Joining list. Calendar reforms.

[Irv Bromberg]

On 2009 Jun 9, at 06:45 , HR-CALNDR-L wrote:

The vernal equinox is when the geocentric ecliptic longitude of the sun's
center equals naught point naught.

Irv replies:  If I'm not mistaken, there is no way to calculate an ecliptic longitude of 0.0° without using 0° solar declination as the reference.  According to the IAU, the solstices and other equinox can be calculated as ecliptic solar longitude relative to that zero (known as "the equinox of date"), so as a consequence the other equinox will not occur at a solar declination of exactly 0°.

Because of the gravity of other heavy things in the universe (e.g. jupiter),
earth's orbit around the sun is NOT in a plane

Irv replies:  Earth's orbit is always in a plane, but that plane does shift relative to the plane of Jupiter's orbit, which dominates the solar system.

, earth can have some non-zero ecliptic latitude

Irv replies:  The ecliptic is the path of Sun in the sky, and Sun can have a small non-zero ecliptic latitude due to small shifts in the Earth orbital inclination, which is certainly not ignored when it matters.

, which is completely ignored in the astronomical definition of the equinox.

And there is nutation, causing the equatorial plane to wobble.
That's also ingored. Just to make the definition of the equinox simple and
easy and its calculations as simple and easy as possible.

Irv replies:  Everything that affects the apparent geocentric solar declination at the northward equinox must be properly taken into account.  This includes the inclination of the ecliptic, Earth axial obliquity and nutations (wobble), planetary precession, lunisolar precession, the careening of Earth and Moon around their common center of gravity, the Earth orbital eccentricity and Earth orbital inclination.  So I don't know where you got the idea that these factors are ignored, they certainly are not ignored by those who know what they are doing.  The result of taking all these factors into account along with a Delta T adjustment for Earth rotation rate changes is the moment of the northward equinox, which is then by definition the moment of the ecliptic solar longitude zero. Behind the scenes, not so simple.

When calculating the moment of any other ecliptic solar longitude, the same factors must likewise be taken into account, otherwise an inaccurate moment will be reckoned.

In the same way the moon phases are defined only by the difference in
longitude between moon and sun, and that is geocentric longitude in the
ecliptic plane. It is not full moon when the moon is exactly round, it hardly
ever (better say never) is exactly round. The simple fact that we do not have
a perfectly central lunar eclips every month is the proof thereof.

Irv replies:  That doesn't prove that.  The reason why there isn't a lunar eclipse every month is that the lunar orbit is tilted about 5° relative to Earth's orbital plane, so an eclipse (solar or lunar) is only possible when Sun and Moon are both near a lunar orbital node, one of two points where the lunar orbit crosses the Earth orbital plane.  The lunar orbital nodes slowly regress westward around Earth (opposite direction to Moon's revolution around Earth), taking almost 18.6 years to regress all the way around, see:

<http://en.wikipedia.org/wiki/Lunar_nodes>

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

[Irv Bromberg]

On 2009 Jun 9, at 09:08 , Irv Bromberg wrote:

Irv replies:  If I'm not mistaken, there is no way to calculate an ecliptic longitude of 0.0° without using 0° solar declination as the reference.  According to the IAU, the solstices and other equinox can be calculated as ecliptic solar longitude relative to that zero (known as "the equinox of date"), so as a consequence the other equinox will not occur at a solar declination of exactly 0°.

Irv adds:  I tried to find some examples of that, where the solar declination of the southward equinox is not exactly 0° at the time that the ecliptic solar longitude relative to the northward equinox of date is exactly 180°, but my solar declination function always returns 0° at the southward equinox.  When I looked at the code, however, I found out why:  my solar declination function reckons the solar declination on the basis of the obliquity of the ecliptic and the solar longitude!  The source formula is at:

http://www.math.niu.edu/~rusin/uses-math/position.sun/solar.position

This approach is probably very widely used, thus leading to the illusion that the southward equinox is at the same moment by either method.  When the solar declination is independently determined by consideration of all the factors that I listed previously, however, slight differences ought to be found, as exist in the southward equinox moments output generated by SOLEX 10.1 when searched for by ecliptic longitude vs. solar declination.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

[Amos Shapir]

Some parts of this message have been removed. Learn more about Nabble's security policy.

The two definitions vary with a ratio of 4999999 : 5000000; the way I have heard it, the difference was only noticed when surveying of land had reached a few hundred miles from the east coast, when measurements on the ground, which were using surveyor's feet, no longer matched the maps, which were made using the other definition.

Amos Shapir
 



 

> Date: Mon, 8 Jun 2009 13:48:51 -0400
> From: markjreed@...
> Subject: Re: Imperial units
> To: CALNDR-L@...
>
> On Mon, Jun 8, 2009 at 1:31 PM, Peter Zilahy Ingerman,
> PhD<pzi@...> wrote:
> > FWIW, 100/3937 yields an inch equalling 2.540005 cm, which was the textbook
> > value in my Physics courses until 1958, when the formal definition of the
> > inch actually changed to exactly 2.54 cm.
> >
> > So the issue is that the surveyor's foot was defined prior to 1958, and
> > hasn't been redefined to be consistant with the "new" inch!
>
> Both feet and inches were changed or unchanged alike; survey values
> with feet and inches meant inches of 100/3937m, while outside of
> surveying a "foot" has been exactly 0.3048m since 1959.
>
> Even in the US, modern geodesy uses meters, so the practical need for
> the survey foot is rapidly dwindling if not already gone.
>
> --
> Mark J. Reed <markjreed@...>
>

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[Mark J. Reed]

2009/6/9 Amos Shapir <amos083@...>:
> The two definitions vary with a ratio of 4999999 : 5000000;

One too many digits there the ratio is:  499,999 / 500,000.

> The way I have heard it, the difference was only noticed when surveying of land had reached
> a few hundred miles from the east coast, when measurements on the ground,
> which were using surveyor's feet, no longer matched the maps, which were
> made using the other definition.

That seems unlikely, as I don't think it's a case of two competing
definitions developed independently.  The first attempt to "metricize"
the foot defined it as 1200/3937 m; the later revision changed it to
an exact decimal fraction of 0.3048m, while maintaining the previous
definition as valid within its specific domain.

The difference amounts to an inch after 8 miles; by 50 miles it
amounts to half a foot, and by 100 miles a full foot.

--
Mark J. Reed <markjreed@...>

[HR-CALNDR-L]

Hello all,

First of all, I think Irv and I talking the same, just using differents ways
to express it. I tried to keep it as simple as possible.

According to Jean Meeus' excellent book about Astronomical Algorithms,
ecliptic longitude refers to the angle w.r.t. the (mean) vernal point (which
slowly shifts due to precession), measured in the ecliptic plane.
There are different ways to define 'ecliptic'; I referred  to the _mean_ plane
of earth's orbit around the sun; the zero latitude is w.r.t. to this plane.

