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sundial & Earth's tilt questions



 
 
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  #2  
Old August 28th 03, 07:58 PM
George Dishman
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Default sundial & Earth's tilt questions


"cgbusch" wrote in message om...
Horizontal Dials
The plane of the shadow-receiving surface is horizontal.

Equatorial
The plane of the shadow-receiving surface is parallel to the equator.

Analemmatic
Time is told by the sun's azimuth on a specific date.

With horiz dials the face is a flat plane cut through a cylinder at
the angle of the latitude. With an equatorial dial, the dial is at
the angle of the latitude. My question is this, should the tilt of
the Earth along its rotational axis (23.45°) be included? With an
Equatorial dial, if you are at 45 deg lat, and it is winter, shouldn't
the dail be set up varying from 68.45 deg in the winter to 21.55deg in
the summer?


Sundials are generally fixed permanently, you don't vary the
orientation. You can make a sundial face for any angle you
choose but the term "Equatorial dial" specifically refers to
one that is parallel to the plane of the equator.

George


  #3  
Old August 29th 03, 02:39 AM
Oriel36
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Default sundial & Earth's tilt questions

"George Dishman" wrote in message ...
"Oriel36" wrote in message om...
To prove that axial tilt does not have any effect on the Equation of
Time involves a quite easy and inexpensive experiment involving only a
sundial,a stopwatch, a clock and the Equation of Time correction
tables which gives a value for each day of the year.


The tables are produced using the tilt, you cannot calculate
the correct values without it. Using only the factor due to
the elliptical orbit you get a single peak:


I had a look at the modern values against the values used by Roemer
and they are different,the modern value gives a positive value for Oct
24th while it was a negative value in Roemer's calculations.I
understand the value in context of the insight of Roemer and
subsequently Newton's definition of the distinction between absolute
time and relative time as the Equation of Time and as addition and
subtraction of minutes are involved,it should be taken as a given that
the Equation of Time parameter should be made distinct from the
sidereal parameter.

http://dibinst.mit.edu/BURNDY/OnlinePubs/Roemer/chapter3(part2).html

http://www.jgiesen.de/SunView/




http://www.analemma.com/Pages/Ellipt...OrbitMath.html

The full equation has two peaks:

http://www.analemma.com/Graphics/sum...inedCharts.GIF


The analemma is generated by putting clocks in the driver seat off
civil time but the original use of the Equation of Time and the
correction from natural noon to clock time involves the appropriate
addition and subtraction of minutes as a planetary meridian aligns
with the Sun depending on where the Earth is in its annual orbit,again
AM and PM reflect the original determination of 24 hours off the
inequality of natural noon to natural noon,there is nothing more basic
and it has nothing to do with axial tilt.All that matters was the
alignment regardless of latitude and it is good from pole to pole.



George
p.s. have you found out how to use Kepler's Second Law yet?


George,I looked at your last posting in a different thread and you do
something I would never do.I have kept this at a level of the
relationship with the planet wrt the Sun and the difference between
axial rotation and the difference in the distance the Earth covers in
its annual orbit as the axial alignment to the Sun repeats itself
(noon) and how this reflects the Equation of Time and ultimately the
relationship between clocks,geometry and astronomy.Anyone who comes to
know the intricate relationship will well acknowledge what Newton was
saying in terms of the difference between absolute and relative time
as the astronomical correction known as the Equation of Time,even a
hasty glance at Roemer's work will show the principle in action.You
think you are doing everyone a favor by bringing the stars and the
sidereal parameter into it but if it comes down to that perhaps the
discipline of astronomy is truly destroyed for against insincerity
there is no amswer.

"Absolute time,
in astronomy, is distinguished from relative, by the
equation or correlation of the vulgar time. For the natural days are
truly unequal, though they are commonly considered as equal and used
for a measure of time; astronomers correct this inequality for their
more accurate deducing of the celestial motions." Principia

By right any astronomer would recognise the definition/distinction for
what it is but without the Equation figures from Newton's era your
concept, that destroys the distinction, survives for another day.
  #4  
Old August 29th 03, 03:36 AM
cgbusch
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Default sundial & Earth's tilt questions

There seems to be some debate here as for the influence the elliptical
orbit and axial tilt of the Earth has on a sundial.

