)" is , strictly speaking, no longer valid ?
"The value of this unit, 1 nautical mile=1852m, was adopted by the
First International Extraordinary Hydrographic Conference, Monaco,
1929, under the name 'International nautical mile'".
Ref: NIST Special Publication 811 (1995 Edition) "Guide for the Use
of the International System of Units (SI)", page 52, footnote 21.
Andrew Mealin
"Brian" <bjk444"Nil Spam Remove"@hotmail.com> wrote in message
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Brian
"Andrew Mealin" <andrew.mealin@*nojunk*ntlworld.com> wrote in message
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Hans-Georg Michna
>I used to think it was shorter near the poles too, but it's actually longer,
>because geodetic latitude is not geocentric. I'm looking at Bowditch at
>present and one degree of latitude at the poles is 11694 metres (60.310 Nm)
>and at the equator is 110574 metres (59.705 Nm).
Brian,
you mean that one degree of latitude isn't one angular degree? I
find that hard to believe.
And even if so, why should the measure be so distorted that it's
now about the opposite of what it should be? If somebody wanted
to distort the angles, then why not distort them so that the
distance at the surface is constant?
Sigurd Humerfelt
An easy explanation is to remember that the Earth is "flatter" at the poles
than at the equator. Make yourself a little drawing and I think you will
realise why a degree of latituse is longer at the poles that at the equator.
Also check http://home.online.no/~sigurdhu/Grid_1deg.htm.
--
Sigurd
N 59°56' E 10°42' (WGS 84)
Size and shape of the Earth (WGS 84)?
Garmin MapSource WorldMap map sizes?
Garmin GPS 12 MAP and III (PLUS) fields and scales?
See http://home.online.no/~sigurdhu
"Hans-Georg Michna" <hans-georgN...@michna.com> skrev i melding
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Sigurd Humerfelt
There are many errors about the nautical mile at
http://www.howstuffworks.com/question79.htm:
A nautical mile is also based on the circumference of the Earth going
through the poles not around the equator. So the meter and the nautical
mile both have the same origin, but are divided differently. As a minute of
arc of latitude varies from the pole to the equator, it was decided in 1929
to define an International Nautical Mile. According to WGS 84 there is
10001.966 km from a pole to the equator. This results in an average minute
of arc of latitude equal to 1852.216 m. This was rounded off to the nearest
integer, hence the International Nautical Mile = 1852 m. A minute of arc
along the equator on the other hand is 1855.32 m. This number is not close
at all to the International Nautical Mile of 1852 m. So the definition of
the nautical miles at http://www.howstuffworks.com/question79.htm does not
fit the numbers!
When it comes to the circumference of the Earth it gets even worse. As an
approximated average value for an other direction is used, the answer will
of course be wrong; the circumference of the Earth at the equator is
40075.017 km or 21638.778 nautical miles. The circumference of the Earth at
http://www.howstuffworks.com/question79.htm is actually less than the
smallest circumference of the Earth!
Those inclined can do the maths themselves using the WGS 84 definition of
the Earth:
Semi-major axis = a = 6378137.0 m
Flattening = f = 1/298.257223563
or check the numbers at http://home.online.no/~sigurdhu/WGS84_Eng.html and
http://home.online.no/~sigurdhu/Grid_1deg.htm.
--
Sigurd
N 59°56' E 10°42' (WGS 84)
Size and shape of the Earth (WGS 84)?
Garmin MapSource WorldMap map sizes?
Garmin GPS 12 MAP and III (PLUS) fields and scales?
See http://home.online.no/~sigurdhu
"Laurie Brown" <lau...@mac.com> skrev i melding
news:Pine.LNX.4.33L2.01112...@grace.speakeasy.net...
Spam Remove"@hotmail.com Brian
I agree it's not intuitive. Please read
http://www.irbs.com/bowditch/pdf/chapt02.pdf
It's an 8 page .PDF. On the right hand column of page 3 it says
"Because of the oblate shape of the ellipsoid, the length
of a degree of geodetic latitude is not everywhere the same,
increasing from about 59.7 nautical miles at the equator to
about 60.3 nautical miles at the poles."
It's still one angular degree, but the origin is different. I can't find you
a good diagram at present but I'll keep looking.
Brian
"Hans-Georg Michna" <hans-georgN...@michna.com> wrote in message
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LShaping
Hi Hans-Georg,
Doing some research before I start making some macros for Starcraft, I
noticed your comments.
http://groups.google.com/groups?hl=en&lr=lang_en&threadm=357e1f3d.27993742%40enews.newsguy.com&rnum=55&prev=/groups%3Fas_q%3Dshortcut%26as_ugroup%3Dalt.games.starcraft%26lr%3Dlang_en%26num%3D100%26hl%3Den
You might not even be playing now, but FYI I intend to be doing
exactly the same stuff you discussed. The idea about the AI
optionally controlling the units is another insight. I might have
that in effect for uninstructed units except when the main map view is
on them. You made some very accurate comments on an issue I am
enthusiastic about. I plan on doing some stuff along those lines for
Starcraft.
http://home.satx.rr.com/lfolder/
Thanks for the post, bye,
LShaping
Hans-Georg Michna
>I agree it's not intuitive. Please read
>http://www.irbs.com/bowditch/pdf/chapt02.pdf
>It's an 8 page .PDF. On the right hand column of page 3 it says
>"Because of the oblate shape of the ellipsoid, the length
>of a degree of geodetic latitude is not everywhere the same,
>increasing from about 59.7 nautical miles at the equator to
>about 60.3 nautical miles at the poles."
>
>It's still one angular degree, but the origin is different. I can't find you
>a good diagram at present but I'll keep looking.
Brian,
this must be a printing error. The earth is flatter around the
poles. The distance from the center of the earth to the surface
is shorter near the poles. Hence one degree covers a shorter
distance near the poles.
Hans-Georg Michna
>An easy explanation is to remember that the Earth is "flatter" at the poles
>than at the equator. Make yourself a little drawing and I think you will
>realise why a degree of latituse is longer at the poles that at the equator.
Sigurd,
yes, this is obvious. No need to tell me. This is the reason why
one degree covers a shorter distance near the poles than near
the equator.
But the opposite was stated. Why should one degree of latitude
be a longer distance near the poles than near the equator?
Hans-Georg Michna
Hey, these comments are over three years old! I'm getting warmed
up for Warcraft 3 now <grin>.
Have little time for playing computer games though.
JF Mezei
latitude is one nautical mile and as such it would be 1.852 km and whatever
equivalent in US miles ?
Or does it calculate the distance relative to how long a degree is at your
current latitude ?
i.e. if I walk due north for 10 minutes near the pole, will the GPS record the
same distance travelled compared to travelling due north for the same 10
minutes from the equator ?
Hans-Georg Michna
>http://www.ncgia.ucsb.edu/education/curricula/giscc/units/u014/u014.html
>"When the earth's shape is based on the WGS 84 Ellipsoid:
>The length of 1° of latitude is not the same everywhere as it is on the
>sphere.
>At the equator, 1° of latitude is 110.57 kilometers (68.7 miles).
>At the poles, 1° of latitude is 111.69 kilometers (69.4 miles). "
>Another printing error?
Brian,
yes.
Please tell me one thing. Do you believe that the distance from
the center of the earth to the pole is shorter than to the
equator?
Do you understand trigonometry?
Spam Remove"@hotmail.com Brian
http://www.ncgia.ucsb.edu/education/curricula/giscc/units/u014/u014.html
"When the earth's shape is based on the WGS 84 Ellipsoid:
The length of 1° of latitude is not the same everywhere as it is on the
sphere.
At the equator, 1° of latitude is 110.57 kilometers (68.7 miles).
At the poles, 1° of latitude is 111.69 kilometers (69.4 miles). "
Another printing error?
Brian
>
MichaelO.
the old log line bearing the same relation to a nautical mile as the period
of the sand glass did to an hour. The nautical mile is 6076 feet or 6080.2
feet (depending on system used), a statute mile is 5280ft. A sea mile =
1.1515 statute mile. The expression knots per hour is incorrect as to speed
but is used in expressing acceleration..
Nautical Mile - One minute of latitude; variously approximated as either
6076 feet or 6080 feet - about 1/8 longer than the statute mile of 5280
feet.Since 1959 the Unites States has used the International Nautical Mile
which states the exact relationship of .9144 meter equals one yard of three
feet. Therefore the length of the US recognized International Nautical is
6,076.11549 feet (approximately). Then rounded to 6076. The use 6080 feet is
also prevalent. However most navigators by convention use 2,000 yards equal
to one nautical mile equal to one degree. Therefore 60 minutes of arc or one
degree equals 60 nautical miles. The difference between using 6076, 6080 or
2000 yards would increase as does the length of the voyage or leg and may
have given rise to comments such as "a miss is as good as a mile". In any
case when measuring distance on any chart the use of the mid-latitude scale
is mandatory.
"JF Mezei" <jfmezei...@videotron.ca> wrote in message
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"Hans-Georg Michna" <hans-georgN...@michna.com> wrote in message
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Dave Martindale
>yes, this is obvious. No need to tell me. This is the reason why
>one degree covers a shorter distance near the poles than near
>the equator.
>But the opposite was stated. Why should one degree of latitude
>be a longer distance near the poles than near the equator?