>> 'Irv replies:
>> Earth's orbit is always in a plane, but that plane does shift (...)'
Actually that is what I meant, but isn't this the same as saying the orbit is
not in one single plane? Jupiters inclination and gravity cause earth to be
pulled 'up' and 'down' w.r.t. earth's mean orbital plane.

The vernal point is the _mean_ direction of the sun when it moves northward
through the equatorial plane, and it lies in the ecliptic plane I just
explained. Together that describes a set of heliocentric polar coordinates:
we've got a plane which we call the ecliptic and a well defined direction
whithin that plane. Based on earth's motion we call one direction
perpendicular to the ecliptic plane 'ecliptic north' and the other 'south',
enabling us to define a sign for the eclpitic latitude. Both this ecliptic
plane and the vernal point are mean values such that on average the sun's
declination equals zero at the moment when its longitude equals zero.

In this coordinate system using mean values, nutation is also averaged out.
And there are several other coordinate systems used by astronomers, but
thatt's not so relevant right now.

Altogether this makes that the sun is usually not exactly in the equatorial
plane when its longitude equals zero. And the latter is the astronomical
definition of the vernal equinox, according to Jean Meeus. So effectively that
is also a mean value. On average the sun is in the equatorial plane at equinox
time, but at every single equinox it will not be exactly.

And yes, the precise calculation of the planet's positions etc. is not simple
and easy. But using Jean meeus' formulas (which is VSOP87, implemented years
ago by myself in javascript on http://henk-reints.nl/astro (works only with
MSIE)), the equinox is based only on earth's _position_ and not its exact
orientation. It is the position in the above mentioned coordinate system where
on average the sun moves n-ward through the equatorial plane. That is what I
meant with 'as simple as possible'. But indeed, computing earth's exact
position is definitely not simple.

About the moon: well that's also what I meant. The fact that we don't have an
eclips each month indeed demonstrates the inclination of the moon, so it does
prove that what we call full moon is not exactly opposite to the sun so it is
not exactly round what we see in the sky.


_________________________________________________
Kind regards / met vriendelijke groeten,

Henk Reints, MSc.



Oorspronkelijke tekst Irv Bromberg

> On 2009 Jun 9, at 06:45 , HR-CALNDR-L wrote:
>> The vernal equinox is when the geocentric ecliptic longitude of the
>> sun's
>> center equals naught point naught.
>
> Irv replies:  If I'm not mistaken, there is no way to calculate an
> ecliptic longitude of 0.0° without using 0° solar declination as the
> reference.  According to the IAU, the solstices and other equinox can
> be calculated as ecliptic solar longitude relative to that zero (known
> as "the equinox of date"), so as a consequence the other equinox will
> not occur at a solar declination of exactly 0°.
>
>> Because of the gravity of other heavy things in the universe (e.g.
>> jupiter),
>> earth's orbit around the sun is NOT in a plane
>
> Irv replies:  Earth's orbit is always in a plane, but that plane does
> shift relative to the plane of Jupiter's orbit, which dominates the
> solar system.
>
>> , earth can have some non-zero ecliptic latitude
>
> Irv replies:  The ecliptic is the path of Sun in the sky, and Sun can
> have a small non-zero ecliptic latitude due to small shifts in the
> Earth orbital inclination, which is certainly not ignored when it
> matters.
>
>> , which is completely ignored in the astronomical definition of the
>> equinox.
>> And there is nutation, causing the equatorial plane to wobble.
>> That's also ingored. Just to make the definition of the equinox
>> simple and
>> easy and its calculations as simple and easy as possible.
>
> Irv replies:  Everything that affects the apparent geocentric solar
> declination at the northward equinox must be properly taken into
> account.  This includes the inclination of the ecliptic, Earth axial
> obliquity and nutations (wobble), planetary precession, lunisolar
> precession, the careening of Earth and Moon around their common center
> of gravity, the Earth orbital eccentricity and Earth orbital
> inclination.  So I don't know where you got the idea that these
> factors are ignored, they certainly are not ignored by those who know
> what they are doing.  The result of taking all these factors into
> account along with a Delta T adjustment for Earth rotation rate
> changes is the moment of the northward equinox, which is then by
> definition the moment of the ecliptic solar longitude zero. Behind the
> scenes, not so simple.
>
> When calculating the moment of any other ecliptic solar longitude, the
> same factors must likewise be taken into account, otherwise an
> inaccurate moment will be reckoned.
>
>> In the same way the moon phases are defined only by the difference in
>> longitude between moon and sun, and that is geocentric longitude in
>> the
>> ecliptic plane. It is not full moon when the moon is exactly round,
>> it hardly
>> ever (better say never) is exactly round. The simple fact that we do
>> not have
>> a perfectly central lunar eclips every month is the proof thereof.
>
> Irv replies:  That doesn't prove that.  The reason why there isn't a
> lunar eclipse every month is that the lunar orbit is tilted about 5°
> relative to Earth's orbital plane, so an eclipse (solar or lunar) is
> only possible when Sun and Moon are both near a lunar orbital node,
> one of two points where the lunar orbit crosses the Earth orbital
> plane.  The lunar orbital nodes slowly regress westward around Earth
> (opposite direction to Moon's revolution around Earth), taking almost
> 18.6 years to regress all the way around, see:
>
> <http://en.wikipedia.org/wiki/Lunar_nodes>
>
>
> -- Irv Bromberg, Toronto, Canada
>
> <http://www.sym454.org/>

[Irv Bromberg]

On 2009 Jun 9, at 11:23 , HR-CALNDR-L wrote:

According to Jean Meeus' excellent book about Astronomical Algorithms,
ecliptic longitude refers to the angle w.r.t. the (mean) vernal point (which
slowly shifts due to precession), measured in the ecliptic plane.
There are different ways to define 'ecliptic'; I referred  to the _mean_ plane
of earth's orbit around the sun; the zero latitude is w.r.t. to this plane.

Irv replies:  Henk referred to several _mean_ parameters.  The upshot of using only _mean_ parameters is that the computed moment of the equinox is only the _mean_ equinox, which can differ by up to ±15 minutes from the actual equinox.  The mean equinox is adequate for many purposes, and one could define a calendar that is regulated by mean equinox arithmetic, or an approximation thereof, but true astronomical calendars such as the modern Persian (Iranian) solar calendar uses actual equinox moments, not the mean equinox.  It would rarely make a difference anyhow, only if the actual equinox is close to midnight according to Iran Standard Time.

I prefer to avoid mean equinox or solstice moments where possible, because the expressions upon which they are based are derived from curve fitting to actual equinox or solstice moments (numerically integrated), or worse, curve fitting to moments based on simplified or truncated astronomical algorithms.  Thus their reliability is uncertain, depending on how the data was generated, reduced and fitted.

The vernal point is the _mean_ direction of the sun when it moves northward
through the equatorial plane, and it lies in the ecliptic plane I just
explained. Together that describes a set of heliocentric polar coordinates:
we've got a plane which we call the ecliptic and a well defined direction
whithin that plane. Based on earth's motion we call one direction
perpendicular to the ecliptic plane 'ecliptic north' and the other 'south',
enabling us to define a sign for the eclpitic latitude. Both this ecliptic
plane and the vernal point are mean values such that on average the sun's
declination equals zero at the moment when its longitude equals zero.

