Fastest Sunset

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Fastest Sunset

Victor Engel
Dear Calendar People,

On the radio, they mentioned that the sun sets the fastest on the upcoming equinox. The reason they gave was that the path of the sun is closest to vertical on that date. Well, how many wrong things are there about that assertion?

After a moment's thought, it seems to me the claim must not be true for anywhere south of the Tropic of Cancer. The question is not well defined near the poles. For the northern hemisphere, between the Tropic of Cancer and the Arctic Circle, though, which probably includes the location of most of the radios in the audience, does it apply? I think so, but I don't like the explanation. It doesn't get to the root cause. In general, we can consider the path of the sun as traveling across a well-defined line in the sky that is tilted at an angle relative to the horizon that is determined by the latitude of the observer. This line moves from day to day, moving northward during the spring and southward during autumn. It moves at its greatest speed southward at the autumnal equinox, and THAT is the reason the sun sets the fastest. But the fastest sunset would be the one closest to the autumnal equinox, not the one that occurs on the same day (however day is defined here).

Does that sound right?

Victor
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Re: Fastest Sunset

Jim Riley-4
How does one measure the time interval of sunset? Why do you think
there is a difference between the March and September equinoxes and
the northern and southern hemisphere?

http://earthsky.org/tonight/fastest-sunsets-around-equinox-time#why

According to this web site the time of sunset varies from 2-3/4
minutes at the equinoxes to 3-1/4 minutes at the solstices at the
solstices (at 40 degrees latitude).

For a given longitude, the quickest sunset will occur when the equinox
and sunset are coincident.

On September 22 in Greenwich, solar noon is 11:53 UTC and sunset at
17:58 UTC. The equinox is at 14:21 UTC. So we need to find where
sunset is 17:58 - 14:21 or 3h37 minutes earlier and Greenwich. 3h37
corresponds to 3-37/60 x 15 degrees or about 54 degrees east (around
Abu Dhabi, where the time of sunset will the quickest not only for the
year, but for a longer period (say 180 years?).

I think your conjecture about the local sunset nearest the equinox is
correct. As you go west from Abu Dhabi, sunset is further south of
west, and at a more oblique angle. Past 126W (between Victoria BC and
Juneau, Alaska) the sunset would have been closer to west on the
previous day (September 21), but once you get the IDL you would be
back on  September 22. I bet for 99% of the World's population, the
quickest sunset will be on September 22.


On Tue, 20 Sep 2016 10:59:49 -0500, Victor Engel <[hidden email]>
wrote:

>Dear Calendar People,
>
>On the radio, they mentioned that the sun sets the fastest on the upcoming
>equinox. The reason they gave was that the path of the sun is closest to
>vertical on that date. Well, how many wrong things are there about that
>assertion?
>
>After a moment's thought, it seems to me the claim must not be true for
>anywhere south of the Tropic of Cancer. The question is not well defined
>near the poles. For the northern hemisphere, between the Tropic of Cancer
>and the Arctic Circle, though, which probably includes the location of most
>of the radios in the audience, does it apply? I think so, but I don't like
>the explanation. It doesn't get to the root cause. In general, we can
>consider the path of the sun as traveling across a well-defined line in the
>sky that is tilted at an angle relative to the horizon that is determined
>by the latitude of the observer. This line moves from day to day, moving
>northward during the spring and southward during autumn. It moves at its
>greatest speed southward at the autumnal equinox, and THAT is the reason
>the sun sets the fastest. But the fastest sunset would be the one closest
>to the autumnal equinox, not the one that occurs on the same day (however
>day is defined here).
>
>Does that sound right?
>
>Victor
--
Jim Riley
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Re: Fastest Sunset

Victor Engel
Well, there may be a flaw in my thinking. Consider the attached illustration.

The parallel lines represent the path of the sun along the ecliptic. However, the ecliptic moves north and south through the seasons, with maximum movement at the equinoxes. I've drawn two additional lines that show what the sun actually does. Since the ecliptic moves, the sun travels from one ecliptic line to the other. During the autumn equinox, the rightmost scenario applies. During the spring equinox, the leftmost scenario applies. This is true no matter the hemisphere, and, of course, the autumn equinox is in different months in the north and south. Likewise for spring equinox.