You're probably thinking that latitude is defined by a polar coordinate
angle at the centre of the earth. So, for example, the 60 degree north
line of latitude is defined to be the set of points on the surface of
the earth where a line from the point to the centre of the earth makes
a 60 degree angle to the plane of the equator. In this sort of system,
the larger radius of the earth near the equator means that latitude lines
would be spaced further apart near the equator.
However, that's not how latitude is defined. Latitude is the angular
difference between a tangent to the surface (local horizontal) at a
particular location, and tangent to the surface at the equator. Or,
equivalently, the angle between the local tangent and the earth's rotation
axis. So 60 degrees north is the place where Polaris is 60 degrees above
the horizon.
If the earth was spherical, the two methods would give the same answer,
because the tangent is always perpendicular to a line joining a surface
point to the centre. But with the earth being ellipsoidal, the tangent
is *not* perpendicular to a "radius" line. The tangent changes
direction *faster* near the equator, and so lines of latitude are
*closer* near the equator.
Dave
Dave Martindale
>this must be a printing error. The earth is flatter around the
>poles. The distance from the center of the earth to the surface
>is shorter near the poles. Hence one degree covers a shorter
>distance near the poles.
You're right, when that one degree is *measured at the centre of the
earth*
But one degree change in latitude occurs when the *tangent to the
surface* changes by one degree.
Draw a nice exaggerated ellipse, with the major axis double the minor
axis or more. Now look at how the tangent slope changes - rapidly at
the "equator" and slowly at the "poles".
Dave
JF Mezei
> Please tell me one thing. Do you believe that the distance from
> the center of the earth to the pole is shorter than to the
> equator?
By about 20km actually. So assuming that the degrees of latitudes are spread
evenly based on angles, then the portion of earth with the shorter radius
would also see shorter distances between angles.
However, because the poles are flat instead of circular, the distance between
2 latitudes would be pure trigonometry since the surface of that distance
would be flat (eg: triangle calculations), whereas near the equator, the
distances would be measured as a proportion of circumference.
JF Mezei
> However, that's not how latitude is defined. Latitude is the angular
> difference between a tangent to the surface (local horizontal) at a
> particular location, and tangent to the surface at the equator.
Ouch !
I think we should revert to thinking that the earth is flat. If we can't agree
on the definition of latitude than we are in trouble.
I do take issue with your definition though:
Lets assume that the pole is perfectly flat, forming a flat plate, centered at
the pole with a diameter of 222 kilometres. (by loose definition, 120 nautical
miles, or 2 degrees).
This means that when you get to 88° on the "angle from equatorial plate"
definition, you are reaching that flat plate and for the next 222km of travel
on the flat plate to the pole, your latitude based on the tangent to the
surface would not change and based on your definition, you would be at 90°
latitude anywhere inside of that 222km flat plate at the top.
The conclusion is simple: buldozers and barges should bring lots of earth from
the equator and move it to the poles to eventually make the earth a perfectly
spherical planet where we would not have problems defining "latitude". :-) :-)
:-) :-)
Mircea Neacsu
> Dave Martindale wrote:
> > However, that's not how latitude is defined. Latitude is the angular
> > difference between a tangent to the surface (local horizontal) at a
> > particular location, and tangent to the surface at the equator.
>
> Ouch !
The confusion between geodetic latitude (the one Dave is talking about) and
geocentric latitude (the one you are thinking of) is so common that I always
start any geodesy talk by stating once again the definition of latitude. If
somebody in the audience is incredulous and asks why my stock answer is that
it's very difficult for somebody on the surface of the earth to spot the
center of the earth and draw a line from it to measure the geocentric
latitude. It is much easier to find the local vertical (using a plumb line
for instance) hence the horizon, and measure the angle of Polaris or any
other star from that one. However even so complications start to creep up as
the plumb line is not exactly perpendicular to the surface of the ellipsoid:
it is normal to the gravitational field and the difference between the two
is called "deflection of the vertical" and has to be taken into account for
accurate measurement.
> This means that when you get to 88° on the "angle from equatorial plate"
> definition, you are reaching that flat plate and for the next 222km of
travel
> on the flat plate to the pole, your latitude based on the tangent to the
> surface would not change and based on your definition, you would be at 90°
> latitude anywhere inside of that 222km flat plate at the top.
See the above para. If there would be such a flat plate on the earth the
plumb line would still not point to the same direction in all points of the
plate so the latitude would change.
> The conclusion is simple: buldozers and barges should bring lots of earth
from
> the equator and move it to the poles to eventually make the earth a
perfectly
> spherical planet where we would not have problems defining "latitude". :-)
:-)
> :-) :-)
This would be such a pity as a lot of people known as geodesists would
remain without their monthly paycheck ;) (I'm not one of them - I just write
lowly programs exploiting their findings)
Mircea
"JF Mezei" <jfmezei...@videotron.ca> wrote in message
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Dale DePriest
accurate that then simple assumption.
There has been some suggestion that Magellan uses a spheroid to do the
calcualtion so it will be off for far distances.
It would be hard to generalize and say how a gps unit works since this
is up to the individual manufacturer.
Dale
--
Dale -- http://users.cwnet.com/dalede
For GPS data, information on Palm Navigation, and more
Read my online manual for Garmin handheld products.
Hans-Georg Michna
>Hans-Georg Michna wrote:
This wouldn't explain the inversion.
Hans-Georg Michna
>You're probably thinking that latitude is defined by a polar coordinate
>angle at the centre of the earth. So, for example, the 60 degree north
>line of latitude is defined to be the set of points on the surface of
>the earth where a line from the point to the centre of the earth makes
>a 60 degree angle to the plane of the equator. In this sort of system,
>the larger radius of the earth near the equator means that latitude lines
>would be spaced further apart near the equator.
>
>However, that's not how latitude is defined. Latitude is the angular
>difference between a tangent to the surface (local horizontal) at a
>particular location, and tangent to the surface at the equator. Or,
>equivalently, the angle between the local tangent and the earth's rotation
>axis. So 60 degrees north is the place where Polaris is 60 degrees above
>the horizon.
Dave,
ah, that's the information I was missing! Thanks for the
information!
But I still don't see how this can make any sense. The center of
the earth is a pretty well defined spot, but the shape of the
surface varies a lot and depends on a lot of factors like mass
distribution, which can even change over time. I cannot imagine
any simple, straightforward definition for the tangent angle,
unless it is again an artificial construct that doesn't bear
much relationship to reality. It would be more complex for no
good reason. What am I overlooking now?
Ask 100 people without any prior knowledge of this and ask them
how they would define latitude. I predict that 99 of them would
propose the normal, straightforward definition, the angle from
the center.
Mircea Neacsu
> the earth is a pretty well defined spot, but the shape of the
> surface varies a lot and depends on a lot of factors like mass
> distribution, which can even change over time. I cannot imagine
> any simple, straightforward definition for the tangent angle,
> unless it is again an artificial construct that doesn't bear
> much relationship to reality. It would be more complex for no
> good reason. What am I overlooking now?
See also my previous post in the newsgroup.
As a matter of fact the center of the Earth is not a well defined point. The
center of the ellipsoid that approximates the Earth is well defined, but
hard to spot from the surface. Also the mass center of Earth is well defined
but it had been hard to find until recently. So, for many years,
cartographers and geodesists have taken an arbitrary point and assumed the
direction of the vertical in that point (as indicated by a lead line)
corresponds with the normal to ellipsoid. Once you decide on an ellipsoid
(defined by it's semi major axis and flattening) and an origin point you get
what it's called a 'datum' and there are hundreds of them currently in use.
Since satellites have started to circle the Earth (and also since VLBI
techniques are available) one can determine the location of the center of
mass of the Earth so datums are no longer related to an arbitrary point but
to the center of mass of the Earth (the center of the ellipsoid coincides
with the mass center of the Earth). To distinguish between old type of
datums and new ones, the old ones are called 'local datums' and the new ones
are called 'global datums'. As you notice, even these global datums change
in time so there is an international body that monitors the changes
(International Earth Rotation Service - www.iers.org) and defines the ITRF
(International Terrestrial Reference Frame). For any practical purposes
WGS-84 and ITRF are one and the same so most people don't have to worry
about this added complexity.
In regard to local datums and their relation to WGS-84, you see every now
and then, even in this newsgroup, a question like 'how do I transform from
Airy to WGS-84'. The short answer is: you cannot. Airy is just an ellipsoid
while WGS-84 is an ellipsoid AND a datum. The question would have to be
reformulated as 'how do I transform from OSGB-36 to WGS-84' because OSGB-36
is a datum based on Airy ellipsoid. The same confusion appears also when
people talk about International ellipsoid: there is no such thing -
International-1924 is a datum based on Hyford-1906 ellipsoid.
> Ask 100 people without any prior knowledge of this and ask them
> how they would define latitude. I predict that 99 of them would
> propose the normal, straightforward definition, the angle from
> the center.
Ask then the 99 people how they can measure the latitude and see how many
come back with a solution.
Mircea
"Hans-Georg Michna" <hans-georgN...@michna.com> wrote in message
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Spam Remove"@hotmail.com Brian
Latitude is not an angle measured at the centre of the earth as you imply.
It's an angle measured from the surface of the earth as Dave indicates.
Think of the curvature of the earth's surface. In your terms the earth does
have a"longer" effective radius at the poles even though the angle at the
intersection of the radii is not how latitude is measured.
