Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

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Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Karl Palmen

Dear Irv, Michael and Calendar People

 

I make a reply below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 09 January 2017 03:59
To: [hidden email]
Subject: Re: New Henry-Hanke calendar/website, old shortcomings

 

 

 

On Sun, Jan 8, 2017 at 6:40 PM, Irv Bromberg <[hidden email]> wrote:

From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Michael Ossipoff [[hidden email]]

Sent: Sunday, January 08, 2017 17:25

 

I'd said:
 

 

But my main point was that year-round accuracy is more practical, and probably better for public acceptability, rather than calendar-stability about one particular ecliptic point.

 

...and that using the mean of the March & September equinoxes doesn't result in serious displacements over the long cycle of back-&-forth tropical-year-length drift.

Bromberg replies:

With regard to what Ossipoff is calling "year-round accuracy", note that I've been there, done that

 

That's great. Why you aren't still there, and are now doing something else, is your business, and none of my business.

Suit yourself.

immune to this drift because it explicitly uses the contemporaneously most accurate Delta T adjustment.


Even though I developed MOY and RAY, I don't particularly promote them, because I became convinced that it is better to use a simple fixed arithmetic leap rule to approximate the mean north solstitial year or the mean northward equinoctial year. Note also that when I detailed them in this CALNDR LISTSERV, they were met by severe criticism, which is why I practically abandoned them -- so I'm surprised that the same critics haven't been blasting you with similar remarks. Possibly it is because my description was very detailed, but yours has been consistently vague?

 

KARL REPLIES: What Michael has proposed is a simple arithmetic rule that approximates the mean tropical year and runs for about a 1000 years, then is changed to another such arithmetic rule determined by astronomical observations made that time. I have criticised this for the frequency of changes of the arithmetic rule. I’d suggest fewer changes and each change is to a calendar mean year (Y) that is less than the mean tropical year of the time and will become more than the mean tropical year before the next change. Also I’d prefer a simple mean calendar year (Y) with either few decimal places or small denominator rather than one that is very near to the tropical year of a specified ecliptic longitude. The less frequent changes could reduce the year round accuracy by a day or two, but this is of little importance for a leap week calendar.

 

Karl

 

16(05(13

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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Michael Ossipoff

On Tue, Jan 10, 2017 at 8:17 AM, Karl Palmen <[hidden email]> wrote:

 

KARL REPLIES: What Michael has proposed is a simple arithmetic rule that approximates the mean tropical year and runs for about a 1000 years, then is changed to another such arithmetic rule determined by astronomical observations made that time.


... whenever it unacceptably displaces the calendar (by maybe 40% of a day?)

 

I have criticised this for the frequency of changes of the arithmetic rule. I’d suggest fewer changes and each change is to a calendar mean year (Y) that is less than the mean tropical year of the time and will become more than the mean tropical year before the next change.


Yes that would allow less frequent changes, if you're interested in calendar-accuracy at one particular time of year. But all of the year is important. It would result in larger maximum calendar displacements around the year.   ...when  the length of a particular equinox year or solstice year (instead of the length of the MTY or the mean of the two equinox-years) is chosen as the value of Y.


 Also I’d prefer a simple mean calendar year (Y) with either few decimal places or small denominator rather than one that is very near to the tropical year of a specified ecliptic longitude.


If it's close to the length of the MTY (about 365.24219?) or the mean of the two equinox years' lengths, then it won't have to be changed as often, to keep the maximum displacement during the year below some desired limit.



The less frequent changes could reduce the year round accuracy by a day or two, but this is of little importance for a leap week calendar.

Use a Y with a shorter decimal fraction than that of 365.24219? What's the advantage of that shorter fraction?

Michael Ossipoff

 

Karl

 

16(05(13


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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Karl Palmen
In reply to this post by Karl Palmen

Dear Michael, Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 10 January 2017 20:27
To: [hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 

 

On Tue, Jan 10, 2017 at 8:17 AM, Karl Palmen <[hidden email]> wrote:

 

KARL REPLIES: What Michael has proposed is a simple arithmetic rule that approximates the mean tropical year and runs for about a 1000 years, then is changed to another such arithmetic rule determined by astronomical observations made that time.

 

... whenever it unacceptably displaces the calendar (by maybe 40% of a day?)

KARL REPLIES: By definition the displacement of the calendar dates is greater than -0.5 week and no greater than +0.5 week. This remains so perpetually regardless of the value of Y.

What Michael means by displacement here must be something different and this different thing is not simple and I think it may be a major cause of the disagreements between Michael and Irv, which I summarised in the “Solar Calendar Accuracy” thread.

I think Michael needs to be clearer in what he is stating. He is overusing the word ‘displacement’ using it to mean different things. I see two types of ‘displacement’:

(1) Displacement used to define a minimum-displacement calendar

(2) Displacement representing a deviation of the calendar from some criterion of accuracy.

I’ve had some thoughts about the second kind of displacement, which I may explain them in a later note.

 

Also Irv criticised Michael for his phrase “"the mean of the March & September equinoxes",”, which is ambiguous. It could be the mean of the March equinox and September equinox times for a calendar year and this would be different for a calendar year beginning in July than a calendar year beginning in January. However a more careful use of wording would prevent such misunderstanding. For example:

The mean of the lengths of the March & September equinox tropical years.

If Michael needs to use this often, he could later abbreviate to say METY (mean equinox tropical year).

 

Also I think Irv is no longer aware that Michael is suggesting an arithmetic calendar and is writing about how this calendar would be modified in the future to keep it accurate. The reference year (such as MTY) is not actually part of the calendar, but is used in the selection of the mean year of the calendar when created or modified, but does not completely determine that mean year or when it is changed. If I’m wrong here, Michael has a lot of clarification to do.

 

I have criticised this for the frequency of changes of the arithmetic rule. I’d suggest fewer changes and each change is to a calendar mean year (Y) that is less than the mean tropical year of the time and will become more than the mean tropical year before the next change.

 

Yes that would allow less frequent changes, if you're interested in calendar-accuracy at one particular time of year. But all of the year is important. It would result in larger maximum calendar displacements around the year.   ...when  the length of a particular equinox year or solstice year (instead of the length of the MTY or the mean of the two equinox-years) is chosen as the value of Y.

KARL REPLIES: This is simply an implementation of the idea, that for a civil calendar, especially a leap week calendar, it is sufficient that the mean year lies within the range of tropical years. Which Michael agrees with in the thread about Solar Calendar accuracy.



 Also I’d prefer a simple mean calendar year (Y) with either few decimal places or small denominator rather than one that is very near to the tropical year of a specified ecliptic longitude.


If it's close to the length of the MTY (about 365.24219?) or the mean of the two equinox years' lengths, then it won't have to be changed as often, to keep the maximum displacement during the year below some desired limit.


The less frequent changes could reduce the year round accuracy by a day or two, but this is of little importance for a leap week calendar.

Use a Y with a shorter decimal fraction than that of 365.24219? What's the advantage of that shorter fraction?

KARL REPLIES: It is simpler and makes the arithmetic simpler.

I don’t see any need for such a long fraction, given that it will be used for just a 1000 years or so and also the 5th decimal place is less than a second per unit and even without taking account of slowdown of Earth’s rotation, the tropical year is getting less by around 5 seconds per millennium.