I think my error in logic was that what I've shown as parallel lines are not, actually parallel.

As to how to measure the length, it is the time between the two limbs intersecting the horizon. Atmospheric effects would just amplify the difference between maxima and minima.

Victor

On Tue, Sep 20, 2016 at 4:40 PM, Jim Riley <[hidden email]> wrote:
How does one measure the time interval of sunset? Why do you think
there is a difference between the March and September equinoxes and
the northern and southern hemisphere?

http://earthsky.org/tonight/fastest-sunsets-around-equinox-time#why

According to this web site the time of sunset varies from 2-3/4
minutes at the equinoxes to 3-1/4 minutes at the solstices at the
solstices (at 40 degrees latitude).

For a given longitude, the quickest sunset will occur when the equinox
and sunset are coincident.

On September 22 in Greenwich, solar noon is 11:53 UTC and sunset at
17:58 UTC. The equinox is at 14:21 UTC. So we need to find where
sunset is 17:58 - 14:21 or 3h37 minutes earlier and Greenwich. 3h37
corresponds to 3-37/60 x 15 degrees or about 54 degrees east (around
Abu Dhabi, where the time of sunset will the quickest not only for the
year, but for a longer period (say 180 years?).

I think your conjecture about the local sunset nearest the equinox is
correct. As you go west from Abu Dhabi, sunset is further south of
west, and at a more oblique angle. Past 126W (between Victoria BC and
Juneau, Alaska) the sunset would have been closer to west on the
previous day (September 21), but once you get the IDL you would be
back on  September 22. I bet for 99% of the World's population, the
quickest sunset will be on September 22.


On Tue, 20 Sep 2016 10:59:49 -0500, Victor Engel <[hidden email]>
wrote:

>Dear Calendar People,
>
>On the radio, they mentioned that the sun sets the fastest on the upcoming
>equinox. The reason they gave was that the path of the sun is closest to
>vertical on that date. Well, how many wrong things are there about that
>assertion?
>
>After a moment's thought, it seems to me the claim must not be true for
>anywhere south of the Tropic of Cancer. The question is not well defined
>near the poles. For the northern hemisphere, between the Tropic of Cancer
>and the Arctic Circle, though, which probably includes the location of most
>of the radios in the audience, does it apply? I think so, but I don't like
>the explanation. It doesn't get to the root cause. In general, we can
>consider the path of the sun as traveling across a well-defined line in the
>sky that is tilted at an angle relative to the horizon that is determined
>by the latitude of the observer. This line moves from day to day, moving
>northward during the spring and southward during autumn. It moves at its
>greatest speed southward at the autumnal equinox, and THAT is the reason
>the sun sets the fastest. But the fastest sunset would be the one closest
>to the autumnal equinox, not the one that occurs on the same day (however
>day is defined here).
>
>Does that sound right?
>
>Victor
--
Jim Riley


sunset.png (6K) Download Attachment
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Re: Fastest Sunset

Victor Engel
In reply to this post by Jim Riley-4
A way to clarify in my mind what is going on is to imagine what goes on at the Arctic Circle. At the summer solstice, the sun travels around the observer, changing elevation from at the horizon to the north to the highest at the south. The path forms a sort of sinusoidal curve. This curve gets moved downward until at winter solstice, it's doing exactly the same thing but below the horizon the whole time. The quickest sunset happens when the angle of the wave pattern is the steepest, which is at the equinoxes (with a small, probably almost insignificant adjustment due to the path changing from one day to the next). Also, the sun does not travel along the ecliptic as I previously implied.

Victor

On Tue, Sep 20, 2016 at 4:40 PM, Jim Riley <[hidden email]> wrote:
How does one measure the time interval of sunset? Why do you think
there is a difference between the March and September equinoxes and
the northern and southern hemisphere?

http://earthsky.org/tonight/fastest-sunsets-around-equinox-time#why

According to this web site the time of sunset varies from 2-3/4
minutes at the equinoxes to 3-1/4 minutes at the solstices at the
solstices (at 40 degrees latitude).