Irv replies:  There is no way to determine Earth's position at the equinox independently of its orientation.  It is the orientation that determines whether or not Earth is at the equinox.  The actual equinox is the moment when the geocentric apparent solar declination crosses the actual celestial equator from south to north.  The mean equinox is the moment when the mean solar declination crosses the mean celestial equator (ignoring nutation) at the Earth-Moon barycenter, which can be calculated, not observed.  SOLEX can get close to this moment by integrating in the "planets only" mode, which combines Earth and Moon into one mass orbiting at the Earth-Moon barycenter (I'm not sure if SOLEX ignores nutation in this mode -- it would make sense to ignore it, since nutation is largely due to the effects of Moon).

Altogether this makes that the sun is usually not exactly in the equatorial
plane when its longitude equals zero. And the latter is the astronomical
definition of the vernal equinox, according to Jean Meeus.

Irv replies:  Actually Jean Meeus stated his preference for solar declination to define all equinoxes and solstices, and was critical of the IAU for adopting solar-longitude-based definitions.

Anyhow, for the northward equinox, by definition it is the moment when the solar declination crosses 0° moving from south to north, and that moment is defined as the ecliptic solar longitude zero position.  For some purposes that could be the actual geocentric moment, for other purposes it may suffice to use the potentially simpler mean barycentric moment.

It is not possible to assign a "position" to the equinox independently of the solar declination, as there is no fixed equinox direction in space, due to planetary and lunisolar precession and due to the orbit of our solar system around the nucleus of the Milky Way galaxy.  Methods that purport to calculate the position directly and without computing solar declination are actually using a mean equinox polynomial corrected for mean precession, but which is ultimately traceable to derivation from solar declination observations. Ultimately such calculations must be observation-traceable, it is not possible to reckon Earth's position "out of thin air".  The gold standard for celestial mechanics is numerical integrations by the Jet Propulsion Laboratory (JPL), but even those algorithms must be fitted to actual observations.  Typically during the fitting the greatest weight is placed on the most accurate near-present-era observations, but that makes such integrations progressively more uncertain the further into the past or future one goes, therefore JPL typically limits their integrations to ±3 millennia (and they ignore solar mass loss).

Unfortunately, we have no way to improve upon this situation.  For Earth orientation itself, present knowledge is insufficient to accurately numerically integrate and predict merely the mean Earth axial tilt cycle over the long term.  Published papers that purported to carry out such integrations over spans of millions of years are utter nonsense (but nevertheless widely cited).  Sure, one can execute such calculations on a main frame system, but that doesn't make them right.  There are too many unknown factors (polar loading / equatorial bulge oblateness, tectonic plate movements, orientation of the continents, ocean depths and the distribution of water, orientation and distribution of mountains, wind speeds and directions, Earth core / mantle dynamics, etc., etc.).

Finding the actual moment when the solar declination crosses 0° is the same as finding the moment when Sun is directly overhead at local apparent noon at the equator (somewhere).  That's about as simple as it gets, but not simple to calculate.

Although the truncated VSOP87 algorithm that Jean Meeus and you use (and likewise I employ in Kalendis) appears to be calculating the position directly, but actually it has such a mean equinox polynomial with precession correction embedded into the math.  More accurate later algorithms, such as the 500-term truncated VSOP2000 published at the SOFA web site at <http://www.iau-sofa.rl.ac.uk/>, the last publicly released by Pierre Bretagnon before his untimely death, don't include precession, calculating the position relative to the equinox of J2000, don't include all of the various necessary 3-dimensional coordinate rotations, because the concept now is to allow the programmer to be in explicit control of each step, and also to avoid calculations that are not necessary where a multi-step procedure is being carried out.

Henk, I saw your note "For eclipses, the given geographic position in the popup summaries is the point on Earth closest to the central line, which (especially for non-central annular eclipses) is not the same as the point of greatest magnitude." -- Their calculations ought to be quite close to yours because they also used the truncated VSOP87 algorithms.  A significant difference could arise if you are not using the same Delta T polynomials that they used, which are posted at:

<http://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html>.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

<http://www.sym454.org/kalendis/>

[MIKE OSSIPOFF]

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Dear Karl and Calendar People,
 
A calendar based on solar declination, maybe through reference to the quarters between solstices & equinoxes, is a type of seasonal calendar, based on a natural phenomenon that results in our year.
 
In addition to posting my proposals, I also joined this mailing-lists in order to get an idea of what is acceptable to calendar reform advocates, because what is said here gives an indication of what kind of proposals are the most acceptable.
 
From reading, I got the impression that Elizabeth Achellis was too inflexible with her proposal. Religious groups had said that the World Calendar would be acceptable if it used leapweeks instead of blank days. Proposals should start out broad. Seasonal calendars are a broad category.
 
I understand that terrestrial seasons isn't going over so well here as a basis for a calendar.  I'm glad to find that declination, maybe via the astronomical quarters related to it, is more acceptable.
 
Though I've argued (and may still say a few words) for a calendar with year-divisions based on perceived terrestrial seasons, I haven't meant to imply that it is the only right calendar. Just as people can correct locally for global variations in seasonal time-lag when a terrestrial seasonal calendar is used, they could of course likewise do so if a declination seasonal calendar is used.
 
You wrote:
 
>The very use of seasonal names constitutes such a claim. The
> use of such names while denying such a claim would be misleading. Better
> to use non-seasonal names that can be given local seasonal
> interpretations.
 
I reply:
 
Or astronomical seasonal quarters, as you mentioned, such as (starting at the winter solstice): "FromSouth, ToNorth, FromNorth, ToSouth". Each of those astronomical seasonal quarters could be divided into three numbered months, I, II, III. So right now it would be ToNorthIII. That would be my favorite astronomical seasonal month-naming, or at least my favorite one likely acceptable to other calendar reform advocates. Same astronomical quarters the media now call "Winter, Spring, Summer, Autumn", but with more realistic naming.
 
You continued:
 
>>So Mike is suggesting names somewhat like Winter US, Spring
> US, etc, where US stands for universal season.
 
I reply:
 
Uni-hemispherically, I'd just call them Calendar Winter, Calendar Spring, etc. ("Calendar" could be omitted but understood). Internationally I'd call them South, Northward, North, Southward.
 
To me these names are
> either misleading or have no advantage over numbers or letters.
 
I reply:
 
True, they're misleading when they don't agree with local environmental perceptions of the times when conditions reside in a distinct high north or south declination mode.
 
But, there's pretty good agreement about those perceptions in such widely separated places as England, California, Florida, and even Australia. When you read what early British writers said about the months and seasons, you recognize it as what you already knew about the relation of months and seasons in the U.S. Certainly in California, but probably elsewhere in the U.S. too. Even in Florida, June is when the distinctive high north-declination things start: Frequent lightning storms, frequent very heavy rain.  
 