I don't believe the axial tilt will affect the noon time from day to
day.
From Kepler's 1st and 2nd laws, with Earth's orbit, the Sun is at one
focal point. This varies the distance and speed at which the Earth
orbits. Hence, the 2 unequal "peaks and valleys" in the Equation of
Time.
(http://www.school-for-champions.com/science/orbit.htm)

Remember, a horizontal sundial has to be crafted specially for a
latitude...

Imagine a magical cylinder of cookie dough log straight from the Sun
to the Earth. If you cut the log straight, you will notice 24 lines
emanating from the center of the log at perfect 15 degree intervals
(hour lines). If you cut the log at an angle, the lines would not be
at 15 degree intervals to the diagonal plane. For this reason, the
hour lines are not evenly marked on a horizontal sundial (except at
the equator).

The axial tilt can change the declination of the sun. This could
change the accurate spacing of the hour lines. So axial tilt doesn't
affect noon, but makes the other hours less accurate. I think that
for a sundial to be most accurate, it needs to be set perpendicular to
the orbital plane of the Earth (plane of the ecliptic).
(http://www.wikipedia.org/wiki/Axial_tilt)

One thing that I am also thinking about, is during the fall and spring
(for example), the sun will not travel across the sky directly east
and west but at an angle. I would presume on Equinox, an Equatorial
dial set up exactly, would have one face lighted in the morning and
the other in the afternoon.

Comments?
  #5  
Old August 29th 03, 08:24 AM
Oriel36
external usenet poster
 
Posts: n/a
Default sundial & Earth's tilt questions

(cgbusch) wrote in message om...
There seems to be some debate here as for the influence the elliptical
orbit and axial tilt of the Earth has on a sundial.

I don't believe the axial tilt will affect the noon time from day to
day.
From Kepler's 1st and 2nd laws, with Earth's orbit, the Sun is at one
focal point. This varies the distance and speed at which the Earth
orbits. Hence, the 2 unequal "peaks and valleys" in the Equation of
Time.
(
http://www.school-for-champions.com/science/orbit.htm)

Remember, a horizontal sundial has to be crafted specially for a
latitude...

Imagine a magical cylinder of cookie dough log straight from the Sun
to the Earth. If you cut the log straight, you will notice 24 lines
emanating from the center of the log at perfect 15 degree intervals
(hour lines). If you cut the log at an angle, the lines would not be
at 15 degree intervals to the diagonal plane. For this reason, the
hour lines are not evenly marked on a horizontal sundial (except at
the equator).

The axial tilt can change the declination of the sun. This could
change the accurate spacing of the hour lines. So axial tilt doesn't
affect noon, but makes the other hours less accurate. I think that
for a sundial to be most accurate, it needs to be set perpendicular to
the orbital plane of the Earth (plane of the ecliptic).
(http://www.wikipedia.org/wiki/Axial_tilt)

One thing that I am also thinking about, is during the fall and spring
(for example), the sun will not travel across the sky directly east
and west but at an angle. I would presume on Equinox, an Equatorial
dial set up exactly, would have one face lighted in the morning and
the other in the afternoon.

Comments?


The problem with using terms such as spring and fall is that they can
only be used hemispherically as they are opposite to each other
depending on which hemisphere the sundial is in.The Equation of Time
correction is valid along any longitude meridian from North to South
pole on a given day and as seasons are irrelevant to the daily figure
in terms of addition and subtraction obviously something is very wrong
if axial tilt is factored in as a component.
  #6  
Old August 29th 03, 08:30 AM
Paul Schlyter
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Posts: n/a
Default sundial & Earth's tilt questions

In article ,
cgbusch wrote:

There seems to be some debate here as for the influence the elliptical
orbit and axial tilt of the Earth has on a sundial.

I don't believe the axial tilt will affect the noon time from day to
day.


You believe wrong.....

It often helps one to understand if one considers an extreme situation.
So let's for a moment imagine that the Earth's axial tilt was exactly
90 degrees. What would happen in such a case?