Brian
"Dave Martindale" <da...@cs.ubc.ca> wrote in message
news:9tip3p$jpf$1...@trappist.cs.ubc.ca...
Dave Martindale
>I do take issue with your definition though:
Well, there are other ways of defining latitude, based on the angle
between the local direction of gravity (measured by a plumb bob or
bubble level or the surface of a pool of liquid). But the definition
I gave is the way latitude was originally measured by sea captains,
comparing the elevation of heavenly bodies above the horizon, since
the horizon at sea is an excellent measure of the local tangent to
the earth's surface. If you assume that the earth's surface is a
liquid, the two definitions are equivalent.
>Lets assume that the pole is perfectly flat, forming a flat plate, centered at
>the pole with a diameter of 222 kilometres. (by loose definition, 120 nautical
>miles, or 2 degrees).
In this case, you have created a local anomaly in curvature, so you
can't depend on the horizon, and my "definition" isn't applicable. But
you can still use the plumb bob or bubble level or surface of liquid
measurements, and those will change smoothly from the edge to the
centre of your plate. And latitudes between 88 and 90 degrees are
still perfectly well defined.
Dave
Dave Martindale
>But I still don't see how this can make any sense. The center of
>the earth is a pretty well defined spot, but the shape of the
>surface varies a lot and depends on a lot of factors like mass
>distribution, which can even change over time. I cannot imagine
>any simple, straightforward definition for the tangent angle,
>unless it is again an artificial construct that doesn't bear
>much relationship to reality. It would be more complex for no
>good reason. What am I overlooking now?
A rather large part of the surface of the earth is water, and there the
presence of the horizon provides a very accurate measure of the local
tangent.
On land, unless you're in Saskatchewan [ :-) ], you can't use the
horizon, and instead you use a plumb bob or bubble level or the
surface of a pool of liquid for your horizontal or vertical reference.
>Ask 100 people without any prior knowledge of this and ask them
>how they would define latitude. I predict that 99 of them would
>propose the normal, straightforward definition, the angle from
>the center.
Sure - but it doesn't matter what they think. Latitude was defined
by what explorers and surveyors could actually measure - the angle
between surface horizontal (or vertical) and celestial bodies. And
you can't just change to a system based on angle at the centre of the
earth without changing the latitude of *every* known place (except
the two poles and any points on the equator).
Dave
Ian Strachan
<ka...@nospam.org> writes
>1nm = 1852m is the current
>definition and it matters not a damn how that distance originated. All
>further discussion on the subject is as pointless as were the other two
>great debates on the very same subject in the past year.
I agree with the above as long as it is clear that the Nautical Mile
that we are talking about is the International Nautical Mile, not that
uses by Columbus, Drake et al, or even more recent Navigators. This
Nautical Mile was presumably based either on knots in a rope (mark twain
and all that) or minutes of latitude on a Mercator chart.
Similarly, I understand that the international conversion between
imperial and metric units of length is based on the assumption that 1
inch is exactly equivalent to 2.54 centimetres.
Was this decided by the same 1929 Monaco convention that defined the INM
as 1852m exactly? What other definitions did they agree on?
--
Ian Strachan
Spam Remove"@hotmail.com Brian
Brian
"Dave Martindale" <da...@cs.ubc.ca> wrote in message
news:9tjt2h$kkl$1...@trappist.cs.ubc.ca...
Sigurd Humerfelt
By agreement between Great Britian, its earlier dominions and USA in 1960 an
international yard was defined to be 0.9144 m exactly, making an inch equal
to 25.4 mm exactly and a foot equal to 304.8 mm exactly.
--
Sigurd
N 59°56' E 10°42' (WGS 84)
Size and shape of the Earth (WGS 84)?
Garmin MapSource WorldMap map sizes?
Garmin GPS 12 MAP and III (PLUS) fields and scales?
See http://home.online.no/~sigurdhu
"Ian Strachan" <I...@ukiws.demon.co.uk> skrev i melding
news:BEzMIMBP$X$7E...@ukiws.demon.co.uk...
Ian Strachan
<ka...@nospam.org> writes
>I seriously doubt the Mr. Columbus or Sir Francis really gave a fig about
>hundred feet here or a thousand feet there on their journeys.
However there was considerable ambiguity in distance units used at that
time. My Jane's glossary says the following about the so-called Statute
Mile which is still used in the UK and USA:
Statute Mile - In 1592 the English Parliament defined the mile by
Statute to be "320 rods, 1760 yards or 5280 feet". This unit replaced
various miles previously used in the British Isles, including the
Scottish mile of 1980 yards and the Irish mile of 2240 yards. Today, the
International Statute Mile is defined as exactly 5,280 International
Feet, where an international foot is 304.8mm exactly. The number 5280 is
derived from 8 furlongs (a traditional furrow-long when ploughing by
horse) to the St Ml, 10 chains (literally, a surveyor's measuring chain)
to the furlong, 22 yards to the chain and three feet to the yard.
--
Ian Strachan
Gene Nygaard
> Hans-Georg,
>
> http://www.ncgia.ucsb.edu/education/curricula/giscc/units/u014/u014.html
>
>
> "When the earth's shape is based on the WGS 84 Ellipsoid:
> The length of 1° of latitude is not the same everywhere as it is on the
> sphere.
> At the equator, 1° of latitude is 110.57 kilometers (68.7 miles).
> At the poles, 1° of latitude is 111.69 kilometers (69.4 miles). "
>
>
> Another printing error?
>
> Brian
This is actually a difficult subject to understand. The above is
true, but only for "geodetic" latitudes--these angles are not formed
at the center of the earth. There are instead the angle between the
axis of the earth and the line normal to the plane tangent to the
surface at a given point on a reference ellipsoid. This line meets
the axis of rotation somewhere on the far side of the center of the
earth. That geodetic latitude is, of course, the latitude usually
given on our maps, etc. (Plumb bobs will be close to that as well,
barring localized nearby mass concentrations.)
If you use geocentric measures of latitude, measured from the angle at
the center of the earth, it would be the opposite way, with a degree
of latitude being longer near the equator and shorter near the poles.
Gene Nygaard
Sigurd Humerfelt
Even if you are wrong you are very persistent. 8-)
The earth we are considering is not sphere, it a spheroid (only two of the
three axes are equal, remember). What you do is sort of comparing two
spheres (one with the polar radius and the other with the equatorial
radius). Of course a degree of arc on the sphere with the shortest radius
will span the shortest distance. But when considering the length of a
degree of arc on the surface of a spheroid you cannot just look at the
ordinary radii, you have to consider the radii of curvature.
According to WGS 84:
a = 6378137.0 m
f = 1/298.257223563
e^2 = 2f-f^2 = 0.0066943799901
The radius of curvature at the equator = ?(0) = a*(1 - e^2) =
6335439.3273 m
The radius of curvature at a pole = ?(90) = a*(1 - e^2)/(1 - e^2)^3/2 =
6399593.6258 m
You may consider the radius of curvature at a point on the surface of a
spheroid as the radius of a sphere with the same curvature.
As you will see, the radius of curvature at a pole is longer than the radius
of curvature at the equator of the earth. This is not surprising as the
earth is flatter at the poles than at the equator.
The difference between the polar radius and the equatorial radius of the
earth is about 0.3 percent (f).
The difference between the two radii of curvature is more than 1 percent.
This indicates that flattening has a greater effect than the shortening of
the polar radius compared to the equatorial radius.
Hence a degree of latitude at a pole is *LONGER* than a degree of latitude
at the equator.
This is also supported by the numbers (even if you do not think so). 8-)
See for instance http://home.online.no/~sigurdhu/Grid_1deg.htm.
End of discussion (I hope).
--
Sigurd
N 59°56' E 10°42' (WGS 84)
Size and shape of the Earth (WGS 84)?
Garmin MapSource WorldMap map sizes?
Garmin GPS 12 MAP and III (PLUS) fields and scales?
See http://home.online.no/~sigurdhu
"Hans-Georg Michna" <hans-georgN...@michna.com> skrev i melding
news:9cdovtkj8pllalsju...@4ax.com...
Hans-Georg Michna
>Latitude is not an angle measured at the centre of the earth as you imply.
>It's an angle measured from the surface of the earth as Dave indicates.
>Think of the curvature of the earth's surface. In your terms the earth does
>have a"longer" effective radius at the poles even though the angle at the
>intersection of the radii is not how latitude is measured.
Brian,
yes, I have learned this now. It is just difficult to find,
because in this particular case I would think that no person in
his right mind would invent such a strange, senseless
definition.
But I have to accept it anyway. Somebody has defined it, so we
have to take it.
I wasn't there at the time to produce a better definition. :-)
Hans-Georg Michna
>Even if you are wrong you are very persistent. 8-)
Sigurd,
hehe, yes, that's what brought me here.
Thanks for your good explanation! I understand this fully now.
(Which doesn't mean I find it sensible.)
Why did those early geographs use such an elusive measure,
rather than a simple pendulum?
Anyway, it is as it is.
Hans-Georg Michna
>Ask then the 99 people how they can measure the latitude and see how many
>come back with a solution.
Mircea,
first of all, thanks for your excellent explanation!
As to your question, the answer would, of course, be to use a
pendulum. Measure its angle against, say, a line to the polar
star.
Nothing could be simpler. And, apart from local gravity
irregularities, it could be made very accurate.