I've been looking on the Internet for information about places where the perceptions are different to a problematic degree. I haven't found that yet, but I haven't been looking very long, and I continue to look. I googled "When does Summer start?". Some said "June 1", some quoted the media definition. Someone in Australia said that, there, Summer is regarded as starting on December 1st.
So, even as far away as Australia, even in the oceanic, expected-high-lag Southern Hemisphere, that person still said that in his country December 1st starts the Summer. They didn't discuss when Summer ends, but I'll look for that too. But, so far, I haven't found a place where the terrestrial seasonal assumptions that I've suggested would be disagreed-with. Admittedly I've barely begun to look.
 
So, though I certainly can't claim to have thoroughly checked the situation out, what little I've found so far hasn't yet shown a problematic amount of perceived mismatch.
 
Anyway, I'm not saying that others should agree with me, and I don't mention the above information as proof that it should be the way that I say. I mention it only to show how I could make the terrestrial seasonal proposal that I've made.
 
I take an extreme position when I suggest that the calendar explicitly refer to the globally-variable terrestrial seasons, an attempt to roughly model what can't precisely be modeled by an international calendar. The only other advocate of such a calendar that I've heard of was Isaac Asimov (and a few websites that support  his proposal), and I don't agree with his use of the media's "seasons". I emphasize that I don't say that others should adopt that extreme position. Instead, I'm delighted to find that the broad seasonal calendar category seems acceptable to other calendar reform advocates, with year-divisions based on and named for declination and maybe measured by the astromical quarters that it's related to. I would help to promote and advocate such a declination seasonal calendar.

 
You wrote:
 
> We could have season names such as
> Northward Sun, Northern Sun, Southward Sun and Southern Sun. Referring
> to the position of the sun gets round the objections.
 
I reply:
 
Yes, that's what I'd use for international names for high-declination and transitional seasons. But the transitional periods are relatively short, in comparison to the periods during which solar declination resides in the top half of its northern and southern ranges (which seems to roughly match the winter & summer perceptions that I've heard of). Anyway, however you look at it, declination transitions repidly, and resides long in high north and south values.
 
So, as my favorite, I wouldn't specify transitional periods whose length is equal to that of the extreme declination periods. I'd previously said that I like the Chinese astronomical quarters centered on solstices & equinoxes, but I now prefer, if we're going to use equal astronomical quarters, that they start on solstices & equinoxes, and have names such as FromSouth, ToNorth, FromNorth, ToSouth.
 
Another possibility would be to use the names you mentioned, Southern Sun, Northward Sun, Northern Sun, Southward Sun, but define Northern Sun and Southern Sun as periods during which the north and south solar declinations are in the outer half of their range. That would be especially terrestrially relevant, it seems to me, because those do seem to be the approximate declination ranges that (after the terrestrial temperature catches up) are closely related  to perceptions of high north and south declination terrestrial conditions.
 
But equal astronomical quarters would be fine too, and maybe would have more agreement among calendar reform advocates.
 
Mike Ossipoff
 

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[MIKE OSSIPOFF]

 

To summarize my difference with y'all:
 
I'd like for a calendar to attempt to be an explicit map of the seasons, as closely as possible. Even if it can only be approximate. To me, "approximate" is better than "not at all".
 
With any new calendar, when making an appointment or vacation-plan for some future month, a person would want to estimate what conditions will be like then. Even if that new calendar has no explict references to seasons, a person would still want to make that estimate. So then, since someone will want to interpret the new calendar seasonally anyway, will want to try to estimate conditions on some future month, then I suggest: Why not make the calendar's named year-divisions simplify that estimate, that rough prediction, by at least mapping the seasons as closely as possible, thereby reducing the work of that estimate of conditions in some future month in the new calendar.
 
Then, even if the seasonal lag where you reside differs from the calendar's estimated average, the calendar-based estimate will at least be a meaningful starting-point for your estimate of conditions at some future part of the year. You'd say "This calendar seems to to be a week early around here", instead of "I wonder what relation this calendar has with the seasons?"
 
Different seasons in tropics? No problem, because the calendar need only refer to a time when conditions reside in a distinct north declination mode, a distinct south declination mode, and the relatively brief transitional periods inbetween. For international purposes, the calendar's seasonal year-divisions needn't be called, "winter", "summer", "rainy season", etc. They could just be called "South", "Northward", "North", "Southward", referring to the declination that causes the terrestrial seasonal conditions.
 
Because of what has been said and written in various mutually distant places, the Subjective Seasonal Calendar would start North on June 1, and would start South on December 1 of the currently-used calendar.
 
My proposal for the fixed version of the Subjective Seasonal Calendar hasn't changed since I first posted it.
 
Four ways of specifying the lengths of North & South, for the nonfixed version of Subjective Seasonal:
 
End and length of North:
 
1. Say by definition that the middle of North is 38 days after the north solstice (the middle of that solstices's cyclical drift during some specified leapyear cycle). That automatically specifies the end and the length of North.
 
2. Say that the end of North is the day when the lag-adjusted solar declination (the solar declination of 38 days previous) is equal to what it was at the beginning of North.
 
End and length of South:
 
1. Define South's length as equal to that of North.
 
2. Specify South's end and length separately in the same way that the end and length of North is specified.
 
[end of list of approaches to the end and length of North & South]
 
No doubt the combination 2,2 is ideally the most appealing. But 1,1 is simpler, and was my proposal that I posted here before. So I'll probably keep 1,1 as my proposal.
 
For the nonfixed version, I'd keep the Gregorian leapyear system, for simplicity of proposal, and to maintain the match of North's and South's starting dates with June 1 and December 1. Leapday would be during South, in order to preserve that match.
 
As I said, though, I would support, and help advocate and promote any seasonal calendar that has significant support, whether based on terrestrial seasons, or only on declination or astronomical quarters beginning on solstices & equinoxes.
 
Mike Ossipoff
 
 
 
 
 
 
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[Tom Peters-6]

Op 9-jun-2009, om 20:00 heeft Irv Bromberg het volgende geschreven:

> On 2009 Jun 9, at 11:23 , HR-CALNDR-L wrote:
>> According to Jean Meeus' excellent book about Astronomical  
>> Algorithms,
>> ecliptic longitude refers to the angle w.r.t. the (mean) vernal  
>> point (which
>> slowly shifts due to precession), measured in the ecliptic plane.
>> There are different ways to define 'ecliptic'; I referred  to the  
>> _mean_ plane
>> of earth's orbit around the sun; the zero latitude is w.r.t. to  
>> this plane.
>
> Irv replies:  Henk referred to several _mean_ parameters.  The  
> upshot of using only _mean_ parameters is that the computed moment  
> of the equinox is only the _mean_ equinox, which can differ by up  
> to ±15 minutes from the actual equinox.