 

Michael Ossipoff

 

Karl

 

16(05(14

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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Walter J Ziobro
Dear Karl and Calendar List:

Perhaps what Michael means when he refers to
"the mean of the March & September equinoxes", is the average of the length of the tropical year for those two points.  According to the Wikipedia article on the Tropical Year,  Meeus and Savoie calculated each of those to be 365.242374 days for the northward equinox, and 365.242018 days for the southward equinox, both at epoch 2000.  The average of these would be 365.242196, which compares to the length of the mean tropical year of 365.242189 days at Epoch 2000.


-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Wed, Jan 11, 2017 8:07 am
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Dear Michael, Irv and Calendar People
 
From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Michael Ossipoff
Sent: 10 January 2017 20:27
To: CALNDR-[hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings
 
 
On Tue, Jan 10, 2017 at 8:17 AM, Karl Palmen <[hidden email]> wrote:
 
KARL REPLIES: What Michael has proposed is a simple arithmetic rule that approximates the mean tropical year and runs for about a 1000 years, then is changed to another such arithmetic rule determined by astronomical observations made that time.
 
... whenever it unacceptably displaces the calendar (by maybe 40% of a day?)
KARL REPLIES: By definition the displacement of the calendar dates is greater than -0.5 week and no greater than +0.5 week. This remains so perpetually regardless of the value of Y.
What Michael means by displacement here must be something different and this different thing is not simple and I think it may be a major cause of the disagreements between Michael and Irv, which I summarised in the “Solar Calendar Accuracy” thread.
I think Michael needs to be clearer in what he is stating. He is overusing the word ‘displacement’ using it to mean different things. I see two types of ‘displacement’:
(1) Displacement used to define a minimum-displacement calendar
(2) Displacement representing a deviation of the calendar from some criterion of accuracy.
I’ve had some thoughts about the second kind of displacement, which I may explain them in a later note.
 
Also Irv criticised Michael for his phrase “"the mean of the March & September equinoxes",”, which is ambiguous. It could be the mean of the March equinox and September equinox times for a calendar year and this would be different for a calendar year beginning in July than a calendar year beginning in January. However a more careful use of wording would prevent such misunderstanding. For example:
The mean of the lengths of the March & September equinox tropical years.
If Michael needs to use this often, he could later abbreviate to say METY (mean equinox tropical year).
 
Also I think Irv is no longer aware that Michael is suggesting an arithmetic calendar and is writing about how this calendar would be modified in the future to keep it accurate. The reference year (such as MTY) is not actually part of the calendar, but is used in the selection of the mean year of the calendar when created or modified, but does not completely determine that mean year or when it is changed. If I’m wrong here, Michael has a lot of clarification to do.
 
I have criticised this for the frequency of changes of the arithmetic rule. I’d suggest fewer changes and each change is to a calendar mean year (Y) that is less than the mean tropical year of the time and will become more than the mean tropical year before the next change.
 
Yes that would allow less frequent changes, if you're interested in calendar-accuracy at one particular time of year. But all of the year is important. It would result in larger maximum calendar displacements around the year.   ...when  the length of a particular equinox year or solstice year (instead of the length of the MTY or the mean of the two equinox-years) is chosen as the value of Y.
KARL REPLIES: This is simply an implementation of the idea, that for a civil calendar, especially a leap week calendar, it is sufficient that the mean year lies within the range of tropical years. Which Michael agrees with in the thread about Solar Calendar accuracy.


 Also I’d prefer a simple mean calendar year (Y) with either few decimal places or small denominator rather than one that is very near to the tropical year of a specified ecliptic longitude.


If it's close to the length of the MTY (about 365.24219?) or the mean of the two equinox years' lengths, then it won't have to be changed as often, to keep the maximum displacement during the year below some desired limit.

The less frequent changes could reduce the year round accuracy by a day or two, but this is of little importance for a leap week calendar.
Use a Y with a shorter decimal fraction than that of 365.24219? What's the advantage of that shorter fraction?
KARL REPLIES: It is simpler and makes the arithmetic simpler.
I don’t see any need for such a long fraction, given that it will be used for just a 1000 years or so and also the 5th decimal place is less than a second per unit and even without taking account of slowdown of Earth’s rotation, the tropical year is getting less by around 5 seconds per millennium.
 
Michael Ossipoff
 
Karl
 
16(05(14
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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Michael Ossipoff
In reply to this post by Karl Palmen





On Wed, Jan 11, 2017 at 8:07 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael, Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 10 January 2017 20:27
To: [hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 

 

On Tue, Jan 10, 2017 at 8:17 AM, Karl Palmen <[hidden email]> wrote:

 

KARL REPLIES: What Michael has proposed is a simple arithmetic rule that approximates the mean tropical year and runs for about a 1000 years, then is changed to another such arithmetic rule determined by astronomical observations made that time.

 

... whenever it unacceptably displaces the calendar (by maybe 40% of a day?)

KARL REPLIES: By definition the displacement of the calendar dates is greater than -0.5 week and no greater than +0.5 week.

You're referring to the definition of D, in my Minimum-Displacement leapyear-rule. But, when we discussed that before, I made it quite clear that D is calculated displacement, as distinct from actual displacement.

Of course, with a suitable value for Y, the actual displacement is kept low, in keeping with the name "Minimum-Displacement".

 

This remains so perpetually regardless of the value of Y.

What Michael means by displacement here must be something different

Something different from D? Of course, and I made that clear in discussion last summer at this forum. D is calculated displacement.

As for "what Michael means by displacement here", it's the same thing that I always meant by displacement. Here is how I've, from the start, defined displacement:

Spatial displacement is change or difference in spatial position.

Calendar displacement is change or difference in the relation between calendar date and solar ecliptic longitude.

But that isn't something new from me. Its what I was saying from the start.

The variable D,, in my Minimum-Displacement leapyear-rule,  is calculated displacement.
...a practical approximation in a simple arithmetic leapyear-rule.

 

and this different thing is not simple


My definition of it is simple & brief. That doesn't mean that complicated things can't be said about displacement. Schroedinger's equation and Maxwell's equations aren't complicated in comparison to the problems that come up in the application of them. The applications of those equations are where the complication comes in.

 

and I think it may be a major cause of the disagreements between Michael and Irv, which I summarised in the “Solar Calendar Accuracy” thread.

I think Michael needs to be clearer in what he is stating. He is overusing the word ‘displacement’ using it to mean different things.

No. I've used one, and only one, definition for displacement.  ...the definition stated above.

When we were discussing my Minimum-Displacement leapyear-rule last summer, I made it quite clear that the variable "D" is calculated displacement, a practical approximation for use in my leapyear-rule.
 

 

Also Irv criticised Michael for his phrase “"the mean of the March & September equinoxes",”, which is ambiguous.

I've often referred to a Y value that's the arithmetic mean of the March equinox year and the September equinox year. I'll check my earlier posts to find out if I actually said it in the abbreviated way that Irv quoted it. But, even if I sometimes said it in that overly-brief unclear way, the fact remains that I often said it fully & clearly.

I've suggested two values for Y:

1. The length of the MTY
2. The mean of the lengths of the March & September equinox years.

The purpose of #1 is to lower displacement all year, instead of just at some favored time of year.

The purpose of #2 is as follows:

The vernal equinox has gotten particularly great attention. For example, the Gregorian leapyear rule was intended to stabilize the calendar with respect to the (north) vernal equinox, to reduce the amount by which the vernal equinox's calendar-date varies.

The equinoxes are times when the solar declination is changing at its most rapid. So is the perceived season and the length of the day. The vernal equinox is regarded by all as a significant time.

Problem: Our vernal equinox is the Southern Hemisphere's autumnal equinox.

