Dear Calendar People
I've recently thought of a zodiac calendar simple for users of the Gregorian calendar. The months have the same length as in the Solar Hijri Calendar, but the leap year rule is such that each month begins on the same Gregorian date every year and the months take their names from the signs of the Western zodiac. The month begin thus: Aries: Mar 21 (Mar 21) Taurus: Apr 21 (Apr 20) Gemini May 22 (May 21) Cancer Jun 22 (Jun 22) Leo Jul 23 (Jul 23) Virgo Aug 23 (Aug 23) Libra Sep 23 (Sep 23) Scorpio Oct 23 (Oct 24) Sagittarius Nov 22 (Nov 22) Capricorn Dec 22 (Dec 22) Aquarius Jan 21 (Jan 20) Pisces Feb 20 (Feb 19) The dates in () are the start dates according to the Encyclopaedia Britannica. https://www.britannica.com/topic/zodiac The first 6 months have 31 days and the remaining 6 months have 30 days in a leap year. In a common year, Pisces has 29 days. Karl Wednesday Delta February 2019

Karl said:
> I've recently thought of a zodiac calendar simple for users of the > Gregorian calendar. The months have the same length as in the Solar > Hijri Calendar, but the leap year rule is such that each month begins > on the same Gregorian date every year and the months take their names > from the signs of the Western zodiac. > The month begin thus: > Aries: Mar 21 (Mar 21) > Taurus: Apr 21 (Apr 20) > ... > Pisces Feb 20 (Feb 19) The dates in () are the start dates according > to the Encyclopaedia Britannica. > https://www.britannica.com/topic/zodiac So this is a rulebased calendar which depends upon the Gregorian Calendar. It could also be described as the Solar Hijri Calendar (a.k.a. the Modern Iranian Calendar) with the names of the months replaced by the names of the Zodiac divisions, which would certainly make this (superior) calendar more acceptable to a Western audience. The leap year rule is that of the Solar Hijri Calendar, involving a cycle of 33 months. If the observationbased Persian Calendar (from which the modern Iranian calendar is derived) were to be used instead then there arises the problem of determining which years are leap years. This is discussed at https://www.projectpluto.com/calendar.htm#jalali Regards, Peter 
In reply to this post by k.palmen@btinternet.com
Dear Karl:
I have given some thought to this matter. There is already a seasonal calendar linked to the Gregorian Calendar: the Indian National Civil Calendar.
I have been thinking of a pure sidereal calendar that uses the zodiac names for months. I would start the calendar with Sagittarius on the south solstice, which is also currently and conveniently the point of the galactic center. Sagittarius A* would be the 0 point of the sidereal ecliptic.
Walter Ziobro
Original Message
From: K PALMEN <[hidden email]> To: CALNDRL <[hidden email]> Sent: Wed, Feb 20, 2019 5:56 am Subject: Simple Zodiac Calendar Dear Calendar People
I've recently thought of a zodiac calendar simple for users of the Gregorian calendar. The months have the same length as in the Solar Hijri Calendar, but the leap year rule is such that each month begins on the same Gregorian date every year and the months take their names from the signs of the Western zodiac.
The month begin thus:
Aries: Mar 21 (Mar 21)
Taurus: Apr 21 (Apr 20)
Gemini May 22 (May 21)
Cancer Jun 22 (Jun 22)
Leo Jul 23 (Jul 23)
Virgo Aug 23 (Aug 23)
Libra Sep 23 (Sep 23)
Scorpio Oct 23 (Oct 24)
Sagittarius Nov 22 (Nov 22)
Capricorn Dec 22 (Dec 22)
Aquarius Jan 21 (Jan 20)
Pisces Feb 20 (Feb 19)
The dates in () are the start dates according to the Encyclopaedia Britannica.
https://www.britannica.com/topic/zodiac
The first 6 months have 31 days and the remaining 6 months have 30 days in a leap year. In a common year, Pisces has 29 days.