   Any definition is problematic.  There are at least 2 different  
definitions for a mean ecliptic (inertial and rotating), both of  
which vary over time ("planetary precession"), but one can also  
define a so-called "osculating" ecliptic based on the instantaneous  
velocity of the Earth, OR the Earth-Moon barycenter, affected by the  
gravitational perturbations of the planets.  Also the direction of  
Earth's pole is affected by short-periodic (nutation) and long-
periodic (luni-solar precession) variations.  And that is for  
geocentric definitions.  If you observe or predict solar altitude  
from the surface of the Earth you also have to take account of polar  
motion, annual aberration, diurnal aberration, geocentric parallax,  
and refraction.

   Astronomers in contrast have tried to define reference frames as  
stable as they can.  So they work with a fixed reference frame, which  
more or less coincides with an inertial ecliptic and aequator of  
2000.  Also they dropped the aequinox as reference point, and  
introduced some other abstract point that is more stable.  Google for  
ICRF and ITRF.

   Numerical integration uses an inertial frame (by definition), but  
affected by all possible perturbations that you put into the  
equations.  That is impossible for a rule-based calendar to follow.  
You might try to integrate with simplified equations that ignore some  
perturbations, but that ruins the accuracy of your medium- and long-
term predictions.

   Calendars need to be stable and predictable for time periods of 1  
year to thousands of years.  So if calendars are to be astronomically  
based, you should remove (average out) all short-periodic  
variations.  With an analytical theory that is much easier to do than  
with numerical integration, where your only option is to average over  
some arbitrary period of time, where your results will always be  
affected by statistical variations (if you take other time points, or  
another period to average over, you get different mean results).  The  
analytical theories allow you to drop various sources of variation  
independently and completely.

   For solar calendars, my preference is to use a pure Keplerian  
orbit for the Earth-Moon barycenter, with secular (long-term)  
variations in the orbital elements, but ignoring planetary (and  
lunar) short-term perturbations, and using expressions for luni-solar  
precession but ignoring nutation.  This will give you fairly stable  
seasonal cardinal points, which will be closer to actual  
astronomically defined cardinal points than if you use a mean mean  
aequinox.

   Also I like to point out that calendars deal with dates, and not  
infinitely accurate points in time.  If like the Iranians do you  
astronomically accurately compute the moment of aequinox to the  
second, for a specific location, then still once in 86400 years on  
average, rounding will put it on the wrong date as compared to an  
even more accurate computation.  And the more accurate you compute,  
the more precise your definitions must be, and the more arbitrary  
your choice for that particular definition becomes.

--
Tom Peters

[MIKE OSSIPOFF]

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Dear Aristeo and Calendar People,
 
Aristeo, you wrote:
 
> The following are when the astronomical phenomena occur in the Northern Hemisphere:
> Vernal Equinox - March 21
> Summer Solstice - June 21 or 22
> Autumnal Equinox - September 23
> Winter Solstice - December 21 or 22

Not only do the dates of the equinoxex and solstices vary for a given longitude, due to calendarical drift, but they also vary with longitude. For instance, as I was saying, this year's vernal equinox was on March 20, in the U.S.
 
> If I am not mistaken, we call the astronomical seasons in the Northern Hemisphere as:
> Spring - March 21 to June 20 or 21
> Summer - June 21 or 22 to September 22
> Autumn or Fall - September 23 to December 20 or 21
> Winter - December 21 or 22 to March 20

Yes the media define the seasons as equal periods beginning on solstices and equinoxes. But I must disagree when you say that _we_ define the seasons in that way. I certainly don't, and I don't think anyone here supports the media's notion of the seasons.
 
The only justification that can be made for equal "seasons" that start on solstices & equinoxes is that it's what we hear on radio and tv.
 
> However, these seasons are also called in some other ways (I forgot the term) on these dates:
> Spring - March 1 to May 31 (March, April, and May)
> Summer - June 1 to August 31 (June, July, and August)
 
Those seasons would lag insufficiently behind solar declination, and would end too soon. Three-month seasons won't match our perception of the seasons.

> Autumn or Fall - September 1 to November 30 (September, October, and November)
> Winter - December 1 to February 28 or 29 (December, January, and February)
>
> What is the term used for these seasons? It is not astronomical seasons.
 
It's a proposed system of terrestrial seasons. But it isn't as accurate as the seasons of the Subjective Seasonal Calendar.
 
In such widely-distributed places as England, U.S. (Including California, Florida and elsewhere), and Australia, people perceive the distinct north and south declination seasons to begin on June 1 and December 1.
 
With the global average seasonal timelag of 1.25 months, that gives us North declination and South declination seasons of 117 or 118 days, with shorter transitional perioids. And, for the North declination season to taper to an end during September is also in accord with people's perceptions.

You continued:
 
Mike, what can you say of fixing the seasons' dates when we are experiencing weather changes?
 
I reply:
 
If global warming messes up the Subjective Seasonal Calendar's good match to seasons worldwide, then I'll write letters of complaint.
 
But sure, if you're talking about yearly and daily fluctuations in temperature and rainfall, it's true that seasons can't predict a date's temperature with perfect accuracy.
 
Mike Ossipoff
 
 

>

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[zengyiping]

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Dear Mike and all calendar people,

    Mike Said That a World calendar must based on four seasons. I agree his idea because calendar has two inportant function:counting time by
dates and getting information of seasons from dates. If calendar is building on base four seasons which start year on a starting day of a
 season, of caurse it is convinent for realization of this two functions.

    But,unfortunategly the thermal seasons are not the same at different places in the same time, so we can't make a world seasonal calend
based on a speachial place. However, the thermal seasons of every place is prodused from the same natural source which is periodical changing of Sun's
declinations. The Orient astronomical seasons are defined by longitute which are bounded by 315° ，45° ，135° ，225°. The Winter's
Sun-declinations are in lowest range ,about less than -16°21´, The Summer's Sun-declinations are in highest range ,about bigger than +16°21´,
The Spring's Sun-declinations are in middle range ,about between -16°21´and +16°21´, The Spring's Sun-declinations are in middle range ,about
between -16°21´and +16°21´. From the astronomical four seasons we can interpret to any local thermal seasons. Therefore ,only if we biult a
calendar which is based on the astronomical seasons ,people in any place of world can get information from the dates of this calendar. My the
Natural  Seasonal World Calendar Proposal is thia proposal.

    Before recommend it I must intruduce the 24 solar terms first,which are the solar part of the traditional Chinese lunar-solar Calendar.

 The acliptic is divided into four 90° segments which boundaries are 315° ，45° ，135° ，225° ,called spring begining ,summer beging,autumn

 beging and winter begining respectively. because the 2nd segment has the highest declination and the 4th segment has the lowest declination.

Obviously the other two segment are named as spring begining and autumn begining. For fair we can also named four astronomical seasons as East season,

 North season, West season and South season . The ancient chinese astronomers divided avery season into 6 subsegments, which every has 15°

 width. Of course their time length are no equal. They are called as 24 solar term points. Their bound points are named according to climat

of central part of China . But we can call them by symble and number as follow:t1,t2,t3,.....t24. So spring is t1~t7,Summer is t7~t13,autumn

is t13~t19,winter is t19~t1.