For international fairness, then, instead of using the length of the March equinox year as Y, it would be much better to use the mean of the lengths of the March & September equinoxes as Y.

Walter pointed out that that mean value is very close to the length of the MTY.

 

It could be the mean of the March equinox and September equinox times for a calendar year and this would be different for a calendar year beginning in July than a calendar year beginning in January. However a more careful use of wording would prevent such misunderstanding. For example:

The mean of the lengths of the March & September equinox tropical years.


If I said it that way, that was an isolated writing-error. Elsewhere I made it clear that I was referring to the mean of the lengths of the March & September Equinox years.
 

If Michael needs to use this often, he could later abbreviate to say METY (mean equinox tropical year).


Not later. I've already done that. I called it the MEY.
 

 

Also I think Irv is no longer aware that Michael is suggesting an arithmetic calendar and is writing about how this calendar would be modified in the future to keep it accurate. The reference year (such as MTY) is not actually part of the calendar, but is used in the selection of the mean year of the calendar

Yes.



 

when created or modified, but does not completely determine that mean year or when it is changed. If I’m wrong here, Michael has a lot of clarification to do.

I'm not entrely sure what you mean there. The value of Y is an approximation to the current length of the MTY (or, alternatively, it could be the MEY instead).

The finite-length decimal fraction in Y, of course, isn't exactly the same as the current length of the MTY or MEY. Additionally, those two year-lengths vary with time, whereas Y is a constant..

Michael Ossipoff
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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Karl Palmen

Dear Michael and Calendar People

 

Michael has produced two different definitions of displacement and has now given names to them.

 

The calculated displacement D, which is used in defining a minimum displacement calendar and

 

The actual displacement. This he defines as

 

Calendar displacement is change or difference in the relation between calendar date and solar ecliptic longitude.

This this is not simple. It involves the complex relationship between calendar date and solar ecliptic longitude! I have thought of a way through this complexity.

To be meaningful, an ideal relationship between calendar date and solar ecliptic longitude needs to be carefully chosen and defined.

 

Then the actual displacement of a solar ecliptic longitude in a given year is

Actual date of this solar ecliptic longitude minus the ideal date of this solar ecliptic longitude

This may be expressed as (date of) Actual Solar Ecliptic Longitude minus (date of) Ideal Solar Ecliptic Longitude (for a given solar ecliptic longitude value).

ASEL - ISEL

 

I haven’t seen any explicit definition of an ideal relationship between calendar date and solar ecliptic longitude for year round accuracy.

 

I suggest choosing an example of the following, which applies to a leap week calendar with leap week at end (similar can be defined for the displacement year of other calendars).

 

The ideal solar ecliptic longitudes (ISEL) are equally spaced starting from the new year and ending exactly one mean year after the new year. Most ISEL will occur on the same date every year, but a few ISEL will occur either in the one of the first two days of next year or in the same day in the leap week. All occur a fixed time after a new year.

 

Now if you postpone these ISELs by the calculated displacement D of its new year, the resulting calculated solar ecliptic longitudes (CSEL) are equally spaced over time.  This is a reason I chose this ISEL definition.

 

We have:

 

Calculated displacement D = CSEL –  ISEL

Actual Displacement =ASEL – ISEL

 

Also it is useful to look at

Drift = Actual displacement – Calculated displacement = ASEL – CSEL.

 

 

Another possible ISEL is the set of the ecliptic longitudes in a given year. I warn against this because it would give unduly good results for nearby years and unduly bad results halfway round the precession cycle.

 

Karl

 

16(05(15

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 11 January 2017 21:13
To: [hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 




 

On Wed, Jan 11, 2017 at 8:07 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael, Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 10 January 2017 20:27
To: [hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 

 

On Tue, Jan 10, 2017 at 8:17 AM, Karl Palmen <[hidden email]> wrote:

 

KARL REPLIES: What Michael has proposed is a simple arithmetic rule that approximates the mean tropical year and runs for about a 1000 years, then is changed to another such arithmetic rule determined by astronomical observations made that time.

 

... whenever it unacceptably displaces the calendar (by maybe 40% of a day?)

KARL REPLIES: By definition the displacement of the calendar dates is greater than -0.5 week and no greater than +0.5 week.

You're referring to the definition of D, in my Minimum-Displacement leapyear-rule. But, when we discussed that before, I made it quite clear that D is calculated displacement, as distinct from actual displacement.

Of course, with a suitable value for Y, the actual displacement is kept low, in keeping with the name "Minimum-Displacement".

 

 

This remains so perpetually regardless of the value of Y.

What Michael means by displacement here must be something different

Something different from D? Of course, and I made that clear in discussion last summer at this forum. D is calculated displacement.

As for "what Michael means by displacement here", it's the same thing that I always meant by displacement. Here is how I've, from the start, defined displacement:

Spatial displacement is change or difference in spatial position.

Calendar displacement is change or difference in the relation between calendar date and solar ecliptic longitude.

But that isn't something new from me. Its what I was saying from the start.

The variable D,, in my Minimum-Displacement leapyear-rule,  is calculated displacement.

...a practical approximation in a simple arithmetic leapyear-rule.

 

 

and this different thing is not simple

 

My definition of it is simple & brief. That doesn't mean that complicated things can't be said about displacement. Schroedinger's equation and Maxwell's equations aren't complicated in comparison to the problems that come up in the application of them. The applications of those equations are where the complication comes in.

 

and I think it may be a major cause of the disagreements between Michael and Irv, which I summarised in the “Solar Calendar Accuracy” thread.

I think Michael needs to be clearer in what he is stating. He is overusing the word ‘displacement’ using it to mean different things.

No. I've used one, and only one, definition for displacement.  ...the definition stated above.

When we were discussing my Minimum-Displacement leapyear-rule last summer, I made it quite clear that the variable "D" is calculated displacement, a practical approximation for use in my leapyear-rule.
 

 

Also Irv criticised Michael for his phrase “"the mean of the March & September equinoxes",”, which is ambiguous.

I've often referred to a Y value that's the arithmetic mean of the March equinox year and the September equinox year. I'll check my earlier posts to find out if I actually said it in the abbreviated way that Irv quoted it. But, even if I sometimes said it in that overly-brief unclear way, the fact remains that I often said it fully & clearly.

I've suggested two values for Y:

1. The length of the MTY

2. The mean of the lengths of the March & September equinox years.

The purpose of #1 is to lower displacement all year, instead of just at some favored time of year.

The purpose of #2 is as follows:

The vernal equinox has gotten particularly great attention. For example, the Gregorian leapyear rule was intended to stabilize the calendar with respect to the (north) vernal equinox, to reduce the amount by which the vernal equinox's calendar-date varies.

 

The equinoxes are times when the solar declination is changing at its most rapid. So is the perceived season and the length of the day. The vernal equinox is regarded by all as a significant time.

Problem: Our vernal equinox is the Southern Hemisphere's autumnal equinox.

For international fairness, then, instead of using the length of the March equinox year as Y, it would be much better to use the mean of the lengths of the March & September equinoxes as Y.

Walter pointed out that that mean value is very close to the length of the MTY.

 

It could be the mean of the March equinox and September equinox times for a calendar year and this would be different for a calendar year beginning in July than a calendar year beginning in January. However a more careful use of wording would prevent such misunderstanding. For example:

The mean of the lengths of the March & September equinox tropical years.

 

If I said it that way, that was an isolated writing-error. Elsewhere I made it clear that I was referring to the mean of the lengths of the March & September Equinox years.
 