Karl
Wednesday Delta February 2019

Dear Karl, Walter, Peter Walter's suggestion is very close to the Mayan zodiac alignment, where the last day of the Scorpius constellation marks the last day of the zodiac as the sidereal period origin, with days aligned at sunset day'sending with an elapsed time perspective instead
of Gregorian's day'sstart alignment with a current time perspective. This is a 364d calendar with 13 constellations, and a sidereal period origin at the Scorpius ecliptic crossing is most convenient. Due to precession this sidereal orbital origin progresses
forward through the year over time at the rate of ~71y per 1d. A 364d zodiac where the 7th constellation is bisected by the Gemini ecliptic crossing could be modified by adding an extra day to "thicken" the Gemini ecliptic crossing for a 365d calendar. I sometimes
use such a 13 constellation calendar, where each constellation is shortened slightly to make room for the new 7th GeminiOrion (or TauGemOrion) constellation, flanked by West Taurus to the west and East Gemini to the east  all other constellation names
stay the same, except each is shortened to ~27.69 deg. To do computations using modulo arithmetic one needs the constellations to be the same size.
Currently the last day of the zodiac is at the Scorpius galactic equator at Dec 20 (winter solstice conjunction). For relative interval excursions a fractional sidereal year > 0.5y relative to the interval's root, the fractional days would be rounded upwards
past fractional tropical year, due to the added Earth rotation annually (i.e. 365 solar days is actually 366 Earth rotations). Computations are simplified if it is assumed an integral tropical year is also an integral sidereal year  i.e. added annual Earth
rotation impacts only the final fractional year residual portion. Any differences will simply appear in a separate precession estimate.
But then again, most might prefer a 12 constellation arrangement. Cheers Cliff
On 2/20/2019 8:50 AM, Walter J Ziobro wrote:
Dear Karl: 
In reply to this post by k.palmen@btinternet.com
Clifford Emeric said:
> Due to precession this sidereal orbital origin progresses forward > through the year over time at the rate of ~71y per 1d. So if unchecked then the start of the year would diverge from the seasonal year by approximately one day every 70 years or so (since a seasonal year is approximately 365 days). Then the calendar dates of the equinoxes and solstices would shift by about 10 days in every 700 years or so. Would the 'corrections' or 'adjustments' that Cliff discusses in the rest of his post have the effect of keeping the calendar year aligned with the seasons? > But then again, most might prefer a 12 constellation arrangement > [rather than 13 constellations]. So that each season (spring, summer, etc.) would have exactly 3 'months'/'constellations'? Regards, Peter 
In reply to this post by Walter J Ziobro
Dear Walter and Calendar People
That thought occurred to me. The months of the Indian National Calendar https://en.wikipedia.org/wiki/Indian_national_calendar begin on the same days, except the first month Chaitra (Aries), which begins a day later in a common year. So the day that is removed from a leap year to form a common year is delayed one month. It loses the advantage of having a leap day at the end of the year. Leap years in the Simple Zodiac Calendar occur one year earlier than in the Indian National Calendar. The issue for year numbering was not addressed. If the Gregorian leap year rule were to be applied to the year number, this year's number would have remainder 19 when divided by 400 and the number of next year, which begins next month has remainder of 20 when divided by 400. Karl Thursday Delta February 2019 2 Pisces
Original message 
In reply to this post by k.palmen@btinternet.com
Dear Clifford et al Sagittarius A* is very close to the boundary between Scorpio and Sagittarius, and so IMO makes a very good starting point for defining asidereal ecliptic. All the other zodiac constellations can pretty much fit into 30 degree segments from that point Walter Ziobro On Wednesday, February 20, 2019 clifford emeric <[hidden email]> wrote: Dear Karl, Walter, Peter Walter's suggestion is very close to the Mayan zodiac alignment, where the last day of the Scorpius constellation marks the last day of the zodiac as the sidereal period origin, with days aligned at sunset day'sending with an elapsed time perspective instead
of Gregorian's day'sstart alignment with a current time perspective. This is a 364d calendar with 13 constellations, and a sidereal period origin at the Scorpius ecliptic crossing is most convenient. Due to precession this sidereal orbital origin progresses
forward through the year over time at the rate of ~71y per 1d. A 364d zodiac where the 7th constellation is bisected by the Gemini ecliptic crossing could be modified by adding an extra day to "thicken" the Gemini ecliptic crossing for a 365d calendar. I sometimes
use such a 13 constellation calendar, where each constellation is shortened slightly to make room for the new 7th GeminiOrion (or TauGemOrion) constellation, flanked by West Taurus to the west and East Gemini to the east  all other constellation names
stay the same, except each is shortened to ~27.69 deg. To do computations using modulo arithmetic one needs the constellations to be the same size.