    From astronomy handkook we can get the length of 24 solar term points. Then we can get the time length of four seasons.which are about

91,94,91,89 days. For biulding a calendar more regular and simple ,I modify them to 90,95,90,90  days. The time of 24 solar terms are vary in

a 1~3 day range. For standarization I fixed them as follow:

solar term     t1        t2        t3        t4        t5        t6    
longitute      315°      330°      345°      0°        15°       30°   
fixed term     T1        T2        T3        T4        T5        T6    
date           1/1       16/1      1/2       16/2      1/3       16/3  
declination    -16°21´   -11°29´   -05°55´   +00°00´   +05°55´   +11°29´

solar term     t7        t8        t9        t10       t11       t12
longitute      45°       60°       75°       90°       105°      120°
fixed term     T7        T8        T9        T10       T11       T12
date           1/4       17/4      3/5       18/5      4/6       20/6
declination    +16°21´   +20°10´   +22°36´   +23°26´   +22°36´   +20°10´

solar term     t13       t14       t15       t16       t17       t18  
longitute      135°      150°      165°      180°      195°      210° 
fixed term     T13       T14       T15       T16       T17       T18  
date           1/7       16/7      1/8       16/8      1/9       16/9 
declination    +16°21´   +11°29´   +05°55´   -00°00´   -05°55´   -11°29´

solar term     t19       t20       t21       t22       t23       t24
longitute      225°      240°      255°      270°      285°      300°
fixed term     T19       T20       T21       T22       T23       T24
date           1/10      16/10     1/11      16/11     1/12      1/12
declination    -16°21´   -20°10´   -22°36´   -23°26´   -22°36´   -20°10´

The fixed terms'error are no more than 2 days in current century.

My propsal  Calendar is as follow:

                           The Natural Seasonal World Calendar
  ES 1stM  T1 1    2    3    4  * 5    6    7    8    9   10   11  *12   13   14   15
           T216   17   18  *19   20   21   22   23   24   25  *26   27   28   29   30
                                                              1/3
 Spr 2ndM  T3 1    2  * 3    4    5    6    7    8    9  *10   11   12   13   14   15
           T416  *17   18    9   20   21   22   23  *24   25   26   27   28   29   30
                                                                   1/4                                        
     3rdM  T5*1    2    3    4    5    6    7  * 8    9   10   11   12   13   14  *15
           T616   17   18   19   20   21   22   23   24   25   26   27   28  *29   30
                                                                   1/5
  NS 4thM  T7 1    2    3    4    5    6    7    8    9   10   11   12  *13   14   15
             16 T817   18   19   20   21   22   23   24   25   26  *27   28   29   30
                                                                        1/6
 Sum 5thM     1    2 T9 3    4    5    6    7    8    9   10  *11   12   13   14   15
             16   17T1018   19   20   21   22   23   24  *25   26   27   28   29   30
                                                                        1/7
     6thM     1    2    3T11 4    5    6    7    8  * 9   10   11   12   13   14   15
             16   17   18   19T1220   21   22  *23   24   25   26   27   28   29  *30
                                                                             1/8
     MY       1    2    3    4    5   (6)

  WS 7thM T13 1  * 2    3    4    5    6    7    8  * 9   10   11   12   13   14   15
         T14*16   17   18   19   20   21   22  *23   24   25   26   27   28   29  *30
                                                         1/9
 Aut 8thM T15 1    2    3    4    5    6  * 7    8    9   10   11   12   13  *14   15
          T1616   17   18   19   20  *21   22   23   24   25   26   27  *28   29   30
                                                        1/10
     9thM T17 1    2    3    4  * 5    6    7    8    9   10   11  *12   13   14   15
          T1816   17   18  *19   20   21   22   23   24   25  *26   27   28   29   30
                                                             1/11
  NS10thM T19 1    2  * 3    4    5    6    7    8    9  *10   11   12   13   14   15
          T2016  *17   18   19   20   21   22   23  *24   25   26   27   28   29   30
                                                             1/12
Win 11thMT21* 1    2    3    4    5    6    7  * 8    9   10   11   12   13   14  *15
          T2216   17   18   19   20   21  *22   23   24   25   26   27   28  *29   30
                                                                   1/1
    12thM T23 1    2    3    4    5  * 6    7    8    9   10   11   12  *13   14   15
          T2416   17   18   19  *20   21   22   23   24   25   26  *27   28   29   30
                                                                        1/2
Note: 1. year is start on feb 4th of Rom Calendar which is sbout the date of spring equinox .1/month reppresent 1st of month of present calendar for common year.
      2. MY are the Middle of Year which can be world holidays. For leapyear it has date (6).
      3. Spr,Sum,Aut and Win represent basic thermal seasons( according to air temperature ) which has timelag assuming 30 days. For more timelag the  thermal seasons move forward (l-30)days. It is similar as 12 time zons.
      4. * represent the Sundays in 2009 year.
Yiping Zeng 14/6/2009

> Date: Thu, 11 Jun 2009 23:36:19 +0000
> From: nkklrp@...
> Subject: Brief seasonal calendar position summary
> To: CALNDR-L@...
>
>
>
> To summarize my difference with y'all:
>
> I'd like for a calendar to attempt to be an explicit map of the seasons, as closely as possible. Even if it can only be approximate. To me, "approximate" is better than "not at all".
>
> With any new calendar, when making an appointment or vacation-plan for some future month, a person would want to estimate what conditions will be like then. Even if that new calendar has no explict references to seasons, a person would still want to make that estimate. So then, since someone will want to interpret the new calendar seasonally anyway, will want to try to estimate conditions on some future month, then I suggest: Why not make the calendar's named year-divisions simplify that estimate, that rough prediction, by at least mapping the seasons as closely as possible, thereby reducing the work of that estimate of conditions in some future month in the new calendar.
>
> Then, even if the seasonal lag where you reside differs from the calendar's estimated average, the calendar-based estimate will at least be a meaningful starting-point for your estimate of conditions at some future part of the year. You'd say "This calendar seems to to be a week early around here", instead of "I wonder what relation this calendar has with the seasons?"
>
> Different seasons in tropics? No problem, because the calendar need only refer to a time when conditions reside in a distinct north declination mode, a distinct south declination mode, and the relatively brief transitional periods inbetween. For international purposes, the calendar's seasonal year-divisions needn't be called, "winter", "summer", "rainy season", etc. They could just be called "South", "Northward", "North", "Southward", referring to the declination that causes the terrestrial seasonal conditions.
>
> Because of what has been said and written in various mutually distant places, the Subjective Seasonal Calendar would start North on June 1, and would start South on December 1 of the currently-used calendar.
>
> My proposal for the fixed version of the Subjective Seasonal Calendar hasn't changed since I first posted it.
>
> Four ways of specifying the lengths of North & South, for the nonfixed version of Subjective Seasonal:
>
> End and length of North:
>
> 1. Say by definition that the middle of North is 38 days after the north solstice (the middle of that solstices's cyclical drift during some specified leapyear cycle). That automatically specifies the end and the length of North.
>
> 2. Say that the end of North is the day when the lag-adjusted solar declination (the solar declination of 38 days previous) is equal to what it was at the beginning of North.
>
> End and length of South:
>
> 1. Define South's length as equal to that of North.
>
> 2. Specify South's end and length separately in the same way that the end and length of North is specified.
>
> [end of list of approaches to the end and length of North & South]
>
> No doubt the combination 2,2 is ideally the most appealing. But 1,1 is simpler, and was my proposal that I posted here before. So I'll probably keep 1,1 as my proposal.
>
> For the nonfixed version, I'd keep the Gregorian leapyear system, for simplicity of proposal, and to maintain the match of North's and South's starting dates with June 1 and December 1. Leapday would be during South, in order to preserve that match.
>
> As I said, though, I would support, and help advocate and promote any seasonal calendar that has significant support, whether based on terrestrial seasons, or only on declination or astronomical quarters beginning on solstices & equinoxes.
>
> Mike Ossipoff
>
>
>
>
>
>
> _________________________________________________________________
> Lauren found her dream laptop. Find the PC that’s right for you.
> http://www.microsoft.com/windows/choosepc/?ocid=ftp_val_wl_290