If Michael needs to use this often, he could later abbreviate to say METY (mean equinox tropical year).

 

Not later. I've already done that. I called it the MEY.
 

 

Also I think Irv is no longer aware that Michael is suggesting an arithmetic calendar and is writing about how this calendar would be modified in the future to keep it accurate. The reference year (such as MTY) is not actually part of the calendar, but is used in the selection of the mean year of the calendar

Yes.



 

when created or modified, but does not completely determine that mean year or when it is changed. If I’m wrong here, Michael has a lot of clarification to do.

I'm not entrely sure what you mean there. The value of Y is an approximation to the current length of the MTY (or, alternatively, it could be the MEY instead).

The finite-length decimal fraction in Y, of course, isn't exactly the same as the current length of the MTY or MEY. Additionally, those two year-lengths vary with time, whereas Y is a constant..

Michael Ossipoff

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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Michael Ossipoff
In a reply, I said that the meaning of "mean tropical year" is based on a fictitious sun that moves at a uniform rate on the ecliptic, and coincides with the real sun at aphelion and at perihelion.

Actually that's only a guess. I can't find a definition of "Mean Tropical Year" anywhere (but no doubt it's in some books that I don' t have).

Where I got the "definition" that I posted:

Someone here said that a mean tropical year is the time that it takes for the mean sun to go around the ecliptic.

Meeus was quoted as saying that the mean sun is a fictitious sun that travels the celestial equator at a uniform rate, and coincides at the equinox points with another fixed sun that circles the ecliptic at a uniform rate and coincides with the real sun at perihelion and aphelion.

So, when someone here said that the mean tropical year is the time it takes for the mean sun to go around the ecliptic, then I'd assume that he was referring to that 2nd fictitious sun mentioned in the Meeus quote.

But I don't know if that's what "mean tropical year" really means.

The reason why I suggest the mean tropical year's length for the value of Y is because I assume that "mean" means that the length of that year is the actual mean (or the best estimate of it) of the lengths of the tropical year, over all of the points of the ecliptic at which a tropical year could be measured.

For all I know about the definition of a mean tropical year, maybe the lengths of the many various tropical years is calculated by solving the Earth's orbit with planetary perturbhations, over an orbit, and recording the time at many points of the ecliptic, and then, from those times, calculating the length of the tropical year measured at each of those many ecliptic points, and then numerically integrating (with respect to ecliptic longitude) those tropical year lengths, over all of those ecliptic points along the entire orbit, and then dividing the result by 2 pi radians.

I not having found any definition of "mean tropical year", then maybe the above paragraph is what it means.

Maybe I'd better clarify that this isn't an assertion about what "mean tropical year" means. It's the opposite. It's a statement that I haven't found a definition of that term.

Karl, could you post the definition of a mean tropical year, and what is meant when speaking of the length of a mean tropical year?

The reason why I suggest the length of the mean tropical year (yes, even without knowing its definition) for the value of Y is because I assume that it's the actual mean (or best estimate of it) of the tropical years measured from the points all around the ecliptic.

The mean of the lengths of sthe longest and shortest tropical years would be a "mid-range" tropical year, and the midrange can differ from the mean. That's why the mean tropical year's length (if it means what I think it means) sounds like a better choice for YI.

Michael Ossipoff

On Thu, Jan 12, 2017 at 8:01 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Michael has produced two different definitions of displacement and has now given names to them.

 

The calculated displacement D, which is used in defining a minimum displacement calendar and

 

The actual displacement. This he defines as

 

Calendar displacement is change or difference in the relation between calendar date and solar ecliptic longitude.

This this is not simple. It involves the complex relationship between calendar date and solar ecliptic longitude! I have thought of a way through this complexity.

To be meaningful, an ideal relationship between calendar date and solar ecliptic longitude needs to be carefully chosen and defined.

 

Then the actual displacement of a solar ecliptic longitude in a given year is

Actual date of this solar ecliptic longitude minus the ideal date of this solar ecliptic longitude

This may be expressed as (date of) Actual Solar Ecliptic Longitude minus (date of) Ideal Solar Ecliptic Longitude (for a given solar ecliptic longitude value).

ASEL - ISEL

 

I haven’t seen any explicit definition of an ideal relationship between calendar date and solar ecliptic longitude for year round accuracy.

 

I suggest choosing an example of the following, which applies to a leap week calendar with leap week at end (similar can be defined for the displacement year of other calendars).

 

The ideal solar ecliptic longitudes (ISEL) are equally spaced starting from the new year and ending exactly one mean year after the new year. Most ISEL will occur on the same date every year, but a few ISEL will occur either in the one of the first two days of next year or in the same day in the leap week. All occur a fixed time after a new year.

 

Now if you postpone these ISELs by the calculated displacement D of its new year, the resulting calculated solar ecliptic longitudes (CSEL) are equally spaced over time.  This is a reason I chose this ISEL definition.

 

We have:

 

Calculated displacement D = CSEL –  ISEL

Actual Displacement =ASEL – ISEL

 

Also it is useful to look at

Drift = Actual displacement – Calculated displacement = ASEL – CSEL.

 

 

Another possible ISEL is the set of the ecliptic longitudes in a given year. I warn against this because it would give unduly good results for nearby years and unduly bad results halfway round the precession cycle.

 

Karl

 

16(05(15

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 11 January 2017 21:13


To: [hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 




 

On Wed, Jan 11, 2017 at 8:07 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael, Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 10 January 2017 20:27
To: [hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 

 

On Tue, Jan 10, 2017 at 8:17 AM, Karl Palmen <[hidden email]> wrote:

 

KARL REPLIES: What Michael has proposed is a simple arithmetic rule that approximates the mean tropical year and runs for about a 1000 years, then is changed to another such arithmetic rule determined by astronomical observations made that time.

 

... whenever it unacceptably displaces the calendar (by maybe 40% of a day?)

KARL REPLIES: By definition the displacement of the calendar dates is greater than -0.5 week and no greater than +0.5 week.

You're referring to the definition of D, in my Minimum-Displacement leapyear-rule. But, when we discussed that before, I made it quite clear that D is calculated displacement, as distinct from actual displacement.

Of course, with a suitable value for Y, the actual displacement is kept low, in keeping with the name "Minimum-Displacement".

 

 

This remains so perpetually regardless of the value of Y.

What Michael means by displacement here must be something different

Something different from D? Of course, and I made that clear in discussion last summer at this forum. D is calculated displacement.

As for "what Michael means by displacement here", it's the same thing that I always meant by displacement. Here is how I've, from the start, defined displacement:

Spatial displacement is change or difference in spatial position.

Calendar displacement is change or difference in the relation between calendar date and solar ecliptic longitude.

But that isn't something new from me. Its what I was saying from the start.

The variable D,, in my Minimum-Displacement leapyear-rule,  is calculated displacement.

...a practical approximation in a simple arithmetic leapyear-rule.

 

 

and this different thing is not simple

 

My definition of it is simple & brief. That doesn't mean that complicated things can't be said about displacement. Schroedinger's equation and Maxwell's equations aren't complicated in comparison to the problems that come up in the application of them. The applications of those equations are where the complication comes in.

 

and I think it may be a major cause of the disagreements between Michael and Irv, which I summarised in the “Solar Calendar Accuracy” thread.

I think Michael needs to be clearer in what he is stating. He is overusing the word ‘displacement’ using it to mean different things.

No. I've used one, and only one, definition for displacement.  ...the definition stated above.