Currently the last day of the zodiac is at the Scorpius galactic equator at Dec 20 (winter solstice conjunction). For relative interval excursions a fractional sidereal year > 0.5y relative to the interval's root, the fractional days would be rounded upwards
past fractional tropical year, due to the added Earth rotation annually (i.e. 365 solar days is actually 366 Earth rotations). Computations are simplified if it is assumed an integral tropical year is also an integral sidereal year  i.e. added annual Earth
rotation impacts only the final fractional year residual portion. Any differences will simply appear in a separate precession estimate.
But then again, most might prefer a 12 constellation arrangement. Cheers Cliff
On 2/20/2019 8:50 AM, Walter J Ziobro wrote:
Dear Karl: 
In reply to this post by Peter Meyer
Dear Peter et al:
The position of Sagittarius A* was RA 17h 45m 40s at Epoch J2000. I have calculated this to be at the tropical ecliptic degree 267.4, which is 2.6 degrees from the south solstice. At the current rate of precession, I estimate that the south solstice will move to the same ecliptic longitude of Sagittarius A* around 21802190 CE/AD. (The beginning of the Age of Scorpio ;) )
I have come up with a leap year rule for a purely sidereal calendar: there need to be 153 leap days in 160 years, or 765 leap days in 800 years, 11 more than the Gregorian Calendar. This could be done by having a leap day every fourth year in 36, then a leap day in the 39th year, until after 4 cycles (156 years), one leap day is added in the 160th, and then the cycle repeats every 160 years.
Walter Ziobro.
Original Message
From: Peter Meyer <[hidden email]> To: CALNDRL <[hidden email]> Sent: Wed, Feb 20, 2019 10:32 pm Subject: Re: Simple Zodiac Calendar Clifford Emeric said:
> Due to precession this sidereal orbital origin progresses forward
> through the year over time at the rate of ~71y per 1d.
So if unchecked then the start of the year would diverge from the
seasonal year by approximately one day every 70 years or so (since a
seasonal year is approximately 365 days). Then the calendar dates of
the equinoxes and solstices would shift by about 10 days in every 700
years or so.
Would the 'corrections' or 'adjustments' that Cliff discusses in the
rest of his post have the effect of keeping the calendar year aligned
with the seasons?
> But then again, most might prefer a 12 constellation arrangement
> [rather than 13 constellations].
So that each season (spring, summer, etc.) would have exactly 3
'months'/'constellations'?
Regards,
Peter

Dear Peter et al:
Oops. Some of the numbers I posted were incorrect: actually, there would be 41 sidereal leap days in 160 years, or 205 in 800 years, which IS 11 more leap days than the Gregorian Calendar.
Walter Ziobro
Original Message
From: Walter J Ziobro <[hidden email]> To: pmcl <[hidden email]>; CALNDRL <[hidden email]> Sent: Thu, Feb 21, 2019 11:10 am Subject: Re: Simple Zodiac Calendar Dear Peter et al:
The position of Sagittarius A* was RA 17h 45m 40s at Epoch J2000. I have calculated this to be at the tropical ecliptic degree 267.4, which is 2.6 degrees from the south solstice. At the current rate of precession, I estimate that the south solstice will move to the same ecliptic longitude of Sagittarius A* around 21802190 CE/AD. (The beginning of the Age of Scorpio ;) )
I have come up with a leap year rule for a purely sidereal calendar: there need to be 153 leap days in 160 years, or 765 leap days in 800 years, 11 more than the Gregorian Calendar. This could be done by having a leap day every fourth year in 36, then a leap day in the 39th year, until after 4 cycles (156 years), one leap day is added in the 160th, and then the cycle repeats every 160 years.