Now tell me how you measure the tangent. I have no clue how you
would do that with any accuracy, except perhaps on the ocean
when there is no wind and no wave. On land, with mountains,
hills, and valleys it is impossible.
Hans-Georg Michna
>A rather large part of the surface of the earth is water, and there the
>presence of the horizon provides a very accurate measure of the local
>tangent.
Dave,
in my experience this is everything but accurate. Often the sky
is hazy and visibility is limited. Compared to a pendulum the
horizon is orders of magnitude less accurate. Not to mention on
land.
>On land, unless you're in Saskatchewan [ :-) ], you can't use the
>horizon, and instead you use a plumb bob or bubble level or the
>surface of a pool of liquid for your horizontal or vertical reference.
Yes, that's what I assumed. But it was said that it is wrong.
Measured this way, one degree of latitude would yield a shorter
distance near the poles than near the equator.
>>Ask 100 people without any prior knowledge of this and ask them
>>how they would define latitude. I predict that 99 of them would
>>propose the normal, straightforward definition, the angle from
>>the center.
>Sure - but it doesn't matter what they think. Latitude was defined
>by what explorers and surveyors could actually measure - the angle
>between surface horizontal (or vertical) and celestial bodies. And
>you can't just change to a system based on angle at the centre of the
>earth without changing the latitude of *every* known place (except
>the two poles and any points on the equator).
Yes, I have to accept this, of course. Grudgingly. :-)
Mircea Neacsu
> As to your question, the answer would, of course, be to use a
> pendulum. Measure its angle against, say, a line to the polar
> star.
From this and other postings you made in this thread it seems you think a
pendulum would somehow indicate the direction toward the center of the
Earth. I seem to remember something from my physics classes (eons ago)
called the 'Foucault experiment' that proved the Earth rotates. If this is
what you are referring to, please give some more details about how this
could be done.
On the other hand if you are referring to lead line as a pendulum and expect
it to point toward the center of the Earth you are plain wrong. The lead
line indicates a direction normal to the gravitational field i.e. the normal
to 'geoid'. If we take the ellipsoid as the approximation of the geoid than
the lead line indicates the normal to ellipsoid which is different from the
radius - the line joining a point with the center of the ellipsoid (if you
want to convince yourself make a drawing with a rather flat ellipsis).
> Now tell me how you measure the tangent. I have no clue how you
> would do that with any accuracy, except perhaps on the ocean
> when there is no wind and no wave. On land, with mountains,
> hills, and valleys it is impossible.
Once you have the normal you don't really need the tangent but you want the
tangent directly you can use a level.
Mircea
"Hans-Georg Michna" <hans-georgN...@michna.com> wrote in message
news:j1ntvtkr742at90md...@4ax.com...
Hans-Georg Michna
>> As to your question, the answer would, of course, be to use a
>> pendulum. Measure its angle against, say, a line to the polar
>> star.
>From this and other postings you made in this thread it seems you think a
>pendulum would somehow indicate the direction toward the center of the
>Earth. I seem to remember something from my physics classes (eons ago)
>called the 'Foucault experiment' that proved the Earth rotates. If this is
>what you are referring to, please give some more details about how this
>could be done.
Mircea,
I think that was the one in which a swinging pendulum changed
the swing direction. Doesn't play a role here. To determine the
direction to the center you would use a dampened pendulum.
I see that my choice of the word "Pendulum" was misleading. The
right word is "perpendicular", if I'm not mistaken again.
>On the other hand if you are referring to lead line as a pendulum and expect
>it to point toward the center of the Earth you are plain wrong. The lead
>line indicates a direction normal to the gravitational field i.e. the normal
>to 'geoid'. If we take the ellipsoid as the approximation of the geoid than
>the lead line indicates the normal to ellipsoid which is different from the
>radius - the line joining a point with the center of the ellipsoid (if you
>want to convince yourself make a drawing with a rather flat ellipsis).
Nothing is absolutely precise. But a perpendicular is an order
of magnitude more precise than peeping at the horizon
(especially on a foggy day). :-)
>> Now tell me how you measure the tangent. I have no clue how you
>> would do that with any accuracy, except perhaps on the ocean
>> when there is no wind and no wave. On land, with mountains,
>> hills, and valleys it is impossible.
>Once you have the normal you don't really need the tangent but you want the
>tangent directly you can use a level.
What do you mean by "normal"? Using a level is equivalent to
using a perpendicular. It measures the direction of gravitation.
Jack Yeazel
Hans-Georg Michna wrote
>
> >From this and other postings you made in this thread it seems you think a
> >pendulum would somehow indicate the direction toward the center of the
> >Earth. I seem to remember something from my physics classes (eons ago)
> >called the 'Foucault experiment' that proved the Earth rotates. If this is
> >what you are referring to, please give some more details about how this
> >could be done.
>
> Mircea,
>
> I think that was the one in which a swinging pendulum changed
> the swing direction. Doesn't play a role here. To determine the
> direction to the center you would use a dampened pendulum.
Correct...
> I see that my choice of the word "Pendulum" was misleading. The
> right word is "perpendicular", if I'm not mistaken again.
Well, I like Pendulum! When talking about a perpendicular one has to indicate
"to what"... In this case probably to a pan of water...
Also "Vertical "is widely used as perpendicular to a pan of water... But
one must be aware of "deflection of the vertical" -an angle usually included
in the data of a survey marker... A nice picture of a "deflected vertical"
is shown here: http://www.irbs.com/bowditch/pdf/chapt02.pdf
But as I understand it, deflection of the vertical is measured from a
perpendicular to the ellipsoid, not a line drawn to the center of the earth...
Someone will have to
correct me...
As for where the center of the earth is, there is a disagreement between NAD-83
and WGS-84, probably giving rise to the difference in positions on the surface
of the earth... A fellow
from the NGS gave me this text: http://joe.mehaffey.com/ngs-accuracy.txt
--
Jack
Get general GPS information at http://joe.mehaffey.com/
Ted Edwards
Hans-Georg,
>
> > As to your question, the answer would, of course, be to use a
> > pendulum. Measure its angle against, say, a line to the polar
> > star.
Perhaps a better term would be plumb bob.
> From this and other postings you made in this thread it seems you think a
> pendulum would somehow indicate the direction toward the center of the
> Earth.
How do you define "center of the earth"?
One definition is center of gravity. This would be fairly accurately
pointed to by a plumb bob or the perpendicular to the surface of a body
of water. You could even use a precision level to set up a platform.
Any attempt at a geometric definition will necessarily restrict you to
an approximation to the shape of the earth - e.g. sphere or WGS84
ellipsoid or ... but all of these are approximations.
> On the other hand if you are referring to lead line as a pendulum and expect
> it to point toward the center of the Earth you are plain wrong. The lead
> line indicates a direction normal to the gravitational field
parallel to the gravitational field not normal.
Ted
JF Mezei
> Hence a degree of latitude at a pole is *LONGER* than a degree of latitude
> at the equator.
In the context of this newsgroup, do handheld GPS units actually deal with
this issue, or assume that you are travelling on a perfect sphere ?
Since the GPS does not use your altitude when calculating distance travelled
(correct ?), whether you are travelling 20 km underground (technically that is
what would happen if you're at the pole) or whether you are travelling 10km up
in thair in a plane, would the GPS unit tell you that you have travelled a
different distance if you moved exactly one degree ?
In the bible of formulas, (the Aviation Formulary), I do not believe that it
takes into consideration the odd shape of the earth when you calculate the
distance between 2 points, correct ?
Would a GPS have much more complex algorithms to factor the odd shape of the
earth when calculating distances between 2 points ?
JF Mezei
> I see that my choice of the word "Pendulum" was misleading. The
> right word is "perpendicular", if I'm not mistaken again.
From my knowledge of physics, gravity is generated by mass and is inversly
proportional to the distance between the two objects.
On a grand scale of things, planet earth is just a small rock in space, so
calculating its center has meaning.
But on earth, if I am in montreal, the gravity generated by Ayers Rock in
Australia some 13,400km away (diameter of earth) would be significantly
smaller than the gravity generated by a chunk of ground of equal mass I am
standing on.
And if you are in Nepal, at the base of and right next to the massive
Himalayas, wouldn't their mass generate sufficient gravity to skew your
pendulum/perpendicular towards the mountains ?
Peter Rathmann
>
> Sigurd Humerfelt wrote:
> > Hence a degree of latitude at a pole is *LONGER* than a degree of latitude
> > at the equator.
>
> In the context of this newsgroup, do handheld GPS units actually deal with
> this issue, or assume that you are travelling on a perfect sphere ?
>
> Since the GPS does not use your altitude when calculating distance travelled
> (correct ?)
Yes, that is correct. However when giving the distance between two
points many GPS rcvrs. will use the more complex formulas for the WGS-84
shape of the earth rather than assuming a perfect sphere. This came up
previously when someone commented that a Magellan and a website distance
calc. agreed but differed slightly from that given by a Garmin. Turned
out the Garmin unit was giving a WGS-84 distance and the other two
sources assumed a sphere.
> whether you are travelling 20 km underground (technically that is
> what would happen if you're at the pole) or whether you are travelling 10km up
> in thair in a plane, would the GPS unit tell you that you have travelled a
> different distance if you moved exactly one degree ?
Don't know for sure, but my guess is that the reported distance will be
the same, i.e. the distance as projected onto a sealevel surface.