For a given longitude, the quickest sunset will occur when the equinox
and sunset are coincident.

On September 22 in Greenwich, solar noon is 11:53 UTC and sunset at
17:58 UTC. The equinox is at 14:21 UTC. So we need to find where
sunset is 17:58 - 14:21 or 3h37 minutes earlier and Greenwich. 3h37
corresponds to 3-37/60 x 15 degrees or about 54 degrees east (around
Abu Dhabi, where the time of sunset will the quickest not only for the
year, but for a longer period (say 180 years?).

I think your conjecture about the local sunset nearest the equinox is
correct. As you go west from Abu Dhabi, sunset is further south of
west, and at a more oblique angle. Past 126W (between Victoria BC and
Juneau, Alaska) the sunset would have been closer to west on the
previous day (September 21), but once you get the IDL you would be
back on  September 22. I bet for 99% of the World's population, the
quickest sunset will be on September 22.


On Tue, 20 Sep 2016 10:59:49 -0500, Victor Engel <[hidden email]>
wrote:

>Dear Calendar People,
>
>On the radio, they mentioned that the sun sets the fastest on the upcoming
>equinox. The reason they gave was that the path of the sun is closest to
>vertical on that date. Well, how many wrong things are there about that
>assertion?
>
>After a moment's thought, it seems to me the claim must not be true for
>anywhere south of the Tropic of Cancer. The question is not well defined
>near the poles. For the northern hemisphere, between the Tropic of Cancer
>and the Arctic Circle, though, which probably includes the location of most
>of the radios in the audience, does it apply? I think so, but I don't like
>the explanation. It doesn't get to the root cause. In general, we can
>consider the path of the sun as traveling across a well-defined line in the
>sky that is tilted at an angle relative to the horizon that is determined
>by the latitude of the observer. This line moves from day to day, moving
>northward during the spring and southward during autumn. It moves at its
>greatest speed southward at the autumnal equinox, and THAT is the reason
>the sun sets the fastest. But the fastest sunset would be the one closest
>to the autumnal equinox, not the one that occurs on the same day (however
>day is defined here).
>
>Does that sound right?
>
>Victor
--
Jim Riley

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Re: Fastest Sunset

Karl Palmen
In reply to this post by Victor Engel

Dear Victor and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Victor Engel
Sent: 20 September 2016 17:00
To: [hidden email]
Subject: Fastest Sunset

 

Dear Calendar People,

 

On the radio, they mentioned that the sun sets the fastest on the upcoming equinox. The reason they gave was that the path of the sun is closest to vertical on that date. Well, how many wrong things are there about that assertion?

 

KARL REPLIES: The assertion is wrong, because the speed of the sun across the sky is not constant. It is fastest very near the equinox, because the sun’s path is nearly a great circle. At other times it is a smaller circle. This causes the fastest equatorial sunset to be at the equinox even though the sunset angle is always right angle. Other considerations include the variation of the speed of the sun along the ecliptic. This would cause the fastest sunset of the southward sun to occur  slightly before the southward equinox.

 

Karl

 

16(01(20

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Re: Fastest Sunset

Gent, R.H. van (Rob)
In reply to this post by Victor Engel

Hi,

 

According to Jean Meeus, _Mathematical Astronomy Morsels V_ (Richmond: Willmann-Bell, 2009), pp. 337-342, this is only approximately true.

 

The date(s) of shortest sunrise/set also depend on the latitude:

 

·         for the equator they are about 6 days after/before the spring/autumnal equinox.

·         for latitude 50 N they are about 2.5 days after/before the spring/autumnal equinox.

 

rvg

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Victor Engel
Sent: dinsdag 20 september 2016 18:00
To: [hidden email]
Subject: Fastest Sunset

 

Dear Calendar People,

 

On the radio, they mentioned that the sun sets the fastest on the upcoming equinox. The reason they gave was that the path of the sun is closest to vertical on that date. Well, how many wrong things are there about that assertion?