Walter Ziobro.
Original Message
From: Peter Meyer <[hidden email]> To: CALNDRL <[hidden email]> Sent: Wed, Feb 20, 2019 10:32 pm Subject: Re: Simple Zodiac Calendar Clifford Emeric said:
> Due to precession this sidereal orbital origin progresses forward
> through the year over time at the rate of ~71y per 1d.
So if unchecked then the start of the year would diverge from the
seasonal year by approximately one day every 70 years or so (since a
seasonal year is approximately 365 days). Then the calendar dates of
the equinoxes and solstices would shift by about 10 days in every 700
years or so.
Would the 'corrections' or 'adjustments' that Cliff discusses in the
rest of his post have the effect of keeping the calendar year aligned
with the seasons?
> But then again, most might prefer a 12 constellation arrangement
> [rather than 13 constellations].
So that each season (spring, summer, etc.) would have exactly 3
'months'/'constellations'?
Regards,
Peter

In reply to this post by Peter Meyer
To All,
Of note in effect instead of having the vernal equinox as a tropical period origin regress against the background stars, the sidereal period origin now progresses forward through a tropical year calendar. If the Gregorian is important then perhaps what is needed is both a sidereal zodiac and a tropical calendar, where this divergence defines the offset relationship between the two. It allows easy conversion between the two. I doubt such an instrument would be of interest to people at large. Cliff On 2/20/2019 19:32 PM, Peter Meyer wrote: > Clifford Emeric said: > >> Due to precession this sidereal orbital origin progresses forward >> through the year over time at the rate of ~71y per 1d. > > So if unchecked then the start of the year would diverge from the > seasonal year by approximately one day every 70 years or so (since a > seasonal year is approximately 365 days). Then the calendar dates of > the equinoxes and solstices would shift by about 10 days in every 700 > years or so. > > Would the 'corrections' or 'adjustments' that Cliff discusses in the > rest of his post have the effect of keeping the calendar year aligned > with the seasons? > >> But then again, most might prefer a 12 constellation arrangement >> [rather than 13 constellations]. > > So that each season (spring, summer, etc.) would have exactly 3 > 'months'/'constellations'? > > Regards, > Peter 
In reply to this post by Walter J Ziobro
Hi All, For the purposes of computation (modulo style), would it not be preferable to unite the tropical and sidereal leap days in the formula: tropical residual  precession = sidereal residual. Instead of fixed leap days one keeps the calendar period fixed, and
then track tropical residual and precession. Leap days complicate protracted arithmetic because of variable calendric periods and calendar jitter. It is better to abandon leap days, and only use dynamic leap days on an as needed basis. Depends what purpose
this calendar is meant to serve. I have abandoned leap day adjustments and replaced them with long term divergence tracking of precession and tropical period residuals, rather than direct leap day adjustments  a.k.a. fixed 365d calendars Mayan style. Makes
computations really easy. As an astronomical instrument it serves its purpose, but as a commercial calendar it might be a disturbing experience. Not sure how a sidereal zodiac as a calendar will work if tropical stations cannot be easily derived from the calendar,
given tropical and sidereal stations divergence at different rates. Cheers Cliff On 2/21/2019 8:10 AM, Walter J Ziobro wrote:

Dear Clifford, Walter and Calendar People
The 800year cycle of 205 leap years fits nicely next to the Gregorian 400year cycle. The Sidereal calendar would have the same leap years as Gregorian except for years whose number ends in 00. Of these 5 out of 8 are leap years instead of 1 out of 4 in Gregorian calendar. For leap week calendars, the 39year cycle of 10 leap days and so 7 leap weeks could be used. Karl Friday Delta February 2019 3 Pisces
Original message 
In reply to this post by k.palmen@btinternet.com