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[Irv Bromberg]

Dear Calendarists:

A pretty good seasonal correlation for mid-latitudes where there is about 6-week lag between equinox or solstice and thermal season could be obtained by arranging the mean northward equinox to fall on average at the winter mid-quarter day, or the mean north solstice to fall on average at  the spring mid-quarter day.  This would then cause the thermal spring season to correlate with the spring quarter, or the thermal summer season to correlate with the summer quarter, respectively.

However, if it is a leap week calendar then the ±3 day medium-term wobble (away from the central average day) of the equinox or solstice relative to the mid-quarter day would be as conspicuous as it would be if an equinox or solstice were intended to fall on average at the start of a quarter.

Six weeks is not quite half of the 13-week quarter length, so if desired one could make the mid-quarter day the earliest date of the equinox or solstice.  Such an approach might eliminate the concern that the equinox or solstice wobble is conspicuous.

At tropical latitudes the seasonal lag is shorter and the thermal changes not so apparent, so any such seasonal calendar will seem irrelevant to people living in the tropics.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

[Karl Palmen]

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Dear Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 15 June 2009 14:01
To: CALNDR-L@...
Subject: Re: Brief seasonal calendar position summary

 

Dear Calendarists:

 

A pretty good seasonal correlation for mid-latitudes where there is about 6-week lag between equinox or solstice and thermal season could be obtained by arranging the mean northward equinox to fall on average at the winter mid-quarter day, or the mean north solstice to fall on average at  the spring mid-quarter day.  This would then cause the thermal spring season to correlate with the spring quarter, or the thermal summer season to correlate with the summer quarter, respectively.

 

However, if it is a leap week calendar then the ±3 day medium-term wobble (away from the central average day) of the equinox or solstice relative to the mid-quarter day would be as conspicuous as it would be if an equinox or solstice were intended to fall on average at the start of a quarter.

 

Six weeks is not quite half of the 13-week quarter length, so if desired one could make the mid-quarter day the earliest date of the equinox or solstice.  Such an approach might eliminate the concern that the equinox or solstice wobble is conspicuous. 13-week quarters would produce their own wobble of +-2 or +-3 owing to variation of the astronomical quarters in different times of the year. This would be in addition to the +-3 wobble mentioned .

 

Karl

 

10(09(23

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[Irv Bromberg]

On 2009 Jun 15, at 09:14 , Palmen, KEV (Karl) wrote:

Irv Bromberg wrote:  Six weeks is not quite half of the 13-week quarter length, so if desired one could make the mid-quarter day the earliest date of the equinox or solstice.

Such an approach might eliminate the concern that the equinox or solstice wobble is conspicuous.

Karl wrote:  13-week quarters would produce their own wobble of +-2 or +-3 owing to variation of the astronomical quarters in different times of the year. This would be in addition to the +-3 wobble mentioned.

Irv replies:  That is true if one is attempting to align all 4 equinoxes and solstices, but that is impossible.  If one of them is aligned such that the earliest date falls at the mid-quarter day, then none of the others will align the same way, due to the unequal lengths of the seasons, and their variations.  I was referring specifically to aligning either the earliest northward equinox to fall at the first mid-quarter day, or the earliest north solstice to fall at the second mid-quarter day, but not both, and one cannot pay any attention to the southward equinox or south solstice because their mean years are getting progressively shorter in the present era and for many millennia into the future.  The correlation of the next thermal season with the next calendar quarter will be good, but the thermal correlation of the other seasons will vary with the season lengths.  This shows the futility of attempting to make a seasonal calendar.

For a leap week calendar, the wobble range ought to span slightly less than 7-days, where either the northward equinox or the north solstice falls on the mid-quarter day or up to 6 days later.  There may be slightly more wobble than that depending on how closely the selected leap cycle approximates the mean northward equinoctial or mean north solstitial year, as appropriate, and there is a small amount of astronomical year-to-year variations of about ±15 minutes in the astronomical lengths of those years, which will slightly extend the wobble range.

For a calendar with smoothly spread leap intervals, the wobble range is smaller than the length of the leap unit by a factor of X/C, where X is the number of days added to a leap year, and C is the number of years per leap cycle.  So for the case of the 293-year leap week calendar approximating the northward equinox, the wobble range is 7/293 of a day = 34 minutes and 24+48/293 seconds less than 7 days, so even with the addition of the astronomical variations the wobble range would be less than 7 days.  For a 389-year leap week calendar approximating the north solstice, the wobble range is 7/389 of a day = 25 minutes and 54+294/389 seconds less than 7 days, which is only a few minutes too small to include the astronomical variation range.

One could employ an average solar year length for the leap cycle, progressively shorter over the long term in parallel with the tidal slowing of the Earth rotation rate, for example using my Mean Orbital Year (MOY) or Rotation-Adjusted Year (RAY) arithmetic, or more simply a fixed cycle of 365+31/128 atomic days with Delta T subtracted to convert to mean solar days.  In such a case the wobble range of any average equinox equinox moment will vary about ±4 days relative to the long-term average, and if it is a leap week calendar then the ±3.5-day wobble due to the leap rule will add to that, generating ±7.5 days of wobble over the long term, for any equinox or solstice.  In such a case it would no longer be meaningful to align the mid-quarter day with an earliest equinox or solstice.  The long-term averages could be aligned with either the start of calendar quarters or the middle of calendar quarters, but with a ±7.5 = 15 days wobble range the seasonal relationship would not be impressive.  On the other hand, lunisolar calendars have been and continue to be widely use, with a 30-day seasonal wobble range that nevertheless has been culturally acceptable for millennia.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

[Karl Palmen]

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Dear Irv, Mike, Victor and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 15 June 2009 15:42
To: CALNDR-L@...
Subject: Re: Brief seasonal calendar position summary

 

On 2009 Jun 15, at 09:14 , Palmen, KEV (Karl) wrote:

Irv Bromberg wrote:  Six weeks is not quite half of the 13-week quarter length, so if desired one could make the mid-quarter day the earliest date of the equinox or solstice.