Let's follow the Sun from the Vernal Equinox (in the northern
hemisphere), assuming the Earth's axial tilt is 90 degrees: at the
Vernal Equinox the Sun is at 0h RA and 0d Decl. Then it moves
straight northward, remaining at 0h RA. The sidereal day and the
solar day will have the same length --- until the northern Summer
Solstice, when the Sun will cross the North Celestial Pole. Then
something dramatic will happen: the RA of the Sun will suddenly jump
from 0h RA to 12h RA --- and the moment of true solar noon will
likewise suddenly jump by 12 hours. For the next half year, the Sun
will have RA = 12h as it travels southward, until the Winter Solstice,
when the Sun will cross the South Celestial Pole and another sudden
jump of 12h in both the Sun's RA and the noon time.

Thus, at least for an axial tilt of 90 degrees the noon time will be
affected by the tilt. And in fact, the noon time will be affected by
any non-zero tilt, although the effect will be less dramatic for
lower tilts. Therefore, for the Earth's actual 23.4 degree tilt
there will be no dramatic sudden jumps in the noon time, but merely
gradual changes.


From Kepler's 1st and 2nd laws, with Earth's orbit, the Sun is at one
focal point. This varies the distance and speed at which the Earth
orbits. Hence, the 2 unequal "peaks and valleys" in the Equation of
Time.


....and if the Earth's orbit had been circular, these two "peaks and
valleys" would have been equal, and due to the tilt of the Earth's
axis.

And if the tilt of the Earth's axis was zero, there would only be
the effect of the Earth's elliptical orbit, which would produce
only one "peak and valley" per year.


(http://www.school-for-champions.com/science/orbit.htm)

Remember, a horizontal sundial has to be crafted specially for a
latitude...

Imagine a magical cylinder of cookie dough log straight from the Sun
to the Earth. If you cut the log straight, you will notice 24 lines
emanating from the center of the log at perfect 15 degree intervals
(hour lines). If you cut the log at an angle, the lines would not be
at 15 degree intervals to the diagonal plane. For this reason, the
hour lines are not evenly marked on a horizontal sundial (except at
the equator).

The axial tilt can change the declination of the sun. This could
change the accurate spacing of the hour lines. So axial tilt doesn't
affect noon, but makes the other hours less accurate.


The axial tilt does not affect the direction of noon of course (which
always is precisely towards the South --- or towards the North if
you're in the southern hemisphere. But it does affect the time of noon.

I think that
for a sundial to be most accurate, it needs to be set perpendicular to
the orbital plane of the Earth (plane of the ecliptic).
(http://www.wikipedia.org/wiki/Axial_tilt)


....and how would you keep it at that orientation? Remember that the
sundial rests on an Earth which rotates along a tilted axis ---- you'd
need some clock machinery to accomplish this. And if you'd go to
all that trouble, you might as well make a mechanical clock instead.

One thing that I am also thinking about, is during the fall and spring
(for example), the sun will not travel across the sky directly east
and west but at an angle. I would presume on Equinox, an Equatorial
dial set up exactly, would have one face lighted in the morning and
the other in the afternoon.

Comments?


You need to reconsider your erroneous idea that the Earth's axial
tilt does not affect the noon time or the equation of time.

--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://www.stjarnhimlen.se/
http://home.tiscali.se/pausch/
  #7  
Old August 29th 03, 12:40 PM
Jeff Root
external usenet poster
 
Posts: n/a
Default sundial & Earth's tilt questions

"cgbusch" wrote:

I don't believe the axial tilt will affect the noon time from
day to day.
From Kepler's 1st and 2nd laws, with Earth's orbit, the Sun is
at one focal point. This varies the distance and speed at which
the Earth orbits. Hence, the 2 unequal "peaks and valleys" in
the Equation of Time.


Can you explain that?

In January, when Earth is at perihelion, closest to the Sun and
moving fastest, noon should be at 12:00 on a standard meridian.
The next day, noon should come a bit later, since the Earth has
moved more than the average amount in that time. By April, the
Earth has slowed to its average speed in orbit, and noon should
be as late as it gets. The next day, noon should come a little
bit sooner. Noon should come a little bit sooner each day for
the next six months. By July, Earth is at perihelion, farthest
from the Sun and moving slowest. Noon should again be at 12:00.
By October, Earth is moving at its average speed again, and noon
should be occurring at its earliest time. The next day, noon
should come a little bit later. Noon should come a little bit
later each day for the next six months. By January, Earth is
closest to the Sun again, moving fastest. Noon should again be
at 12:00.