 

After a moment's thought, it seems to me the claim must not be true for anywhere south of the Tropic of Cancer. The question is not well defined near the poles. For the northern hemisphere, between the Tropic of Cancer and the Arctic Circle, though, which probably includes the location of most of the radios in the audience, does it apply? I think so, but I don't like the explanation. It doesn't get to the root cause. In general, we can consider the path of the sun as traveling across a well-defined line in the sky that is tilted at an angle relative to the horizon that is determined by the latitude of the observer. This line moves from day to day, moving northward during the spring and southward during autumn. It moves at its greatest speed southward at the autumnal equinox, and THAT is the reason the sun sets the fastest. But the fastest sunset would be the one closest to the autumnal equinox, not the one that occurs on the same day (however day is defined here).

 

Does that sound right?

 

Victor

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Re: Fastest Sunset

Jim Riley-4
Using

http://aa.usno.navy.mil/data/docs/RS_OneDay.php

and calculating the time between sunset (apparent center of sun 0.5
degrees below horizon, and civil twilight sun 6 degrees below
horizon), the variation at the equator is small, 21 minutes near the
equinoxes and 22 minutes near the solstices.

The period of sunset should be roughly proportional to the period of
twilight. So at the equator, the semiannual variation in the period of
sunset should be around 10 seconds. The daily variation could be about
0.1 seconds, but since there is a minima near the equinoxes, it should
be much less. So at the equator the effect of the eccentricity of the
earth's orbit has greater effect, and so the quickest sunset is
shifted towards aphelion. But doesn't that imply that the quickest
sunset is near to the September equinox, because it is closer to
aphelion than the March equinox.

Though the period of twilight is longer at the solstices than the
equinoxes, this is particularly profound with the June equinox for
northern latitudes, and the December equinox for southern latitudes
for




On Wed, 21 Sep 2016 12:48:01 +0000, "Gent, R.H. van (Rob)"
<[hidden email]> wrote:

>Hi,
>According to Jean Meeus, _Mathematical Astronomy Morsels V_ (Richmond: Willmann-Bell, 2009), pp. 337-342, this is only approximately true.
>
>The date(s) of shortest sunrise/set also depend on the latitude:
>
>
>·         for the equator they are about 6 days after/before the spring/autumnal equinox.
>
>·         for latitude 50 N they are about 2.5 days after/before the spring/autumnal equinox.
>
>rvg
>
>From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Victor Engel
>Sent: dinsdag 20 september 2016 18:00
>To: [hidden email]
>Subject: Fastest Sunset
>
>Dear Calendar People,
>
>On the radio, they mentioned that the sun sets the fastest on the upcoming equinox. The reason they gave was that the path of the sun is closest to vertical on that date. Well, how many wrong things are there about that assertion?
>
>After a moment's thought, it seems to me the claim must not be true for anywhere south of the Tropic of Cancer. The question is not well defined near the poles. For the northern hemisphere, between the Tropic of Cancer and the Arctic Circle, though, which probably includes the location of most of the radios in the audience, does it apply? I think so, but I don't like the explanation. It doesn't get to the root cause. In general, we can consider the path of the sun as traveling across a well-defined line in the sky that is tilted at an angle relative to the horizon that is determined by the latitude of the observer. This line moves from day to day, moving northward during the spring and southward during autumn. It moves at its greatest speed southward at the autumnal equinox, and THAT is the reason the sun sets the fastest. But the fastest sunset would be the one closest to the autumnal equinox, not the one that occurs on the same day (however day is defined here).
>
>Does that sound right?
>
>Victor
--
Jim Riley
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Re: Fastest Sunset

Karl Palmen
Dear Jim, Rob and Calendar People

Thank you Jim for your reply.

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Jim Riley
Sent: 22 September 2016 17:04
To: [hidden email]
Subject: Re: Fastest Sunset

Using

http://aa.usno.navy.mil/data/docs/RS_OneDay.php

and calculating the time between sunset (apparent center of sun 0.5
degrees below horizon, and civil twilight sun 6 degrees below
horizon), the variation at the equator is small, 21 minutes near the
equinoxes and 22 minutes near the solstices.