JF Mezei
> As for where the center of the earth is, there is a disagreement between NAD-83
> and WGS-84, probably giving rise to the difference in positions on the surface
> of the earth...
I give up. With all those measures that vary in length depending on where you
are, no knowing where the centre of the earth is and having to use pendulums
to determine where you are, won't this make all of the existing highway
distance markers totally moot ? :-) ;-)
Heck, why not simply use the length of your dick as a tool to measure your
latitude ? Your latitude would be inversely proportional to its length.
Longer at equator, and damned small at the north pole where it is very cold
:-) :-) :-) :-)
Also, someone told me that Everest wasn't actually the highest mountain on
earth, it was some mountain in Ecuador that was about 6300m high, since at 28°
latitude where everest is located, the distance from the centre of the earth
is less by more than 2.5km compared to that ecuador mountain. Can anyone
confirm this ? If so, won't they have to rewrite all of the geography and
guiness book of records books around to the world ?
Somehow, when I walk the 600m to the convenience store tonight to buy the
lottery tickets, I won't really know how far it is anymore. :-)
Jack Yeazel
JF Mezei wrote:
> Somehow, when I walk the 600m to the convenience store tonight to buy the
> lottery tickets, I won't really know how far it is anymore. :-)
Do you think knowing the exact answer would improve your luck???!!! Maybe you
could win some sort of bet with the store clerk -such as what is the southern,
northern, western, and eastern most States?
JF Mezei
> Do you think knowing the exact answer would improve your luck???!!! Maybe you
> could win some sort of bet with the store clerk -such as what is the southern,
> northern, western, and eastern most States?
southern would be hawaii, northern would be alaska, western would be alaska
(aleutians), and eastern would have to be maine. right ?
(although guam might win as eastern most, and american samoa might win as
western most if they were states).
But what good does that information do if we can't know the distance to these
points ? :-) ;-) ;-)
Ken Ashe
says...
Again, you can win or lose bets without knowing exact distances. A year
ago, I would have bet against someone who told me I was born in Dixie. Then I
found out the Mason-Dixon line runs just north of Chico, CA and I was born in
San Francisco. They could have taken me to the cleaners. If I knew which
direction the cleaners was.
Dave Martindale
>How do you define "center of the earth"?
>One definition is center of gravity. This would be fairly accurately
>pointed to by a plumb bob or the perpendicular to the surface of a body
>of water. You could even use a precision level to set up a platform.
That's true for a spherical object. It would probably be true of the
earth if it didn't rotate. But the earth is roughly elliptical in
cross section due to rotation. With an ellipse, a perpendicular to
the tangent usually does *not* go through the centre. Yet, at least
on the ocean surface, the plumb bob *will* be perpendicular to the
water's surface.
Dave
Dave Martindale
>in my experience this is everything but accurate. Often the sky
>is hazy and visibility is limited. Compared to a pendulum the
>horizon is orders of magnitude less accurate. Not to mention on
>land.
On land, you can't use the horizon. But you can use a plumb bob
or bubble level. On the ocean, you'll have some difficulty using
the latter because of motion of the ship, but the angle between the
horizon and a celestial body remains fixed even as the ship moves.
>Yes, that's what I assumed. But it was said that it is wrong.
>Measured this way, one degree of latitude would yield a shorter
>distance near the poles than near the equator.
No, that's still backwards. A bubble level or a plumb bob will tell
you the local direction of "down", which is the same thing as the
local tangent on water. It will *not* point to the centre of the
earth except at the equator or poles. If you like, think of it as
gravity and centripetal acceleration from the earth's rotation
combining to make the apparent "down" direction point outwards from
the gravitational centre of the earth. That's why the earth is
ellipsoidal, not spherical.
And because of this ellipsoidal shape, the angle of the plumb bob
or bubble level relative to the stars changes more rapidly near the
equator, making on degree of latitude a *shorter* distance near the
equator than at the poles.
A plumb bob, a bubble level, and the surface of liquid all give you
exactly the same information.
Dave
Dave Martindale
>yes, I have learned this now. It is just difficult to find,
>because in this particular case I would think that no person in
>his right mind would invent such a strange, senseless
>definition.
Having grown up knowing about polar and spherical coordinates, I
thought latitude was pretty strange too. But think about it: the latitude
was defined by the only thing that a sea captain or surveyor could
actually observe - the change in direction of local vertical (or
horizontal) relative to the stars. There was no way to measure
angle at the centre of the earth.
Dave
Dave Martindale
>Why did those early geographs use such an elusive measure,
>rather than a simple pendulum?
A pendulum tells you the same thing as a sextant reading the horizon on
a ship. Both tell you the apparent direction of "down", but for a
force that has both gravitational and centripetal acceleration
components. Neither a pendulum nor a bubble level will tell you
where the centre of mass of the earth is.
Dave
Hans-Georg Michna
>Hans-Georg Michna wrote:
Yes, but it doesn't matter much. It's still better by orders of
magnitude than any other method, especially in the Himalayas,
where you cannot even see the far away horizon.
Anyway, the discussion leads nowhere. Nobody seems to know why
those buggers a long time ago defined latitude in this stupid
way, so I'll die dumb. :-)
Hans-Georg
p.s. No, I won't die dumb---see my next message below.
--
No mail, please.
Hans-Georg Michna
thanks, you finally cleared it up. My mistake was that I didn't
consider the centrifugal force that acts on a plumb bob in the
middle latitudes due to the earth's rotation.
In fact, the plumb does hang perpendicular to the tangent.
It seems that I had it all wrong. In fact those early
geographers who defined latitude were unable to determine where
the center of the earth is, so they sprung for the perpendicular
instead. The distortion leads to a degree of latitude near the
pole being longer than near the equator.
In other words, on the pole the perpendicular points at the
center of the earth (ignoring gravitation irregularities). The
same happens at the equator. However, anywhere in between the
perpendicular is deflected outwards by the centrifugal force of
the rotating earth, such that the perpendicular points to a
point beyond the center of gravity of the earth. In yet other
words, walking from the pole, you have to walk longer until the
perpendicular swings by one angular degree, because the
centrifugal force increasingly pulls it away from the pole, away
from the rotational axis.
In yet other words, the perpendicular indeed always is at a
right angle to the tangent. (There is an additional, but very
minor effect due to the "misshapen" gravity of a geoid, compared
with a sphere, but I would guess that this doesn't play any
significant role here.)
Contrary to what I first thought, the early geographers might
have liked to measure the angle from the center of the earth,
but they couldn't. So they did use the pendulum and simply
measured the perpendicular.
Sorry for the long-winded discussion, but, at least for me, it
was worth it. I can only hope that other readers have also
learned something. Thanks for this good discussion. I'm glad we
haven't given up before resolving this issue entirely.
JF Mezei
> It seems that I had it all wrong. In fact those early
> geographers who defined latitude were unable to determine where
> the center of the earth is, so they sprung for the perpendicular
> instead. The distortion leads to a degree of latitude near the
> pole being longer than near the equator.
At what point and how was it determined that the earth wasn't a perfect sphere
and the poles had a radius about 20km shorter than at equator ?
When they defined the concept of the metre and the nautical mile, were they
aware that the earth was flattened at the poles ?
Hans-Georg Michna
>Hans-Georg Michna wrote:
I don't know, but the shape of the earth is, in a way,
irrelevant. Assuming the impossible, namely a perfectly
spherical, yet rotating earth, the early geographers would still
have had the problem that their only good measurement is the
plumb and that the plumb doesn't point to the center of gravity
in the middle latitudes due to the centrifugal force.
Jack Yeazel
JF Mezei wrote:
> > Do you think knowing the exact answer would improve your luck???!!! Maybe you
> > could win some sort of bet with the store clerk -such as what is the southern,
> > northern, western, and eastern most States?
>
> southern would be hawaii, northern would be alaska, western would be alaska
> (aleutians), and eastern would have to be maine. right ?
Close, but no cigar...
Terje Mathisen
>
> JF Mezei wrote:
>
> > > Do you think knowing the exact answer would improve your luck???!!! Maybe you
> > > could win some sort of bet with the store clerk -such as what is the southern,
> > > northern, western, and eastern most States?
> >
> > southern would be hawaii, northern would be alaska, western would be alaska
> > (aleutians), and eastern would have to be maine. right ?
>
> Close, but no cigar...
Interesting...
Could one or more of the US Virgin Islands be further south than Hawaii?
PR is about 18N, while Hawaii is 20N.
Terje
--
- <Terje.M...@hda.hydro.com>
Using self-discipline, see http://www.eiffel.com/discipline
"almost all programming can be viewed as an exercise in caching"
Jack Yeazel
Terje Mathisen wrote:
> Interesting...
>
> Could one or more of the US Virgin Islands be further south than Hawaii?
>
> PR is about 18N, while Hawaii is 20N.
>
> Terje
No the southern-most state is Hawaii as JF correctly noted... Remember we're
talking about states...
Dave Martindale
>> southern would be hawaii, northern would be alaska, western would be alaska
>> (aleutians), and eastern would have to be maine. right ?
>Close, but no cigar...
I'll bet the "correct" answer makes Alaska the easternmost state because
some of the Aleutians are far enough west to have east longitude.