Such an approach might eliminate the concern that the equinox or solstice wobble is conspicuous.

Karl wrote:  13-week quarters would produce their own wobble of +-2 or +-3 owing to variation of the astronomical quarters in different times of the year. This would be in addition to the +-3 wobble mentioned.

 

Irv replies:  That is true if one is attempting to align all 4 equinoxes and solstices, but that is impossible.  If one of them is aligned such that the earliest date falls at the mid-quarter day, then none of the others will align the same way, due to the unequal lengths of the seasons, and their variations

 

Karl replies: One idea I’ve had is to have all the solstices and equinoxes occur in the same week each year in weeks 13 weeks apart. This cannot be done with a fixed 7-day week, but with a solar week  defined to occasionally extend so  there are exactly 52 weeks into each year (of 365 or 366 days). This is the basic idea behind the Rainbow Alphabet Calendar http://www.hermetic.ch/cal_stud/palmen/rainbow.htm#abc . Here the Solstices occur in Rainbow weeks z and Z, while the solstices occur in Rainbow weeks m an M and the Rainbow week as a solar week as previously defined.

 

Irv could investigate leap year rules that would give a good fit for a Rainbow Alphabet calendar.

 

Karl

 

10(09(23

 

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[MIKE OSSIPOFF]

 
 
Dear Calendarists,
 
Irv wrote:
 

> A pretty good seasonal correlation for mid-latitudes where there is about 6-week lag between equinox or solstice and thermal season ...
 
I comment:
 
Nearly everywhere in the north and south temperate zones--nearly every inhaibited (non-arctic) place outside the astronomically-defined tropics, the seasonal timelag varies between about .75 month and 1.75 month. So 1.25 month is a good average value, and is only off by up to .5 month, or about two weeks, in those places. That's borne out by temperature records in Scandinavia, Russia, West Europe, U.S., Canada, China, and Australia.
 
I've seen estimates that the variation is between 1 month and 1.5 month, but temperature records show it to be more like .75 to 1.75
 
By the way, the media's usual equal "seasons" beginning on solstices & equinoxes imply a time-lag of 1.5 months. That's a little long, but the worst problem of those "seasons" is that they start three weeks later than we all perceive the beginning of summer and winter.
 
Irv continued:
 
...could be obtained by arranging the mean northward equinox to fall on average at the winter mid-quarter day, or the mean north solstice to fall on average at the spring mid-quarter day.
 
I comment:
 
That would imply a seasonal timelag of about 3 months, if the middle of calendar winter coincides with the northward equinox.
 
It would also mean that the calendar "summer" would start about 1.5 months before the autumnal equinox, at somewhere around August 6th. As I said, people perceive north-temperate summer to begin with the month of June.
 
Irv continued:
 
This would then cause the thermal spring season to correlate with the spring quarter, or the thermal summer season to correlate with the summer quarter, respectively.
 
I reply:
 
I disagree. You've made an error.
 
Irv continued:

> At tropical latitudes the seasonal lag is shorter and the thermal changes not so apparent, so any such seasonal calendar will seem irrelevant to people living in the tropics.

I reply:
 
It's ok if it isn't relevant everywhere. It's relevant and useful throughout nearly the entire north and south temperate zones. Where it isn't relevant, its irrelevance is harmless.
 
At the equator, the temperature records didn't show a predictable relation between temperatures or rainfall and equinoxes or solstices, or at least I didn't find one.
 
In the tropics, but away from the equator, the time of lowest temperature or rainfall did tend to lag the winter solstice by the expected amount. But usually I didn't find that relation between the time of hightest rainfall or temperature and the summer solstice.
 
But, one thing about the tropics: I don't remember if it was the Brittanica or a climate reference book that said that the intertropical convergence zone (ITCZ) is in the high latitude part of its range June-September, and in the low latitude part of its range December-March. That's about the same as the North and South seasons of the Subjective Seasonal Calendar.
 
Mike Ossipoff
 
>
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[MIKE OSSIPOFF]

 
 
I'd said:
 
"In the tropics, but away from the equator, the time of lowest temperature or rainfall did tend to lag the winter solstice by the expected amount. But usually I didn't find that relation between the time of hightest rainfall or temperature and the summer solstice"
 
I meant instead to say: "...But usually I didn't find that relation between the time of highest rainfall or temperature and the time when dec = lat."
 
Mike Ossipoff
 

 
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[MIKE OSSIPOFF]

 
To summarize my reply to Irv's posting: No season-system consisting of four equal seasons can even come close to matching the seasons that we perceive, and that we speak of when we say "summer" or "winter". Not the media's equal seasons starting on the solstices & equinoxes. Not the system where the middle of each equal quarter coincides with a solstice or equinox. Not any other equal-season system either.
 
Mike Ossipoff
 
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[MIKE OSSIPOFF]

 
Dear Karl, Yiping and Calendar People,
 
As Karl and Yiping suggested, a calendar based on solar declination, and not attempting to match the terrestrial thermal seasons, would still be useful for those terrestrial seasons, because people could take into account the seasonal lag in their own local region.
 
I just want a little more than that. So I add a timelag of 1.25 months, so nearly all north and south temperate timelags will only differ by up to .5 month from that of the calendar. That just means that, in those places, people won't have to correct as much for their timelag.
 
But a calendar based on equal astronomical quarters would be difficult to relate to terrestrial seasons, which, as we all perceive them, are _not_ equal.
 
And, if you start calendar Summer when the sun's ecliptic longitude is 45 degrees, with the middle of calendar Summer at the summer solstice, then you're assuming that there's no seasonal timelag, when actually, in the north and south temperate regions, that lag averages 1.25 months.
 
Mike Ossipoff
 
 
 
 
 
 
 
 
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[Irv Bromberg]

On 2009 Jun 15, at 19:18 , MIKE OSSIPOFF wrote:

I disagree. You've made an error.

Irv replies:  I rechecked what I wrote, it is OK.  Try re-reading it.

I was assuming at least a 6 week lag because that's what we get here in Canada.  Placing the mid-quarter day at the earliest northward equinox or the earliest north solstice has the effect of reducing the average from 6.5 weeks to 6 weeks prior to the thermal season.  If the northward equinox is at the winter mid-quarter day then the thermal spring season will start about 6 weeks later at the start of the spring quarter.  If the north solstice is at the spring mid-quarter day then the thermal summer season will start about 6 weeks later at the start of the summer quarter.  This is all good, except that the figures Mike presented implied that the seasonal lag we see in Canada may be exceptionally long compared to global patterns.  If one is determined to shorten the lag to 5 weeks, then the mid-quarter day concept can be tossed and a having the earliest equinox or solstice fall 5.5 weeks prior to the start of the quarter might be more appropriate globally.  Hmm, that's 38+1/2 days, perhaps an even 40 days instead?

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>