The period of sunset should be roughly proportional to the period of
twilight. So at the equator, the semiannual variation in the period of
sunset should be around 10 seconds. The daily variation could be about
0.1 seconds, but since there is a minima near the equinoxes, it should
be much less. So at the equator the effect of the eccentricity of the
earth's orbit has greater effect, and so the quickest sunset is
shifted towards aphelion. But doesn't that imply that the quickest
sunset is near to the September equinox, because it is closer to
aphelion than the March equinox.

KARL REPLIES: This alone done not imply that the quickest sunset is near to the September equinox, because it is closer to aphelion than the March equinox. One has to consider why this is the case. I reckon it is because nearer the aphelion the sun is moving slower along the ecliptic and so faster across the sky, for a daily sun-path of the same length. So I too would expect the fastest sunset near the September equinox to be a little faster than the fastest sunset near the March equinox and this difference will increase until the perihelion reaches the March equinox in about 5000 years' time.

This difference in sunset speed may be so small as to modify twilight duration by only a few seconds and so not show up on a web site such as the one linked above.

Karl

16(01(22
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Re: Fastest Sunset

Jim Riley-4
I should have figured out to find something like this (by Irv
Bromberg)

http://www.sym454.org/twilight/

Something that I had thought about but which the above web site makes
clear is the effect of refraction, which increases the duration of
sunset due to it retarding the apparent motion of the sun. The effect
of refraction which is around 17% is probably profound enough that the
duration of sunset is weather dependent.

On Fri, 23 Sep 2016 12:03:12 +0000, Karl Palmen
<[hidden email]> wrote:

>Dear Jim, Rob and Calendar People
>
>Thank you Jim for your reply.
>
>-----Original Message-----
>From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Jim Riley
>Sent: 22 September 2016 17:04
>To: [hidden email]
>Subject: Re: Fastest Sunset
>
>Using
>
>http://aa.usno.navy.mil/data/docs/RS_OneDay.php
>
>and calculating the time between sunset (apparent center of sun 0.5
>degrees below horizon, and civil twilight sun 6 degrees below
>horizon), the variation at the equator is small, 21 minutes near the
>equinoxes and 22 minutes near the solstices.
>
>The period of sunset should be roughly proportional to the period of
>twilight. So at the equator, the semiannual variation in the period of
>sunset should be around 10 seconds. The daily variation could be about
>0.1 seconds, but since there is a minima near the equinoxes, it should
>be much less. So at the equator the effect of the eccentricity of the
>earth's orbit has greater effect, and so the quickest sunset is
>shifted towards aphelion. But doesn't that imply that the quickest
>sunset is near to the September equinox, because it is closer to
>aphelion than the March equinox.
>
>KARL REPLIES: This alone done not imply that the quickest sunset is near to the September equinox, because it is closer to aphelion than the March equinox. One has to consider why this is the case. I reckon it is because nearer the aphelion the sun is moving slower along the ecliptic and so faster across the sky, for a daily sun-path of the same length. So I too would expect the fastest sunset near the September equinox to be a little faster than the fastest sunset near the March equinox and this difference will increase until the perihelion reaches the March equinox in about 5000 years' time.
>
>This difference in sunset speed may be so small as to modify twilight duration by only a few seconds and so not show up on a web site such as the one linked above.
>
>Karl
>
>16(01(22
--
Jim Riley
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Re: Fastest Sunset

Victor Engel
... and altitude-dependent

On Fri, Sep 23, 2016 at 12:11 PM, Jim Riley <[hidden email]> wrote:
I should have figured out to find something like this (by Irv
Bromberg)

http://www.sym454.org/twilight/

Something that I had thought about but which the above web site makes
clear is the effect of refraction, which increases the duration of
sunset due to it retarding the apparent motion of the sun. The effect
of refraction which is around 17% is probably profound enough that the
duration of sunset is weather dependent.