But this is really a stupid answer. The fact that the Aleutians extend
to east longitude is a completely artificial side effect of where the
zero longitude meridian is placed (in England). Given a choice of
declaring the Aleutians to be either 80 degrees west or 280 degrees
east of the middle of the USA, anyone with common sense or some experience
with modular arithmetic would say that the Aleutians are west, not east.
Dave
J. J. Lodder
> Is it correct to state that the traditional definition of a nautical mile "one
> minute (1/60 of a degree at equator)" is , strictly speaking, no longer valid
?
Yes.
> If the nautical mile was fixed to 1852 metres in 1929 and since then, the
> actual measurements of the earth would have changed, that would explain why
> the nautical mile no longer precisely represents one minute of longitude at eq
uator.
You can have only one definition.
> Is this a correct interpretation ?
No, the dimensions of the earth have not changed.
Originally both the meter and the mile were defined
by the dimensions of the earth.
For the meter the connection was lost when it was redefined to be the
length of a bar kept in Paris. (1860 or so)
For the mile as you noted when it was redefined as 1852 metres. (exact)
Any relation betwee the meter/mile and the size of the earth
is since then only approximate.
Best,
Jan
JF Mezei
> > southern would be hawaii, northern would be alaska, western would be alaska
> > (aleutians), and eastern would have to be maine. right ?
>
> Close, but no cigar...
is hawaii more to the west than the aleutians in alaska ?
JF Mezei
> Could one or more of the US Virgin Islands be further south than Hawaii?
>
> PR is about 18N, while Hawaii is 20N.
Are they states ?
If you include territories, then Guam would be the easternmost and southern
most state. And I think that american samoa would be the westernmost.
Jack Yeazel
Dave Martindale wrote:
> I'll bet the "correct" answer makes Alaska the easternmost state because
> some of the Aleutians are far enough west to have east longitude.
You get the cigar!
> But this is really a stupid answer. The fact that the Aleutians extend
> to east longitude is a completely artificial side effect of where the
> zero longitude meridian is placed (in England). Given a choice of
> declaring the Aleutians to be either 80 degrees west or 280 degrees
> east of the middle of the USA, anyone with common sense or some experience
> with modular arithmetic would say that the Aleutians are west, not east.
Nevertheless, the Aleutians (part of Alaska) have a longitude that is farther
east
than any other state... Don't be sore, enjoy your superior analysis! (-8
Sigurd Humerfelt
Before 1735 the French insisted that the Earth had shorter equatorial radius
than polar radius as the English (e.g. Newton) insisted on the opposite.
Quote from the "Geodesy for the Layman"
(http://164.214.2.59/publications/pub.html):
"To settle the controversy, once and for all, the French Academy of Sciences
sent a geodetic expedition to Peru in 1735 to measure the length of a
meridian degree close to the Equator and another to Lapland to make a
similar measurement near the Arctic Circle. The measurements conclusively
proved the earth to be flattened, as Newton had forecast."
See also figure 2 in this book.
IIRC the metre was defined for the first time (10000 km from a pole to the
equator) in 1791 and the international nautical mile (1852 m) in 1929.
The distance from a pole to the equator is 10001.966 km based on WGS 84.
This means that the original defintion of the metre deviates less than 2 per
thousand from what it would have been if it were defined today, not bad at
all.
--
Sigurd
N 59°56' E 10°42' (WGS 84)
Size and shape of the Earth (WGS 84)?
Garmin MapSource WorldMap map sizes?
Garmin GPS 12 MAP and III (PLUS) fields and scales?
See http://home.online.no/~sigurdhu
"JF Mezei" <jfmezei...@videotron.ca> skrev i melding
news:3C00ED9D...@videotron.ca...
J. J. Lodder
> Hans-Georg Michna wrote:
> > It seems that I had it all wrong. In fact those early
> > geographers who defined latitude were unable to determine where
> > the center of the earth is, so they sprung for the perpendicular
> > instead. The distortion leads to a degree of latitude near the
> > pole being longer than near the equator.
>
> At what point and how was it determined that the earth wasn't a perfect sphere
> and the poles had a radius about 20km shorter than at equator ?
Newton -predicted- it, in the Principia.
It was a hot issue during the 18th century,
some even claiming to have measured an elongated shape. (Cassini)
The matter was settled definitively by Maupertuis,
by measuring the length of the degree in Peru and in Lapland.
> When they defined the concept of the metre and the nautical mile, were they
> aware that the earth was flattened at the poles ?
Of course, and expeditions were sent (ą1793)
to do precission measurements of the degree on the meridian of Paris,
near Boulogne ans Barcelona, to establish the meter.
(Not just any meridian of course :-)
They did a good job, given the possibilities of the day,
Jan
--
"Vive Maupertuis, le grand aplanisateur de la terre et des Cassini"
(Voltaire)
Mircea Neacsu
> those buggers a long time ago defined latitude in this stupid
> way, so I'll die dumb. :-)
I'll try to spell it out: the gravity vector does not point to the center of
ellipsoid. It goes along a direction that is perpendicular to the surface of
the ellipsoid. So the 'buggers' chose this direction for the definition of
latitude because it was the only one available.
If you think this is counter-intuitive try the following mental experiment:
take a very large perfect sphere. The gravity vector will be pointing toward
the center of the sphere, so it will be oriented along the radius, so it
will be perpendicular to the surface of the sphere. Now take a very large
disk: in a point that is not close the margins the gravity vector will be
perpendicular to the disc but it will not be pointing toward the center of
the disk. The ellipsoid is a sphere in the process of being flattened out
toward a disk. The invariant of this process is the fact that the gravity
vector is perpendicular to the surface, not the fact that gravity vector
points toward the center of the ellipsoid.
Mircea
"Hans-Georg Michna" <hans-georgN...@michna.com> wrote in message
news:hfm10ugjfbasohr2o...@4ax.com...
Dave Martindale
>Dave Martindale wrote:
>> I'll bet the "correct" answer makes Alaska the easternmost state because
>> some of the Aleutians are far enough west to have east longitude.
Jack Yeazel <Ja...@FinalApproach.net> writes:
>You get the cigar!
Sigh. I was afraid that's the right answer.
>> But this is really a stupid answer. The fact that the Aleutians extend
>> to east longitude is a completely artificial side effect of where the
>> zero longitude meridian is placed (in England). Given a choice of
>> declaring the Aleutians to be either 80 degrees west or 280 degrees
>> east of the middle of the USA, anyone with common sense or some experience
>> with modular arithmetic would say that the Aleutians are west, not east.
>Nevertheless, the Aleutians (part of Alaska) have a longitude that is farther
>east
>than any other state... Don't be sore, enjoy your superior analysis! (-8
I'm not sore. But I still think it's a stupid answer. My "superior
analysis" is just enough experience with encountering trick questions
on tests. It's still a trick question, and the "right" answer requires
thinking that "largest eastern longitude as measured in a particular
coordinate system" is equivalent to "easternmost state".
The Aleutians are *both* 80 degrees west of the central USA and 280
degrees east. *Any* point on the earth is some nonzero distance both
west and east of any other point, unless their longitude is equal.
That's the nature of the coordinate system, which is periodic with a
period of 360 degrees. For the phrase "A is east/west of B" to make
sense, we need to agree that we'll use the direction in which the
distance is least, and ignore the other direction. So it should be
clear to everyone that 179 degrees east is really 2 degrees *west* of
179 degrees west - not 358 degrees *east*.
And so the Aleutians are pretty clearly all located *west* of the centre
of the USA, just like Japan is *west* of the USA, not east. Thus it's
silly to call Alaska the easternmost state, unless the question actually
says "what state has the easternmost longitude".
Dave
David Ness
>
>
> And so the Aleutians are pretty clearly all located *west* of the centre
> of the USA, just like Japan is *west* of the USA, not east. Thus it's
> silly to call Alaska the easternmost state, unless the question actually
> says "what state has the easternmost longitude".
Funny. I always thought that Japan was in the Far East.
JF Mezei
> And so the Aleutians are pretty clearly all located *west* of the centre
> of the USA, just like Japan is *west* of the USA, not east.
Fair point. If you ask your GPS to tell you where Japan is compared you your
location in the USA, it will tell you that you have to travel in a direction
that has a string west component. It will not tell you that because it has a
positive longitude, you must first travel east through london and then east to japan.
And as you go over the -180 longitude, your compass and GPS still tell you
that you are travelling west.
So, the aleutians would be the "left most" portion of the USA, maine would be
the "right most" portion. (talking about states).
Jack Yeazel
Dave Martindale wrote:
> And so the Aleutians are pretty clearly all located *west* of the centre
> of the USA, just like Japan is *west* of the USA, not east. Thus it's
> silly to call Alaska the easternmost state, unless the question actually
> says "what state has the easternmost longitude".
Well, remember that the Far East (Asia) is west of the US, so we're stuck with
that one too!
Mircea Neacsu
> center of the earth (ignoring gravitation irregularities). The
> same happens at the equator. However, anywhere in between the
> perpendicular is deflected outwards by the centrifugal force of
> the rotating earth, such that the perpendicular points to a
> point beyond the center of gravity of the earth.
You got it right except for the cause. The main cause for the deflection is
not the rotation of the Earth (it contributes but it is not a determining
factor). The main factor is the ellipsoidal shape of the Earth. The
gravitational field of an ellipsoid is not oriented toward the center but it
is perpendicular to the ellipsoid surface.
Mircea
"Hans-Georg Michna" <hans-georgN...@michna.com> wrote in message
news:rjl10us2q9n930a8g...@4ax.com...