Dear Clifford et al Admittedly a pure sidereal calendar is a bit of an academic exercise It might be of interest to astronomers, or even astrologists Some Southeast Asian countries have sidereal lunar calendars Walter Ziobro On Thursday, February 21, 2019 clifford emeric <[hidden email]> wrote: Hi All, For the purposes of computation (modulo style), would it not be preferable to unite the tropical and sidereal leap days in the formula: tropical residual  precession = sidereal residual. Instead of fixed leap days one keeps the calendar period fixed, and
then track tropical residual and precession. Leap days complicate protracted arithmetic because of variable calendric periods and calendar jitter. It is better to abandon leap days, and only use dynamic leap days on an as needed basis. Depends what purpose
this calendar is meant to serve. I have abandoned leap day adjustments and replaced them with long term divergence tracking of precession and tropical period residuals, rather than direct leap day adjustments  a.k.a. fixed 365d calendars Mayan style. Makes
computations really easy. As an astronomical instrument it serves its purpose, but as a commercial calendar it might be a disturbing experience. Not sure how a sidereal zodiac as a calendar will work if tropical stations cannot be easily derived from the calendar,
given tropical and sidereal stations divergence at different rates. Cheers Cliff On 2/21/2019 8:10 AM, Walter J Ziobro wrote:

Walter, Cliff, Karl sirs:
>...pure sidereal calendar is a bit of an >academic exercise It might be of interest to >astronomers, ....
I recall having discussed my idea of “humans NEVER used a caldndar, using the duration of a ‘Sidereal day’. While doing my calculations, it occurred to me of using such
a duration; since Year’s duration =365.242189669781 solar days and duration of ‘Sidereal days’ during this period=365.2421897943 Sidereal days. These results were projected in my published document in Standards India (1992) and also reported during my
discussions with CalndrL. Format of this is reproduced above.
While I agree that such a duration may not be useful (considering the amount of expense & tabulation required), I switched to my latest thought of shifting July 31 to 2nd month as February 29 (all years) on shifting the Leap Day (or Leap Week, If introduced)
to between June 30& July 01; along with my 2*(448years/5541 Lunation) cycle on adding a slight EXTRA DURATION, needed for aligning “Solar Years & Lunar Moons” as:
resulting in current duration of Tropical Year and Lunar period of 29.5 Tithi to get Mean Lunation=29d12h44m2s.877470166923227.This is a slightly improved period over my previous result (discounting the extra duration between my Mean Year= 365.2421875 days & the actual Astronomer’s Average YEAR= 365.242189669781
days. Calculations are placed above.
This, surely, is not only as academic exercise BUT a serious proposal as discussed with the group, however within my limits as a nonastronomy engineer  bumped into strange land.
Regards,
Flt Lt Brij Bhushan VIJ (Retd.), IAF
FRIDAY, 2019 February 22H15:28(decimal)
Sent from my iPhone

Hi Brij and calendar people, On Sat, Feb 23, 2019 at 12:18 AM Brij Bhushan metric VIJ <[hidden email]> wrote:
This begs the questions: Which year? Which lunation? These figures are precise down to 10^12 day (about 10^7 sec) for year's length, and 10^15 seconds for lunation's length. But precision is not the same as accuracy! There is no such thing as THE year's length of THE lunation length. Beside the fact that each year and lunation is slightly different (and its length depends on how it's measured), according to the formulas of Meeuse average tropical years over the 21st century will be 1215 seconds shorter than over the 20th century, and average lunations will be 68 second shorter (measured in tropical days). This means that the least significant digits of the precision used by Brij become meaningless within 26 seconds for the cited year length, and within 45 nanoseconds for the cited length of a lunation!  Amos Shapir

Amos, cc sirs:
>..... Year’s duration =365.242189669781 solar days and duration of ‘Sidereal days’ during this period=365.2421897943 >Sidereal days.
My apology for ‘typographic mistake’. This was corrected to read: “.. Year’s duration =365.242189669781 solar days and duration of ‘Sidereal days’ during this period=366.242198943 Sidereal days.”
The point intended was that: MAN HAD NEVER TRIED USING SIDEREAL DAY duration to construct the Tropical year; and the calculation I did c.1990 corrected...