When we were discussing my Minimum-Displacement leapyear-rule last summer, I made it quite clear that the variable "D" is calculated displacement, a practical approximation for use in my leapyear-rule.
 

 

Also Irv criticised Michael for his phrase “"the mean of the March & September equinoxes",”, which is ambiguous.

I've often referred to a Y value that's the arithmetic mean of the March equinox year and the September equinox year. I'll check my earlier posts to find out if I actually said it in the abbreviated way that Irv quoted it. But, even if I sometimes said it in that overly-brief unclear way, the fact remains that I often said it fully & clearly.

I've suggested two values for Y:

1. The length of the MTY

2. The mean of the lengths of the March & September equinox years.

The purpose of #1 is to lower displacement all year, instead of just at some favored time of year.

The purpose of #2 is as follows:

The vernal equinox has gotten particularly great attention. For example, the Gregorian leapyear rule was intended to stabilize the calendar with respect to the (north) vernal equinox, to reduce the amount by which the vernal equinox's calendar-date varies.

 

The equinoxes are times when the solar declination is changing at its most rapid. So is the perceived season and the length of the day. The vernal equinox is regarded by all as a significant time.

Problem: Our vernal equinox is the Southern Hemisphere's autumnal equinox.

For international fairness, then, instead of using the length of the March equinox year as Y, it would be much better to use the mean of the lengths of the March & September equinoxes as Y.

Walter pointed out that that mean value is very close to the length of the MTY.

 

It could be the mean of the March equinox and September equinox times for a calendar year and this would be different for a calendar year beginning in July than a calendar year beginning in January. However a more careful use of wording would prevent such misunderstanding. For example:

The mean of the lengths of the March & September equinox tropical years.

 

If I said it that way, that was an isolated writing-error. Elsewhere I made it clear that I was referring to the mean of the lengths of the March & September Equinox years.
 

If Michael needs to use this often, he could later abbreviate to say METY (mean equinox tropical year).

 

Not later. I've already done that. I called it the MEY.
 

 

Also I think Irv is no longer aware that Michael is suggesting an arithmetic calendar and is writing about how this calendar would be modified in the future to keep it accurate. The reference year (such as MTY) is not actually part of the calendar, but is used in the selection of the mean year of the calendar

Yes.



 

when created or modified, but does not completely determine that mean year or when it is changed. If I’m wrong here, Michael has a lot of clarification to do.

I'm not entrely sure what you mean there. The value of Y is an approximation to the current length of the MTY (or, alternatively, it could be the MEY instead).

The finite-length decimal fraction in Y, of course, isn't exactly the same as the current length of the MTY or MEY. Additionally, those two year-lengths vary with time, whereas Y is a constant..

Michael Ossipoff


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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Michael Ossipoff

Typo:

I posted:

"Meeus was quoted as saying that the mean sun is a fictitious sun that travels the celestial equator at a uniform rate, and coincides at the equinox points with another fixed sun that circles the ecliptic at a uniform rate and coincides with the real sun at perihelion and aphelion."

When I said "fixed sun", I meant "fictitious sun".

Michael Ossipoff

On Thu, Jan 12, 2017 at 12:38 PM, Michael Ossipoff <[hidden email]> wrote:
In a reply, I said that the meaning of "mean tropical year" is based on a fictitious sun that moves at a uniform rate on the ecliptic, and coincides with the real sun at aphelion and at perihelion.

Actually that's only a guess. I can't find a definition of "Mean Tropical Year" anywhere (but no doubt it's in some books that I don' t have).

Where I got the "definition" that I posted:

Someone here said that a mean tropical year is the time that it takes for the mean sun to go around the ecliptic.

Meeus was quoted as saying that the mean sun is a fictitious sun that travels the celestial equator at a uniform rate, and coincides at the equinox points with another fixed sun that circles the ecliptic at a uniform rate and coincides with the real sun at perihelion and aphelion.

So, when someone here said that the mean tropical year is the time it takes for the mean sun to go around the ecliptic, then I'd assume that he was referring to that 2nd fictitious sun mentioned in the Meeus quote.

But I don't know if that's what "mean tropical year" really means.

The reason why I suggest the mean tropical year's length for the value of Y is because I assume that "mean" means that the length of that year is the actual mean (or the best estimate of it) of the lengths of the tropical year, over all of the points of the ecliptic at which a tropical year could be measured.

For all I know about the definition of a mean tropical year, maybe the lengths of the many various tropical years is calculated by solving the Earth's orbit with planetary perturbhations, over an orbit, and recording the time at many points of the ecliptic, and then, from those times, calculating the length of the tropical year measured at each of those many ecliptic points, and then numerically integrating (with respect to ecliptic longitude) those tropical year lengths, over all of those ecliptic points along the entire orbit, and then dividing the result by 2 pi radians.

I not having found any definition of "mean tropical year", then maybe the above paragraph is what it means.

Maybe I'd better clarify that this isn't an assertion about what "mean tropical year" means. It's the opposite. It's a statement that I haven't found a definition of that term.

Karl, could you post the definition of a mean tropical year, and what is meant when speaking of the length of a mean tropical year?

The reason why I suggest the length of the mean tropical year (yes, even without knowing its definition) for the value of Y is because I assume that it's the actual mean (or best estimate of it) of the tropical years measured from the points all around the ecliptic.

The mean of the lengths of sthe longest and shortest tropical years would be a "mid-range" tropical year, and the midrange can differ from the mean. That's why the mean tropical year's length (if it means what I think it means) sounds like a better choice for YI.

Michael Ossipoff

On Thu, Jan 12, 2017 at 8:01 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Michael has produced two different definitions of displacement and has now given names to them.

 

The calculated displacement D, which is used in defining a minimum displacement calendar and

 

The actual displacement. This he defines as

 

Calendar displacement is change or difference in the relation between calendar date and solar ecliptic longitude.

This this is not simple. It involves the complex relationship between calendar date and solar ecliptic longitude! I have thought of a way through this complexity.

To be meaningful, an ideal relationship between calendar date and solar ecliptic longitude needs to be carefully chosen and defined.

 

Then the actual displacement of a solar ecliptic longitude in a given year is

Actual date of this solar ecliptic longitude minus the ideal date of this solar ecliptic longitude

This may be expressed as (date of) Actual Solar Ecliptic Longitude minus (date of) Ideal Solar Ecliptic Longitude (for a given solar ecliptic longitude value).

ASEL - ISEL

 

I haven’t seen any explicit definition of an ideal relationship between calendar date and solar ecliptic longitude for year round accuracy.

 

I suggest choosing an example of the following, which applies to a leap week calendar with leap week at end (similar can be defined for the displacement year of other calendars).

 

The ideal solar ecliptic longitudes (ISEL) are equally spaced starting from the new year and ending exactly one mean year after the new year. Most ISEL will occur on the same date every year, but a few ISEL will occur either in the one of the first two days of next year or in the same day in the leap week. All occur a fixed time after a new year.

 

Now if you postpone these ISELs by the calculated displacement D of its new year, the resulting calculated solar ecliptic longitudes (CSEL) are equally spaced over time.  This is a reason I chose this ISEL definition.

 

We have:

 

Calculated displacement D = CSEL –  ISEL

Actual Displacement =ASEL – ISEL

 

Also it is useful to look at

Drift = Actual displacement – Calculated displacement = ASEL – CSEL.

 

 

Another possible ISEL is the set of the ecliptic longitudes in a given year. I warn against this because it would give unduly good results for nearby years and unduly bad results halfway round the precession cycle.