Dave Martindale
>Funny. I always thought that Japan was in the Far East.
Sure it is - because it's east of Europe, which did the naming.
But if you were flying from the USA to Japan, would you head east or west?
Dave
David Ness
I pretty invariably fly East as I prefer stops in Europe to stops in the Pacific.
Dave Martindale
>Well, remember that the Far East (Asia) is west of the US, so we're stuck with
>that one too!
Yeah, and the West Indies are actually east of most of North and South
America. That's because the naming was done when the major powers were
in Europe and names were relative to there.
But this is really an argument about absolute vs. relative position.
To assign an address to a place, you need a fixed number - an absolute
position. So we adopt the convention that zero degrees longitude is in
England and the rest of the latitude markings are relative to that. In
this system, some of Alaska gets an east longitude label, while the
rest gets a west longitude label.
But to talk about whether something is east or west of *here*, what
matters is relative position. If the fastest way to get to Japan is
heading west not east, then Japan is west of here, by convention. It
simply doesn't matter that my absolute longitude is labelled west and
Japan's is labelled east, and it doesn't matter that the zero longitude
mark is in England. Japan is always west of here no matter what origin
you use - because this is a relative position measurement, not an
absolute one.
It's not difficult to do modular arithmetic that gets this right,
either. To find the relative longitude change between two points,
subtract their "absolute" longitudes. Then, if the absolute value of
the result is greater than 180 degrees, add or subtract 360 degrees
(depending on whether the result is negative or positive). This *will*
give you an answer with an absolute value of 180 degrees or less, and
whose sign indicates the direction (east is positive).
Thus, it's clear that the "eastern" Aleutians are really only a degree
or two west of the rest of Aleutians, not very far from the rest of
Alaska, and definitely west of most of the USA. But any idiot can see
that on a map. Most people can even figure that out *even* if they're
looking at a map of the world that is split at 180 degrees longitude,
so some of the Aleutians appear on the other side of the map from the
rest.
So the person who created the "correct" answer to this particular quiz
question was either less clever than most people, or they were
deliberately being misleading in order to make the question
"difficult". I dislike questions where actually understanding the
problem gives one a disadvantage over being pedantic and
literal-minded.
Dave
Dave Martindale
>You got it right except for the cause. The main cause for the deflection is
>not the rotation of the Earth (it contributes but it is not a determining
>factor). The main factor is the ellipsoidal shape of the Earth. The
>gravitational field of an ellipsoid is not oriented toward the center but it
>is perpendicular to the ellipsoid surface.
If the earth wasn't rotating, it would be basically spherical due to
gravity. If it was absolutely rigid and rotating, the rotation would
cause a force that causes a pendulum to deflect away from perpendicular
to the surface. But the earth is basically liquid, so the liquid flows
*until* it's back in equilibrium, at which point the pendulum is again
perpendicular to the surface.
So some of the force on the pendulum is directly due to rotation, and
some is due to the fact that the earth's shape is ellipsoidal - which
is also due to rotation.
Dave
J. J. Lodder
Who cares where the pendulum points to.
The art is to find out where -you are-,
from local measurements only,
not to find out where something else is.
Best,
Jan
Gene Nygaard
>x-no-archive: yes
>Ian Strachan <I...@ukiws.demon.co.uk> wrote:
>
>
>>Was this decided by the same 1929 Monaco convention that defined the INM
>>as 1852m exactly? What other definitions did they agree on?
>
>AFAIK it defined a metre as the distance between two marks on a metal rod
>(popularly known as the Paris metre) stored in some vault in Paris kept a
>certain constant temperature. Screw all the alleged fractions of any
>geodetic distances.
That happened back in the 1790s, as soon as the first measurements
were made.
The one maintained by the French then was replaced in the 1880s by the
one you are talking about, maintained by the international
organizations (CGPM, CIPM, BIPM) set up under the Metre Convention of
1875 (aka Treaty of the Meter).
The 1929 Monaco convention being discussed had nothing to do with
defining the meter--it was only the First International Extraordinary
Hydrographic Conference, by an organization that is only a minor
player in the world of metrology. Their definition was not, of
course, self-implementing. The U.S. adopted that international
nautical mile in 1954. The British used their old definition, at
least for some purposes, much longer--into the 1980s at least. The
Admiralty mile was 6080 ft (different from the old U.S. nautical
mile), and it was used long enough so that the number of metres it
equaled changed in 1963 (or perhaps 1959).
>Of course the metre has since been redefined in term of
>light.
A nautical mile is now the distance light travels in vacuum in
926/149896229 second.
>I seriously doubt the Mr. Columbus or Sir Francis really gave a fig about
>hundred feet here or a thousand feet there on their journeys. Such
>precision was neither practicable, nor desired at the time. To try to
>recalculate their measures by means of today's technology and knowledge is
>nothing more than pedantic lunacy.
Where was the line established by the 7 Jun 1494 Treaty of
Tordesillas, dividing the western hemisphere between Portugal and
Spain? This limited Spain to those lands more than 370 leagues west
of the Cape Verde Islands. It takes some pretty good definitions to
be able to determine this.
Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/t_jeff.htm
But if it be thought that, either now, or at any future time, the
citizens of the United States may be induced to undertake a thorough
reformation of their whole system of measures, weights and coins,
reducing every branch to the same decimal ratio already established
in their coins, and thus bringing the calculation of the principal
affairs of life within the arithmetic of every man who can multiply
and divide plain numbers, greater changes will be necessary.
U.S. Secretary of State Thomas Jefferson, 1790
Gene Nygaard
<Ja...@FinalApproach.net> wrote:
>
>
>JF Mezei wrote:
>
>> > Do you think knowing the exact answer would improve your luck???!!! Maybe you
>> > could win some sort of bet with the store clerk -such as what is the southern,
>> > northern, western, and eastern most States?
>>
>> southern would be hawaii, northern would be alaska, western would be alaska
>> (aleutians), and eastern would have to be maine. right ?
>
>Close, but no cigar...
He's exactly right.
What are you, foolish enough to base your determination on some
arbitrarily chosen starting point for longitude measurements? What
happens if we use the Washington, DC meridian? Or the Oslo meridian?
The Beijing meridian?
Or are you using some other faulty logic, based on some kind of
projection onto a plane, for example?
Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/
Gene Nygaard
Lodder) wrote:
>JF Mezei <jfmezei...@videotron.ca> wrote:
>
>> Is it correct to state that the traditional definition of a nautical mile "one
>> minute (1/60 of a degree at equator)" is , strictly speaking, no longer valid
> ?
>
>Yes.
>
>> If the nautical mile was fixed to 1852 metres in 1929 and since then, the
>> actual measurements of the earth would have changed, that would explain why
>> the nautical mile no longer precisely represents one minute of longitude at eq
>uator.
>
>You can have only one definition.
Where'd you ever get such a weird idea?
>> Is this a correct interpretation ?
>
>No, the dimensions of the earth have not changed.
Right. Nor has their been any significant change in their
measurement--sure, we are a little better, but all the 1929 definition
was was a value for 1 minute of longitude at some midrange latitudes,
and that is still true today.
Note that if they had tried to stick with the original 10 Mm meridian
quadrant, a nautical mile should have been 1851.851851851... m, or 1
km = 0.54 nautical mile exactly.
>
>Originally both the meter and the mile were defined
>by the dimensions of the earth.
>For the meter the connection was lost when it was redefined to be the
>length of a bar kept in Paris. (1860 or so)
Actually that happened in the 1790s. What you are probably thinking
of is the replacement of the old French standards with the new
international ones. That happened with the 1st General Conference on
Weights and Measures (CGPM) in 1889.
>For the mile as you noted when it was redefined as 1852 metres. (exact)
It had happened in various different ways in different places long
before then--defined as exactly 6080 ft in Great Britain, defined as
6080.20 slightly different feet in the United States, and various
other values in other places.
>Any relation betwee the meter/mile and the size of the earth
>is since then only approximate.
It never has been exact in any practical sense. There were some
geographical miles defined as 4 minutes of arc on the equator (i.e.,
approximately 7.421 km). Those were probably closer to being
officially defined on the basis of the shape of the earth than the
meter or the nautical mile ever were--but even those miles were on a
sea level basis, and in practice based on one reference ellipsoid or
another.
Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/
Gene Nygaard
It is--of Africa/Eurasia, the old known world.
It was still the Far East for people using Washington, DC coordinates
too--though it has a longitude of about 135° W to 150 °W in that
system.
Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/
Dale DePriest
Dave Martindale wrote:
>
> Jack Yeazel <Ja...@FinalApproach.net> writes:
>
> >Well, remember that the Far East (Asia) is west of the US, so we're stuck with
> >that one too!
>
> Yeah, and the West Indies are actually east of most of North and South
> America. That's because the naming was done when the major powers were
> in Europe and names were relative to there.
>
> But this is really an argument about absolute vs. relative position.
>
> To assign an address to a place, you need a fixed number - an absolute
> position. So we adopt the convention that zero degrees longitude is in
> England and the rest of the latitude markings are relative to that. In
> this system, some of Alaska gets an east longitude label, while the
> rest gets a west longitude label.