Attempts have been to calculations arriving to ‘newer accuracy’; and you rightly observed these, compared to most modern values for Astronomers’ Average Mean Year & Astronomically used Mean Lunation, I used in relation to my developed {2*448years/ 5541 moons} in my 896year cycle. Thanks & regards;
Flt Lt Brij Bhushan VIJ (Retd.), IAF
Monday, 2019 February 25H02:69(decimal)
Sent from my iPhone

In reply to this post by Amos Shapir2
To Amos, Brij and others Absolutely there must be a well defined Epoch from tropical, sidereal and lunar prerequisites  hence an astronomical referent is necessary as a basis for the measurements  or at least for defining an absolute starting reference. Amos forget to mention
that dates are integer based, and hence by definition computations would always be rounded to the closest integer date. It is not just about letting a calendar freerun autonomously, but also temporal calculations are relevant. You cannot force the Earth to
follow your level of precision, but you can find a way to adhere to an average sidereal, tropical year or lunar month, in which case a much lower level precision is used anyway during rounding of results. 6 decimal places suffices with the understanding all
intervals are average and not absolute representations. Further a zodiac is only used for short term (1 year or so) representations of ecliptic segments, and thus the zodiac is not the same thing as the underlying long term sidereal calendar. Certainly zodiac
leap days make no sense at all. However the formula "tropical azimuth  precession = sidereal azimuth" serves for computations in relating the two. All these elements preempt simple year length constant estimates, when we should be talking about the
practical aspects of ( a) an absolute Epoch and (b) long term precession effects and how to make this overtly visible in the sidereal calendar  rounded of course to the nearest zodiac ecliptic segment (date). A sidereal calendar's Epoch and current divergence
from that Epoch is marked in the sidereal calendar itself. This preempts considerations of just how long any given year really ought to be. If I am 50d from the calendar's defined Epoch then I am in the region of 50*70.5 = 3525y from that Epoch give or take
35 years, and hence I would be forced to incorporate a lunar component into the Epoch, to narrow this down to 1d. Precession is easily observed if one is not looking at the vernal equinox, but rather looking at the sun when it coincides with Scorpius ecliptic
crossing at sunset, where the constellation's dust clouds offers all manner of patterns for making measurements. It is not possible to talk about a sidereal calendar in terms of year lengths to 12 digit precision, when precession is the primary matter of concern
 to wit: how does it align to the tropical azimuths. A standalone pure sidereal calendar makes no sense to me.
The Elephant in the Room 365d solar days is the subject of an added Earth rotation annually for a 366d sidereal year and this offers an arithmetical simplification, which allows us to eliminate the 366d calendar period as a candidate (we are not counting earth rotations). In other
words, a whole (integer) earth rotation means solar and sidereal ecliptic orientation are approximately equal (both pointing at the same ecliptic position), and hence the 366d sidereal year is unnecessary as the sidereal year can be characterized using the
365d period. That is is say, if one peels off integral tropical years from a protracted interval of time, then one can assume that this is also an integral number of sidereal years, and that is the whole point of the precession formula above, as after peeling
of integral years one is left with just a fractional year remainder  and it is this remainder that the formula applies to which yields a fractional year ecliptic segment relationship. Now given each sidereal day is 3'56" less than a solar day then as this
remainder gets larger, then that added annual earth rotation is further advanced forward and after the fractional year remainder exceeds half year, then sidereal residual will be rounded beyond the tropical year (i.e. fractional day portion only). This is
only important as regards the zodiac which only applies in context to the current year. In other words, there is another formula associated with a broader interval, where tropical year is also characterized using the 365d period, with "365d calendar remainder
 leap days = tropical year remainder". So the annual earth rotation's impact is limited to a rounded sidereal remainder that might be rounded up an additional day for purposes of position in the zodiac, but over long intervals the relationship between
365d and tropical years is a separate portion of the peeled off integral years. The precession and leap day formulae are similar in purpose. Precession is tracked separately as offset factor. Leap days could be tracked separately as an offset factor.