One minimum, when the Sun is as far behind the clock as it gets,
creating a single valley in the graph, in April. One maximum,
when the Sun is as far ahead of the clock as it gets, creating
a single peak in the graph, in October. Two days during the
year when noon is right at 12:00, in January and July.

So why are there actually two unequal peaks and two unequal
valleys in the graph of the equation of time? Why are there
four days during the year when noon is at 12:00? Why are
those four days in April, June, September, and December?

-- Jeff, in Minneapolis

..
  #8  
Old August 29th 03, 04:19 PM
Oriel36
external usenet poster
 
Posts: n/a
Default sundial & Earth's tilt questions

(Paul Schlyter) wrote in message ...
In article ,
cgbusch wrote:

There seems to be some debate here as for the influence the elliptical
orbit and axial tilt of the Earth has on a sundial.

I don't believe the axial tilt will affect the noon time from day to
day.


You believe wrong.....


He is correct,the tilt of the Earth may lenghten and shorten the
shadow cast on a sundial but it does not affect the pace of the shadow
across the sundial.Common sense should tell you that the axial
alignment of a planetary longitude meridian at noon when the location
faces the Sun directly and when it repeats it is the only factor that
counts,tilt the Earth anyway you want,as long as axial rotation is
constant it neither accelerates on retards the observed motion of the
Sun this being basic mechanics never mind astronomy.


It often helps one to understand if one considers an extreme situation.
So let's for a moment imagine that the Earth's axial tilt was exactly
90 degrees. What would happen in such a case?


This bluster often begs an explanation and diverts attension from the
fact that the Equation of Time applies addition and subtraction of
minutes and seconds when a longitude meridian faces the Sun
directly,because of the natural variation from one alignment to
another the addition and subtraction of minutes and seconds brings it
in line with a 24 hour clock which is fixed to the longitude
meridians.



Let's follow the Sun from the Vernal Equinox (in the northern
hemisphere), assuming the Earth's axial tilt is 90 degrees: at the
Vernal Equinox the Sun is at 0h RA and 0d Decl. Then it moves
straight northward, remaining at 0h RA. The sidereal day and the
solar day will have the same length --- until the northern Summer
Solstice, when the Sun will cross the North Celestial Pole.


Why introduce the sidereal parameter when sundials refer only to the
shadow cast by the Earth's rotation on its axis and its orbital
rotation around the Sun and the question refers only to axial tilt in
determination of the noon alignment.You are going to an awful lot of
trouble to introduce imaginary tilts and references to the stars for
an instrument that makes use of the Earth's rotations, the Sun and the
Equation of Time correction which has been known for centuries.



Then
something dramatic will happen: the RA of the Sun will suddenly jump
from 0h RA to 12h RA --- and the moment of true solar noon will
likewise suddenly jump by 12 hours. For the next half year, the Sun
will have RA = 12h as it travels southward, until the Winter Solstice,
when the Sun will cross the South Celestial Pole and another sudden
jump of 12h in both the Sun's RA and the noon time.


Yeah,something dramatic happened alright,the guys in the early part of
the 20th century misread Newton and his phrasing of the inequality of
the natural days of longitudinal planetary alignment from one axial
rotation to the next,forgot or did'nt know what the Equation of Time
does both astronomically and for purposes of navigation and went along
with Flamsteed's botch job which included an axial tilt component to
justify the sidereal parameter.

Were it any less important I would not repeat it for historically
accurate clocks were developed as physical rulers of distance in
tandem with the Equation and determination of noon.No axial tilt was
involved,only the determination of the alignment of the longitudinal
alignment with the Sun.It would not have been possible for astronomers
to make sense of planetary motion for the purpose of heliocentric
modelling without the astronomical correction which removed the
natural variation of a day and it was so commonplace in Newton's era
that he hardly would expect his readers to make a fuss as he outlines
it in terms of absolute and relative time.