>
> But to talk about whether something is east or west of *here*, what
> matters is relative position. If the fastest way to get to Japan is
> heading west not east, then Japan is west of here, by convention. It
> simply doesn't matter that my absolute longitude is labelled west and
> Japan's is labelled east, and it doesn't matter that the zero longitude
> mark is in England. Japan is always west of here no matter what origin
> you use - because this is a relative position measurement, not an
> absolute one.
But when you ask for the western known point in the US, or the eastern
it is not clear from the question that relative points are wanted. In
this case a geographic answer based on the georaphic map of the world
would surmise that the 180 degree meridian determies W and E just as it
does for lat/lon numbers themselves.
>
> It's not difficult to do modular arithmetic that gets this right,
> either. To find the relative longitude change between two points,
> subtract their "absolute" longitudes. Then, if the absolute value of
> the result is greater than 180 degrees, add or subtract 360 degrees
> (depending on whether the result is negative or positive). This *will*
> give you an answer with an absolute value of 180 degrees or less, and
> whose sign indicates the direction (east is positive).
If relative is the mind set you are in. Which is what the question was
designed to explore. Sometimes we get inside a box and can't think
beyound the boundaries.
> Thus, it's clear that the "eastern" Aleutians are really only a degree
> or two west of the rest of Aleutians, not very far from the rest of
> Alaska, and definitely west of most of the USA. But any idiot can see
> that on a map. Most people can even figure that out *even* if they're
> looking at a map of the world that is split at 180 degrees longitude,
> so some of the Aleutians appear on the other side of the map from the
> rest.
>
> So the person who created the "correct" answer to this particular quiz
> question was either less clever than most people, or they were
> deliberately being misleading in order to make the question
> "difficult". I dislike questions where actually understanding the
> problem gives one a disadvantage over being pedantic and
> literal-minded.
I didn't create the question but I have used it and do not think that it
is an unreasonable question or that the person who dreamed it up is an
idiot (i.e. has an IQ below 90 or so.) If you get hung up thinking only
one way then perhaps you need to be jogged once in a while to think in
someone elses shoes for a bit. IN navigation we have very specific
definitions of east and west which are boxes in an of themselves. It is
interesting that in the Bible, when a great distance is being referenced
the distance is said to be as far as the east is from the west. Indeed
this is a vast distance.
Lighten up
Dale
> Dave
--
Dale -- http://users.cwnet.com/dalede
For GPS data, information on Palm Navigation, and more
Read my online manual for Garmin handheld products.
Gene Nygaard
wrote:
Not at all. The easternmost point in the United States is the one
which you can reach from any other point in the U.S. in less distance
by traveling in an easterly direction than in a westerly direction.
It is in Maine.
Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/
Surendar Jeyadev
Hans-Georg Michna <hans-georgN...@michna.com> wrote:
>
>But I still don't see how this can make any sense. The center of
>the earth is a pretty well defined spot, but the shape of the
>surface varies a lot and depends on a lot of factors like mass
>distribution, which can even change over time. I cannot imagine
If that is the case, how is it that "The center of
>the earth is a pretty well defined spot ...". In fact, what
is the "centre" for such an object?
>any simple, straightforward definition for the tangent angle,
>unless it is again an artificial construct that doesn't bear
>much relationship to reality. It would be more complex for no
>good reason. What am I overlooking now?
>
>Ask 100 people without any prior knowledge of this and ask them
>how they would define latitude. I predict that 99 of them would
>propose the normal, straightforward definition, the angle from
>the center.
I guess Galileo must have had a vexing time.
--
Surendar Jeyadev jey...@wrc.xerox.com
Dale DePriest
Where is the world did you get this definition. There are many points
(about an infinite number) in the US that I can get to by traveling less
distance easterly than westerly. Are they all the eastern most point?
Here is another question. Where is the northern most point in the
continental US?
Dale
JF Mezei
> Here is another question. Where is the northern most point in the
> continental US?
If Alaska is considered continental USA, then Point Barrow, just north of
Barrow alaska.
If Alaska is not included, then it would be any point along the 50° parralel
which makes the border between USA and British Columbia, Alberta, Saskatchewan
and Manitoba.
Richard Kaszeta
The continenental US sticks up from 50 deg north a bit. The Northwest
Angle in Minnesota sticks up above 50 deg. (It *is* mostly water, and
the only land parts are only reachable via boat or via Canada, but it
*is* part of Minnesota).
And it has very good fishing.
--
Richard W Kaszeta
ri...@kaszeta.org
http://www.kaszeta.org/rich
Dave Martindale
>The continenental US sticks up from 50 deg north a bit.
I think you'll find that the Canada/US border follows the 49 degree
line of latitude (approximately), not 50 degrees. If the border was
50 degrees, I'd be in the USA right now.
>The Northwest
>Angle in Minnesota sticks up above 50 deg. (It *is* mostly water, and
>the only land parts are only reachable via boat or via Canada, but it
>*is* part of Minnesota).
I think you're right about this being the northernmost chunk of the
USA not including Alaska.
Does anyone know *why* that tiny chunk of land is part of the USA? The
border obviously made a special excursion northward to include it; a more
straightforward border would have made it part of Canada.
The opposite thing happens in Point Roberts, Washington. The border,
by making a straight line at 49 degrees, creates this little spit of
land that's connected only to Canada but is part of the USA. It would
seem that it would have made more sense to divert the border south to
keep it part of Canada, like was done for Vancouver Island, but that
didn't happen.
Dave
MichaelO.
"Jack Yeazel" <Ja...@FinalApproach.net> wrote in message
news:3C011069...@FinalApproach.net...
>
>
> JF Mezei wrote:
>
> > > Do you think knowing the exact answer would improve your luck???!!!
Maybe you
> > > could win some sort of bet with the store clerk -such as what is the
southern,
> > > northern, western, and eastern most States?
> >
> > southern would be hawaii, northern would be alaska, western would be
alaska
> > (aleutians), and eastern would have to be maine. right ?
>
> Close, but no cigar...
> --
> Jack
>
> Get general GPS information at http://joe.mehaffey.com/
>
______________________________________________________________________________
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Gene Nygaard
wrote:
There is only one such point.
It doesn't have to do with what you can reach from your location.
Yes, you can reach many points in less distance by traveling east than
by traveling west. All that shows is that you are not at the
easternmost point in the United States.
There is only one place in the United States from which there is no
point that is closer by traveling in an easterly direction than by
traveling in a westerly direction. That is the easternmost point.
>Here is another question. Where is the northern most point in the
>continental US?
Part of the Northwest Angle in Minnesota.
Fishing on Lake of the Woods, in various parts of the lake you need
fishing licenses from Minnesota, Manitoba, and Ontario.
Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/
MichaelO.
Little Diomedes Island for example is across the 180 degree line. It's in
the Bering Straits. Politically the line is adjusted but geographically
it's still in the Eastern Hemisphere. Likewise you have Tonga claiming they
start the day when in fact they finish it. The lines are adjusted for ease
of use. Little Diomedes is on schedule with the US and Tonga is on schedule
with New Zealand - a major trading/political partner. There's a practical
reason for those slight adjustments. However in navigational terms the line
is straight as an arrow from North Pole to South. The adjustment is to
local time after the computation is made.
Does it ever get impractical? Sure does but once you start throwing out
this or that definition of all those that make a system work you toss the
whole system and replace it with . . .what? In truth what you are left
with is a bunch of people who can't count and think the millenium started on
the first day of 2000. But I digress into silliness so back to the
discussion.
Historically the world is divided (not just at the equator but on any great
circle) into hours, minutes, and seconds or into degrees all of which equate
to the convenient term 'nautical miles'. 60 seconds times 60 minutes times
360 degrees equals that certain distance on the great circles. Works nicely
with the navigation system you see. The comparison to statute miles or
meters for that matter doesn't matter. The only thing worth noting is the
difference in feet per nautical mile in the two definitions and then only if
it's an extremely long distance.
Laser accurate satellite based measurements taught us the world is not a
perfect sphere . . . .and the close to perfect nature of the GPS system puts
certain land forms in slightly different spots than they are shown on a
chart or a map. A more accurate measurement of the great circles may in
fact change the number of feet in a nautical mile but for most purposes . .
.it matters not a whit. Any decent sailor or orienteer will not rely solely
on any single form of navigation in any case and the differences are so
slight he or she will still make a good landfall. The rest deserve to hit
reefs.
The other extreme is agonizing over meaningless minutia. Better than that
just go out and use the damn thing. See if your feet care which definition
of a nautical mile is correct. Unless your trekking around the world it
really doesn't matter.
Cheers and fair winds (or blisters as the case may be)
Michael
"Jack Yeazel" <Ja...@FinalApproach.net> wrote in message
news:3C0167BC...@FinalApproach.net...
>
>
> Dave Martindale wrote:
>
> > I'll bet the "correct" answer makes Alaska the easternmost state because
> > some of the Aleutians are far enough west to have east longitude.
>
> You get the cigar!
>
> > But this is really a stupid answer. The fact that the Aleutians extend
> > to east longitude is a completely artificial side effect of where the
> > zero longitude meridian is placed (in England). Given a choice of
> > declaring the Aleutians to be either 80 degrees west or 280 degrees
> > east of the middle of the USA, anyone with common sense or some
experience
> > with modular arithmetic would say that the Aleutians are west, not east.
>
> Nevertheless, the Aleutians (part of Alaska) have a longitude that is
farther
> east
> than any other state... Don't be sore, enjoy your superior analysis!
(-8
>