Now we have a choice why not a 364d zodiac? The same arithmetical simplification is possible where 364d solar days approximates 365 sidereal days, and again a 365d period may be used to characterize a 364d zodiac. In other words, one can assume integral
tropical years peeled off a protracted interval will also be an integral sidereal interval as above, as any deviation from this assumption will simply emerge in the precession offset estimate. And any resulting remainder is the only portion which will be impacted
by the position of the added annual earth rotation, which will impact sidereal rounding decisions for purposes of the 364d zodiac (no more than a 1d difference). The size of that remainder is dealt with as a separate current fractional year remainder portion.
Looks like our choice comes down to BOTH. We can have both a 364d zodiac and a 365d solar calendar representing "1 average year", as any difference between the two over long intervals of time only comes down to a final fractional year component to be represented
within the 365d and 364d calendar as regards current position of the added annual earth rotation. I believe 364d standalone sidereal calendars are not required. I also believe a 365d zodiac is not necessary, as these two base periods can be combined processed
simply using the 365d period, and the solar calendar and sidereal zodiac may be combined also with the 365d period. This also shows a 365d zodiac per se is not necessary either.
SUMMARY A sidereal calendar is not about accurate sidereal year precision to 12 decimal places, but a more practical aspect that involves an intimate relationship with the tropical calendar  hence the formula: "Tropical remainder  precession = Sidereal remainder".
Therefore tropical year estimate is just as important as sidereal year estimate, and precession rate is NOT A CONSTANT either. These considerations all involve rounding decisions as the final result. Of course there is one more choice involving that other
formula: "365d calendar remainder  leap days = Tropical remainder", to directly apply leap days to the calendar or deal with them separately computationally as well. Leap day divergence is just another factor similar to precession. if you opt to adjust
the calendar with leap days then you have the problem of calendar jitter due to uneven distribution of leap days. If you opt to not adjust the calendar directly, but only use leap days in computations then you eliminate the jitter. Just like the precession
measurement estimate, one could have a modulo (365) leap day measurement incorporated into the calendar and avoid direct leap day adjustments. The problem with tropical leap days here is one is then left with a companion sidereal leap day factor that is different
due to the precession formula above  that is way to complicated. In conclusion it is the calendar's purpose which dictates structure, and combining tropical and sidereal calendars reduces the matter to mean year estimates, rather than absolute fixed constant year estimates given to 12 digit precision. If one is to have
both a sidereal calendar and a representative zodiac (one long term the other short term), then the added annual earth rotation is an important factor here. I have shown you can ignore the 366d sidereal year period, and it is not necessary to insist only on
a 364d or 365d choice  one can have both and treat them both computationally as a simple 365d characterization over protracted intervals. A true sidereal calendar that uses a specific astronomical event to define sidereal year is impacted directly by counting
earth rotations, where 365 earth rotations will be viewed as 364d solar days, and combining a tropical calendar is potentially more problematic as one now has both sidereal and tropical leap days. An explicit 364d sidereal year with intercalations of various
kinds tends to complicate everything without necessarily any added benefit (except it eliminates precession offset).
So are we talking about a combined tropical and sidereal calendar or just a standalone sidereal calendar? Or simpler yet a 364d zodiac with no leap days, emulating the the combined tropical and sidereal calendar. Adding Gregorian leap days to a 365d tropical
zodiac is by all accounts not a sidereal calendar at all, but only an exotic tropical calendar that does not need a sidereal period origin Epoch  a calendar with 365 ecliptic gradations instead of 360 degree gradations (i.e. a Gregorian with different month
names). A pure tropical calendar representation alone I believe would be a waste of time, as would a pure sidereal calendar alone. If one is to have a zodiac then it should be a sidereal zodiac and not a tropical zodiac! We need practical elements to enter the discussion
of calendar design. I favor keeping both precession offset and leap day offset as separate from the pure 365d calendar with fixed base period. A very uncomfortable prospect for the Eurocentric mind.
Cheers Cliff
On 2/25/2019 0:49 AM, Amos Shapir wrote:
hin 26 seconds for the cited year length, and within 45 nanoseconds for the cited length of a lunatio 
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