"Absolute time,
in astronomy, is distinguished from relative, by the
equation or correlation of the vulgar time. For the natural days are
truly unequal, though they are commonly considered as equal and used
for a measure of time; astronomers correct this inequality for their
more accurate deducing of the celestial motions." Principia

As clocks are rulers of physical distance,spacetime freaks as yourself
can't have your silly 4th dimension bottled up in a clock but it all
hinges on how you interpret Newton and his phrasing of the Equation of
Time.




Thus, at least for an axial tilt of 90 degrees the noon time will be
affected by the tilt. And in fact, the noon time will be affected by
any non-zero tilt, although the effect will be less dramatic for
lower tilts. Therefore, for the Earth's actual 23.4 degree tilt
there will be no dramatic sudden jumps in the noon time, but merely
gradual changes.


From Kepler's 1st and 2nd laws, with Earth's orbit, the Sun is at one
focal point. This varies the distance and speed at which the Earth
orbits. Hence, the 2 unequal "peaks and valleys" in the Equation of
Time.


...and if the Earth's orbit had been circular, these two "peaks and
valleys" would have been equal, and due to the tilt of the Earth's
axis.

And if the tilt of the Earth's axis was zero, there would only be
the effect of the Earth's elliptical orbit, which would produce
only one "peak and valley" per year.


(
http://www.school-for-champions.com/science/orbit.htm)

Remember, a horizontal sundial has to be crafted specially for a
latitude...

Imagine a magical cylinder of cookie dough log straight from the Sun
to the Earth. If you cut the log straight, you will notice 24 lines
emanating from the center of the log at perfect 15 degree intervals
(hour lines). If you cut the log at an angle, the lines would not be
at 15 degree intervals to the diagonal plane. For this reason, the
hour lines are not evenly marked on a horizontal sundial (except at
the equator).

The axial tilt can change the declination of the sun. This could
change the accurate spacing of the hour lines. So axial tilt doesn't
affect noon, but makes the other hours less accurate.


The axial tilt does not affect the direction of noon of course (which
always is precisely towards the South --- or towards the North if
you're in the southern hemisphere. But it does affect the time of noon.



Noon is a geometric alignment generated by the rotation of the
Earth,you and George always slip 'time' in as relativists are want to
do but fundamentally tilt is a property of equatorial orientation and
neither accelerates or retards the observed motion of the Sun or what
amounts to the same thing the axial rotation of the Earth from one
noon alignment to another.



I think that
for a sundial to be most accurate, it needs to be set perpendicular to
the orbital plane of the Earth (plane of the ecliptic).
(http://www.wikipedia.org/wiki/Axial_tilt)


...and how would you keep it at that orientation? Remember that the
sundial rests on an Earth which rotates along a tilted axis


Don't be silly,the sundial rotates with the Earth and tilt the Earth
all you want it has no effect on the pace of the shadow across the
dial.



---- you'd
need some clock machinery to accomplish this. And if you'd go to
all that trouble, you might as well make a mechanical clock instead.


Clocks emerged from the equality introduced by the Equation of Time
from the inequality of the natural day.I'm sure in the era of cheap
watches it is easy to forget which came first but obviously you and
your spoacetime colleagues forgot or did'nt know and spent a lifetime
chasing rainbows,no wonder you defend the nonsense tooth and nail
instead of dumping it wholesale.


One thing that I am also thinking about, is during the fall and spring
(for example), the sun will not travel across the sky directly east
and west but at an angle. I would presume on Equinox, an Equatorial
dial set up exactly, would have one face lighted in the morning and
the other in the afternoon.

Comments?


You need to reconsider your erroneous idea that the Earth's axial
tilt does not affect the noon time or the equation of time.


He may also consider that he can expect nothing but grief if he
does'nt go along with axial tilt and the Equation of Time for the
domino effect it would have with a century old concept and people like
you who are proponents of that cult.
  #9  
Old August 29th 03, 05:07 PM
George Dishman
external usenet poster
 
Posts: n/a
Default sundial & Earth's tilt questions


"Oriel36" wrote in message om...
"George Dishman" wrote in message ...
p.s. have you found out how to use Kepler's Second Law yet?