 

Karl

 

16(05(15

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 11 January 2017 21:13


To: [hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 




 

On Wed, Jan 11, 2017 at 8:07 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael, Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 10 January 2017 20:27
To: [hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 

 

On Tue, Jan 10, 2017 at 8:17 AM, Karl Palmen <[hidden email]> wrote:

 

KARL REPLIES: What Michael has proposed is a simple arithmetic rule that approximates the mean tropical year and runs for about a 1000 years, then is changed to another such arithmetic rule determined by astronomical observations made that time.

 

... whenever it unacceptably displaces the calendar (by maybe 40% of a day?)

KARL REPLIES: By definition the displacement of the calendar dates is greater than -0.5 week and no greater than +0.5 week.

You're referring to the definition of D, in my Minimum-Displacement leapyear-rule. But, when we discussed that before, I made it quite clear that D is calculated displacement, as distinct from actual displacement.

Of course, with a suitable value for Y, the actual displacement is kept low, in keeping with the name "Minimum-Displacement".

 

 

This remains so perpetually regardless of the value of Y.

What Michael means by displacement here must be something different

Something different from D? Of course, and I made that clear in discussion last summer at this forum. D is calculated displacement.

As for "what Michael means by displacement here", it's the same thing that I always meant by displacement. Here is how I've, from the start, defined displacement:

Spatial displacement is change or difference in spatial position.

Calendar displacement is change or difference in the relation between calendar date and solar ecliptic longitude.

But that isn't something new from me. Its what I was saying from the start.

The variable D,, in my Minimum-Displacement leapyear-rule,  is calculated displacement.

...a practical approximation in a simple arithmetic leapyear-rule.

 

 

and this different thing is not simple

 

My definition of it is simple & brief. That doesn't mean that complicated things can't be said about displacement. Schroedinger's equation and Maxwell's equations aren't complicated in comparison to the problems that come up in the application of them. The applications of those equations are where the complication comes in.

 

and I think it may be a major cause of the disagreements between Michael and Irv, which I summarised in the “Solar Calendar Accuracy” thread.

I think Michael needs to be clearer in what he is stating. He is overusing the word ‘displacement’ using it to mean different things.

No. I've used one, and only one, definition for displacement.  ...the definition stated above.

When we were discussing my Minimum-Displacement leapyear-rule last summer, I made it quite clear that the variable "D" is calculated displacement, a practical approximation for use in my leapyear-rule.
 

 

Also Irv criticised Michael for his phrase “"the mean of the March & September equinoxes",”, which is ambiguous.

I've often referred to a Y value that's the arithmetic mean of the March equinox year and the September equinox year. I'll check my earlier posts to find out if I actually said it in the abbreviated way that Irv quoted it. But, even if I sometimes said it in that overly-brief unclear way, the fact remains that I often said it fully & clearly.

I've suggested two values for Y:

1. The length of the MTY

2. The mean of the lengths of the March & September equinox years.

The purpose of #1 is to lower displacement all year, instead of just at some favored time of year.

The purpose of #2 is as follows:

The vernal equinox has gotten particularly great attention. For example, the Gregorian leapyear rule was intended to stabilize the calendar with respect to the (north) vernal equinox, to reduce the amount by which the vernal equinox's calendar-date varies.

 

The equinoxes are times when the solar declination is changing at its most rapid. So is the perceived season and the length of the day. The vernal equinox is regarded by all as a significant time.

Problem: Our vernal equinox is the Southern Hemisphere's autumnal equinox.

For international fairness, then, instead of using the length of the March equinox year as Y, it would be much better to use the mean of the lengths of the March & September equinoxes as Y.

Walter pointed out that that mean value is very close to the length of the MTY.

 

It could be the mean of the March equinox and September equinox times for a calendar year and this would be different for a calendar year beginning in July than a calendar year beginning in January. However a more careful use of wording would prevent such misunderstanding. For example:

The mean of the lengths of the March & September equinox tropical years.

 

If I said it that way, that was an isolated writing-error. Elsewhere I made it clear that I was referring to the mean of the lengths of the March & September Equinox years.
 

If Michael needs to use this often, he could later abbreviate to say METY (mean equinox tropical year).

 

Not later. I've already done that. I called it the MEY.
 

 

Also I think Irv is no longer aware that Michael is suggesting an arithmetic calendar and is writing about how this calendar would be modified in the future to keep it accurate. The reference year (such as MTY) is not actually part of the calendar, but is used in the selection of the mean year of the calendar

Yes.



 

when created or modified, but does not completely determine that mean year or when it is changed. If I’m wrong here, Michael has a lot of clarification to do.

I'm not entrely sure what you mean there. The value of Y is an approximation to the current length of the MTY (or, alternatively, it could be the MEY instead).

The finite-length decimal fraction in Y, of course, isn't exactly the same as the current length of the MTY or MEY. Additionally, those two year-lengths vary with time, whereas Y is a constant..

Michael Ossipoff



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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Amos Shapir-2
Hi Michael and calendar people,

The term "tropical" in astronomy usually means "pertaining to the seasons", so a tropical year has nothing to do with aphelion and perihelion.  Meeus (2nd edition, p.133) defines the tropical year's length as equal to that of the Besselian year, which is defined as the time it takes the Earth's axis to turn a full circle between consecutive positions of 280 degrees to the Sun (where its angle at the northward equinox is defined as 0).

So calculating the tropical year is concerned only with the movement of the Earth's axis, mainly due to precession.  A "mean tropical year", like any calculation of an average, depends on the interval over which it's calculated.

I hope this helps.

On Thu, Jan 12, 2017 at 10:03 PM, Michael Ossipoff <[hidden email]> wrote:

Typo:

I posted:

"Meeus was quoted as saying that the mean sun is a fictitious sun that travels the celestial equator at a uniform rate, and coincides at the equinox points with another fixed sun that circles the ecliptic at a uniform rate and coincides with the real sun at perihelion and aphelion."

When I said "fixed sun", I meant "fictitious sun".

Michael Ossipoff

On Thu, Jan 12, 2017 at 12:38 PM, Michael Ossipoff <[hidden email]> wrote:
In a reply, I said that the meaning of "mean tropical year" is based on a fictitious sun that moves at a uniform rate on the ecliptic, and coincides with the real sun at aphelion and at perihelion.

Actually that's only a guess. I can't find a definition of "Mean Tropical Year" anywhere (but no doubt it's in some books that I don' t have).

Where I got the "definition" that I posted:

Someone here said that a mean tropical year is the time that it takes for the mean sun to go around the ecliptic.

Meeus was quoted as saying that the mean sun is a fictitious sun that travels the celestial equator at a uniform rate, and coincides at the equinox points with another fixed sun that circles the ecliptic at a uniform rate and coincides with the real sun at perihelion and aphelion.

So, when someone here said that the mean tropical year is the time it takes for the mean sun to go around the ecliptic, then I'd assume that he was referring to that 2nd fictitious sun mentioned in the Meeus quote.

But I don't know if that's what "mean tropical year" really means.

The reason why I suggest the mean tropical year's length for the value of Y is because I assume that "mean" means that the length of that year is the actual mean (or the best estimate of it) of the lengths of the tropical year, over all of the points of the ecliptic at which a tropical year could be measured.