On Fri, 23 Sep 2016 12:03:12 +0000, Karl Palmen
<[hidden email]> wrote:

>Dear Jim, Rob and Calendar People
>
>Thank you Jim for your reply.
>
>-----Original Message-----
>From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Jim Riley
>Sent: 22 September 2016 17:04
>To: [hidden email]
>Subject: Re: Fastest Sunset
>
>Using
>
>http://aa.usno.navy.mil/data/docs/RS_OneDay.php
>
>and calculating the time between sunset (apparent center of sun 0.5
>degrees below horizon, and civil twilight sun 6 degrees below
>horizon), the variation at the equator is small, 21 minutes near the
>equinoxes and 22 minutes near the solstices.
>
>The period of sunset should be roughly proportional to the period of
>twilight. So at the equator, the semiannual variation in the period of
>sunset should be around 10 seconds. The daily variation could be about
>0.1 seconds, but since there is a minima near the equinoxes, it should
>be much less. So at the equator the effect of the eccentricity of the
>earth's orbit has greater effect, and so the quickest sunset is
>shifted towards aphelion. But doesn't that imply that the quickest
>sunset is near to the September equinox, because it is closer to
>aphelion than the March equinox.
>
>KARL REPLIES: This alone done not imply that the quickest sunset is near to the September equinox, because it is closer to aphelion than the March equinox. One has to consider why this is the case. I reckon it is because nearer the aphelion the sun is moving slower along the ecliptic and so faster across the sky, for a daily sun-path of the same length. So I too would expect the fastest sunset near the September equinox to be a little faster than the fastest sunset near the March equinox and this difference will increase until the perihelion reaches the March equinox in about 5000 years' time.
>
>This difference in sunset speed may be so small as to modify twilight duration by only a few seconds and so not show up on a web site such as the one linked above.
>
>Karl
>
>16(01(22
--
Jim Riley

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Re: Fastest Sunset

Victor Engel
In reply to this post by Jim Riley-4

On Fri, Sep 23, 2016 at 12:11 PM, Jim Riley <[hidden email]> wrote:
I should have figured out to find something like this (by Irv
Bromberg)

http://www.sym454.org/twilight/

Something that I had thought about but which the above web site makes
clear is the effect of refraction, which increases the duration of
sunset due to it retarding the apparent motion of the sun. The effect
of refraction which is around 17% is probably profound enough that the
duration of sunset is weather dependent.

On Fri, 23 Sep 2016 12:03:12 +0000, Karl Palmen
<[hidden email]> wrote:

>Dear Jim, Rob and Calendar People
>
>Thank you Jim for your reply.
>
>-----Original Message-----
>From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Jim Riley
>Sent: 22 September 2016 17:04
>To: [hidden email]
>Subject: Re: Fastest Sunset
>
>Using
>
>http://aa.usno.navy.mil/data/docs/RS_OneDay.php
>
>and calculating the time between sunset (apparent center of sun 0.5
>degrees below horizon, and civil twilight sun 6 degrees below
>horizon), the variation at the equator is small, 21 minutes near the
>equinoxes and 22 minutes near the solstices.
>
>The period of sunset should be roughly proportional to the period of
>twilight. So at the equator, the semiannual variation in the period of
>sunset should be around 10 seconds. The daily variation could be about
>0.1 seconds, but since there is a minima near the equinoxes, it should
>be much less. So at the equator the effect of the eccentricity of the
>earth's orbit has greater effect, and so the quickest sunset is
>shifted towards aphelion. But doesn't that imply that the quickest
>sunset is near to the September equinox, because it is closer to
>aphelion than the March equinox.
>
>KARL REPLIES: This alone done not imply that the quickest sunset is near to the September equinox, because it is closer to aphelion than the March equinox. One has to consider why this is the case. I reckon it is because nearer the aphelion the sun is moving slower along the ecliptic and so faster across the sky, for a daily sun-path of the same length. So I too would expect the fastest sunset near the September equinox to be a little faster than the fastest sunset near the March equinox and this difference will increase until the perihelion reaches the March equinox in about 5000 years' time.
>
>This difference in sunset speed may be so small as to modify twilight duration by only a few seconds and so not show up on a web site such as the one linked above.
>
>Karl
>
>16(01(22
--
Jim Riley