George,I looked at your last posting in a different thread and you do
something I would never do.


It would help if you had said what that is! All I asked is
whether you had applied Kepler's second law or not. My web
page drawings assumed you had done this calculation and were
familiar with the result. If you have not then it will appear
as though I am just inventing the numbers so we should go
over how I got them using Kepler's first and second laws.
I just don't want to waste our time doing that if you have
already done that calculation, but if you have I expect you
to know the answers or be able to work them out.

I have kept this at a level of the
relationship with the planet wrt the Sun and the difference between
axial rotation and the difference in the distance the Earth covers in
its annual orbit as the axial alignment to the Sun repeats itself
(noon) and how this reflects the Equation of Time and ultimately the
relationship between clocks,geometry and astronomy.


Same here, but I am taking it one step at a time. The first
is to apply Kepler's Laws to the orbit of the Earth. If you
haven't already done that, we should go through it. Your
comments suggest you have not, is that correct?

George


  #10  
Old August 29th 03, 05:07 PM
George Dishman
external usenet poster
 
Posts: n/a
Default sundial & Earth's tilt questions


"Oriel36" wrote in message om...
"George Dishman" wrote in message ...
"Oriel36" wrote in message om...
To prove that axial tilt does not have any effect on the Equation of
Time involves a quite easy and inexpensive experiment involving only a
sundial,a stopwatch, a clock and the Equation of Time correction
tables which gives a value for each day of the year.


The tables are produced using the tilt, you cannot calculate
the correct values without it. Using only the factor due to
the elliptical orbit you get a single peak:


I had a look at the modern values against the values used by Roemer
and they are different,the modern value gives a positive value for Oct
24th while it was a negative value in Roemer's calculations.


If you look at the vertical scale on the Analemma site graph

http://www.analemma.com/Graphics/sum...inedCharts.GIF

you will see that the value for late october is nearly +16 minutes
and the scale is marked "True sun ahead -" meaning that the natural
noon is fifteen minutes ahead of noon based on mean time. Now look
at the annotation on the right of Roemer's notes

http://dibinst.mit.edu/BURNDY/OnlinePubs/Roemer/chapter3(part2).html


He starts with 'Solar Time' which is ahead so he has to subtract
the 15 minutes, 45 seconds to get back to mean time. The values
are the same but one gives solar relative to mean while the other
is finding mean from solar, hence the sign changes. Both tell you
that natural or observed noon is ahead of noon, mean time in October.

I understand the value in context of the insight of Roemer and
subsequently Newton's definition of the distinction between absolute
time and relative time as the Equation of Time and as addition and
subtraction of minutes are involved,it should be taken as a given that
the Equation of Time parameter should be made distinct from the
sidereal parameter.


Right, the Equation of Time is the difference between natural noon
and mean noon and does not directly involve sidereal time.


http://www.analemma.com/Pages/Ellipt...OrbitMath.html

The full equation has two peaks:

http://www.analemma.com/Graphics/sum...inedCharts.GIF


The analemma is generated by putting clocks in the driver seat off
civil time but the original use of the Equation of Time and the
correction from natural noon to clock time involves the appropriate
addition and subtraction of minutes as a planetary meridian aligns
with the Sun depending on where the Earth is in its annual orbit,again
AM and PM reflect the original determination of 24 hours off the
inequality of natural noon to natural noon,there is nothing more basic
and it has nothing to do with axial tilt.All that matters was the
alignment regardless of latitude and it is good from pole to pole.


This is Flamsteed's table:

http://www.burnley.gov.uk/towneley/tryall/jftable.htm

Look along the row just above the figures where he indicates
A for Add or S for Subtract. It goes "A S S A A A S S S S A A"
but again note this is to give you mean time from observation
of natural time whereas the modern graph is the other way round
so 'S' in Flamsteed's table corresponds to a positive value in
the modern table.

Notice that there are two periods in the year when you add and
two when you subtract. Plot these values on a graph and you should
get something very similar to the Analemma site graph.

The elliptical motion of the Earth would only give one cycle
such as "A A A A S S S S S S A A". The question you have to
answer is why does Flamsteed's table say "S" for May and June
when the effect of the elliptical motion should produce an "A"?

George


 




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