For all I know about the definition of a mean tropical year, maybe the lengths of the many various tropical years is calculated by solving the Earth's orbit with planetary perturbhations, over an orbit, and recording the time at many points of the ecliptic, and then, from those times, calculating the length of the tropical year measured at each of those many ecliptic points, and then numerically integrating (with respect to ecliptic longitude) those tropical year lengths, over all of those ecliptic points along the entire orbit, and then dividing the result by 2 pi radians.

I not having found any definition of "mean tropical year", then maybe the above paragraph is what it means.

Maybe I'd better clarify that this isn't an assertion about what "mean tropical year" means. It's the opposite. It's a statement that I haven't found a definition of that term.

Karl, could you post the definition of a mean tropical year, and what is meant when speaking of the length of a mean tropical year?

The reason why I suggest the length of the mean tropical year (yes, even without knowing its definition) for the value of Y is because I assume that it's the actual mean (or best estimate of it) of the tropical years measured from the points all around the ecliptic.

The mean of the lengths of sthe longest and shortest tropical years would be a "mid-range" tropical year, and the midrange can differ from the mean. That's why the mean tropical year's length (if it means what I think it means) sounds like a better choice for YI.

Michael Ossipoff






--
Amos Shapir
 
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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Irv Bromberg
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Amos Shapir [[hidden email]]
Sent: Friday, January 13, 2017 02:52

The term "tropical" in astronomy usually means "pertaining to the seasons", so a tropical year has nothing to do with aphelion and perihelion.

Irv replies: As I explained, the average solar cycle length equals the average of the aphelion mean year and the perihelion mean year, therefore it is pointless to argue that these have nothing to do with the seasons. Once again, on my chart (numerically integrated using Prof. Aldo Vitagliano's SOLEX program), see the lavender curve = mean year at aphelion, grey curve = mean year at perihelion, everything else is in-between, with the average of the aphelion mean year and the perihelion mean year plotted as the black curve:


Meeus (2nd edition, p.133) defines the tropical year's length as equal to that of the Besselian year, which is defined as the time it takes the Earth's axis to turn a full circle between consecutive positions of 280 degrees to the Sun (where its angle at the northward equinox is defined as 0).

Irv replies: The Besselian mean year is currently rather long, about 365d 5h 49m 40s, which is considerably longer than the Gregorian mean year, and it is rapidly getting shorter, see:


So does it make any sense to select the Besselian mean year as representative of the tropical year length, if it is exceptionally long and is rapidly getting shorter?

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/leap/

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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Michael Ossipoff
In reply to this post by Amos Shapir-2


On Fri, Jan 13, 2017 at 2:52 AM, Amos Shapir <[hidden email]> wrote:
Hi Michael and calendar people,

The term "tropical" in astronomy usually means "pertaining to the seasons"

Yes, we pretty much had agreement on that.
 
, so a tropical year has nothing to do with aphelion and perihelion. 

Fine. I was, as I said, just quoting what someone here said. Someone here said that a mean tropical year is the time it takes for the mean sun to make a complete circuit (a circuit of ...I don't remember what they said.)

Meeus defined the mean sun as a fictitious sun that moves at a uniform rate on the celestial equator, coinciding at the equinoxes with another fictitious sun that moves uniformly on the ecliptic and coincides with the real sun at aphelion and perihelion.

I was just quoting (as much as I remembered of) what someone here said. I wasn't asserting that it was true.

Whatever the definition of a mean tropical year is, I hope and assume that it's what its name implies, and that its length is the mean of the many tropical-year-lengths, as measured from all of the points along the ecliptic.

That would make it a fine compromise, to use for Y, to give the calendar its best accuracy year-round.

Michael Ossipoff




 
Meeus (2nd edition, p.133) defines the tropical year's length as equal to that of the Besselian year, which is defined as the time it takes the Earth's axis to turn a full circle between consecutive positions of 280 degrees to the Sun (where its angle at the northward equinox is defined as 0).

So calculating the tropical year is concerned only with the movement of the Earth's axis, mainly due to precession.  A "mean tropical year", like any calculation of an average, depends on the interval over which it's calculated.

I hope this helps.

On Thu, Jan 12, 2017 at 10:03 PM, Michael Ossipoff <[hidden email]> wrote:

Typo:

I posted:

"Meeus was quoted as saying that the mean sun is a fictitious sun that travels the celestial equator at a uniform rate, and coincides at the equinox points with another fixed sun that circles the ecliptic at a uniform rate and coincides with the real sun at perihelion and aphelion."

When I said "fixed sun", I meant "fictitious sun".

Michael Ossipoff

On Thu, Jan 12, 2017 at 12:38 PM, Michael Ossipoff <[hidden email]> wrote:
In a reply, I said that the meaning of "mean tropical year" is based on a fictitious sun that moves at a uniform rate on the ecliptic, and coincides with the real sun at aphelion and at perihelion.

Actually that's only a guess. I can't find a definition of "Mean Tropical Year" anywhere (but no doubt it's in some books that I don' t have).

Where I got the "definition" that I posted:

Someone here said that a mean tropical year is the time that it takes for the mean sun to go around the ecliptic.

Meeus was quoted as saying that the mean sun is a fictitious sun that travels the celestial equator at a uniform rate, and coincides at the equinox points with another fixed sun that circles the ecliptic at a uniform rate and coincides with the real sun at perihelion and aphelion.

So, when someone here said that the mean tropical year is the time it takes for the mean sun to go around the ecliptic, then I'd assume that he was referring to that 2nd fictitious sun mentioned in the Meeus quote.

But I don't know if that's what "mean tropical year" really means.

The reason why I suggest the mean tropical year's length for the value of Y is because I assume that "mean" means that the length of that year is the actual mean (or the best estimate of it) of the lengths of the tropical year, over all of the points of the ecliptic at which a tropical year could be measured.

For all I know about the definition of a mean tropical year, maybe the lengths of the many various tropical years is calculated by solving the Earth's orbit with planetary perturbhations, over an orbit, and recording the time at many points of the ecliptic, and then, from those times, calculating the length of the tropical year measured at each of those many ecliptic points, and then numerically integrating (with respect to ecliptic longitude) those tropical year lengths, over all of those ecliptic points along the entire orbit, and then dividing the result by 2 pi radians.

I not having found any definition of "mean tropical year", then maybe the above paragraph is what it means.

Maybe I'd better clarify that this isn't an assertion about what "mean tropical year" means. It's the opposite. It's a statement that I haven't found a definition of that term.

Karl, could you post the definition of a mean tropical year, and what is meant when speaking of the length of a mean tropical year?

The reason why I suggest the length of the mean tropical year (yes, even without knowing its definition) for the value of Y is because I assume that it's the actual mean (or best estimate of it) of the tropical years measured from the points all around the ecliptic.

The mean of the lengths of sthe longest and shortest tropical years would be a "mid-range" tropical year, and the midrange can differ from the mean. That's why the mean tropical year's length (if it means what I think it means) sounds like a better choice for YI.

Michael Ossipoff






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Amos Shapir
 

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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Michael Ossipoff
In reply to this post by Amos Shapir-2
I should say better what I interpreted that person here to mean. I assumed that he meant that the mean tropical year is a complete circuit of the ecliptic by a uniformly-moving fictitious sun that coincides with the real sun at aphelion & perihelion.


On Fri, Jan 13, 2017 at 2:52 AM, Amos Shapir <[hidden email]> wrote:


The term "tropical" in astronomy usually means "pertaining to the seasons"

Yes, and that's why that person here spoke of a fictitious sun that moves uniformly and is intended to approximate the real sun's movement on the ecliptic.


 
, so a tropical year has nothing to do with aphelion and perihelion. 

Here's a possible reason  why that person mentioned aphelion & perihelion:

To be useful, that uniformly-moving fictitious sun would have to approximate the real  sun. As that person described it, then, it does so by coinciding with the real sun somewhere.

It was probably felt that the perihelion and the aphelion are places where it's feasible & convenient to have that fixed sun coincide with the real sun. 

..not because perihelion & aphelion are about the seasons, but just because those are convenient & feasible places for the real & fictitious suns to coincide.

But, as I've emphasized, I'm merely quoting, but not asserting, what that person said.

What's important, as a reason for using the mean tropical year's length for Y, is that it be the mean of the lengths of all the tropical years defined with respect to all the points on the ecliptic.

Until told otherwise, I assume that that is the purpose of, and an attribute of, the mean tropical year, however defined.

I suggested a procedure that might be used to determine the length of such a mean tropical year.

Michael Ossipoff


 
Meeus (2nd edition, p.133) defines the tropical year's length as equal to that of the Besselian year, which is defined as the time it takes the Earth's axis to turn a full circle between consecutive positions of 280 degrees to the Sun (where its angle at the northward equinox is defined as 0).

So calculating the tropical year is concerned only with the movement of the Earth's axis, mainly due to precession.  A "mean tropical year", like any calculation of an average, depends on the interval over which it's calculated.

I hope this helps.

On Thu, Jan 12, 2017 at 10:03 PM, Michael Ossipoff <[hidden email]> wrote:

Typo:

I posted:

"Meeus was quoted as saying that the mean sun is a fictitious sun that travels the celestial equator at a uniform rate, and coincides at the equinox points with another fixed sun that circles the ecliptic at a uniform rate and coincides with the real sun at perihelion and aphelion."

When I said "fixed sun", I meant "fictitious sun".

Michael Ossipoff

On Thu, Jan 12, 2017 at 12:38 PM, Michael Ossipoff <[hidden email]> wrote:
In a reply, I said that the meaning of "mean tropical year" is based on a fictitious sun that moves at a uniform rate on the ecliptic, and coincides with the real sun at aphelion and at perihelion.

Actually that's only a guess. I can't find a definition of "Mean Tropical Year" anywhere (but no doubt it's in some books that I don' t have).

Where I got the "definition" that I posted:

Someone here said that a mean tropical year is the time that it takes for the mean sun to go around the ecliptic.

Meeus was quoted as saying that the mean sun is a fictitious sun that travels the celestial equator at a uniform rate, and coincides at the equinox points with another fixed sun that circles the ecliptic at a uniform rate and coincides with the real sun at perihelion and aphelion.

So, when someone here said that the mean tropical year is the time it takes for the mean sun to go around the ecliptic, then I'd assume that he was referring to that 2nd fictitious sun mentioned in the Meeus quote.

But I don't know if that's what "mean tropical year" really means.

The reason why I suggest the mean tropical year's length for the value of Y is because I assume that "mean" means that the length of that year is the actual mean (or the best estimate of it) of the lengths of the tropical year, over all of the points of the ecliptic at which a tropical year could be measured.

For all I know about the definition of a mean tropical year, maybe the lengths of the many various tropical years is calculated by solving the Earth's orbit with planetary perturbhations, over an orbit, and recording the time at many points of the ecliptic, and then, from those times, calculating the length of the tropical year measured at each of those many ecliptic points, and then numerically integrating (with respect to ecliptic longitude) those tropical year lengths, over all of those ecliptic points along the entire orbit, and then dividing the result by 2 pi radians.

I not having found any definition of "mean tropical year", then maybe the above paragraph is what it means.

Maybe I'd better clarify that this isn't an assertion about what "mean tropical year" means. It's the opposite. It's a statement that I haven't found a definition of that term.

Karl, could you post the definition of a mean tropical year, and what is meant when speaking of the length of a mean tropical year?

The reason why I suggest the length of the mean tropical year (yes, even without knowing its definition) for the value of Y is because I assume that it's the actual mean (or best estimate of it) of the tropical years measured from the points all around the ecliptic.

The mean of the lengths of sthe longest and shortest tropical years would be a "mid-range" tropical year, and the midrange can differ from the mean. That's why the mean tropical year's length (if it means what I think it means) sounds like a better choice for YI.

Michael Ossipoff






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Amos Shapir
 

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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Irv Bromberg
In reply to this post by Amos Shapir-2
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Amos Shapir [[hidden email]]
Sent: Friday, January 13, 2017 02:52

The term "tropical" in astronomy usually means "pertaining to the seasons", so a tropical year has nothing to do with aphelion and perihelion.

Irv replies further:

The progressive tidal slowing of the Earth rotation rate is unavoidable, notwithstanding that the rate of slowing isn't constant and with present knowledge is partially unpredictable. Therefore, if one isn't "married" to a particular equinox or solstice for religious or other reasons, it makes sense to choose a calendar mean year that is currently equal to the shortest current solar mean year, at aphelion, and let it run until it eventually becomes the mean year at perihelion.

Presently, the aphelion mean year is very close to the mean year of the 327-year cycle (with 58 leap weeks or 79 leap days), whose mean year is 365+79/327 days = 365d 5h 47m 53+43/109s (approximately 53.4 seconds) = approximately 365.241590214 days, and, because of the current proximity of aphelion to the north solstice, it so happens that it is also an excellent leap cycle for approximating the current mean north solstitial mean year until beyond the year 12000 AD (depending on what happens to Delta T in the future).

For most calendar cycles there exist two distinctly separated "calendar seasons": the more stable primary season where the variation over the long term is quite small, and the less stable secondary season that has more variation over the long term. For example, see these charts for the 293-, 524-, 33-, and 400-year cycles:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-293.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-524.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-33.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-400.pdf

In the case of a calendar cycle having a mean year equal to that at aphelion, however, the primary and secondary calendar seasons are very close together, as can be seen in this chart for the 327-year cycle:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-327.pdf

This indicates that the 327-year cycle has extended seasonal stability for calendrical purposes, and will be essentially the longest lasting of any within-range cycle that could be picked today. Although it starts out currently having the shortest mean year of all points in the solar cycle, by the time that will eventually reach perihelion, all other points in the solar cycle will have shorter mean years, and after that it will go "out-of-range" (too long).

If one chooses a cycle having a slightly shorter mean year then the primary calendar season gets closer to aphelion, but the secondary season becomes quite unstable and shifts to perihelion.

Anybody who wishes to experiment with calendar seasons is welcome to download my freeware Excel spreadsheet "Find Solar Calendar Seasons" with macro that can compute and plot the calendar seasons for any desired leap cycle (and was used to generate the above calendar seasons charts):

http://individual.utoronto.ca/kalendis/leap/Find-Solar-Calendar-Seasons.xls

The 327-year leap week cycle is built into my freeware calendrical calculator, Kalendis, as an optional experimental alternative for the Symmetry454 or Symmetry010 or related leap week variants.

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/leap/
http://www.sym454.org/seasons/
http://www.sym454.org/kalendis/

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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Walter J Ziobro
Dear Irv, and calendar list:

Recently, Irv made the following statement in a discussion about Solar Calendar Design:

"Therefore, if one isn't "married" to a particular equinox or solstice for religious or other reasons, it makes sense to choose a calendar mean year that is currently equal to the shortest current solar mean year, at aphelion, and let it run until it eventually becomes the mean year at perihelion."

I find this statement rather interesting, and, if I understand it correctly, I believe that it can be implemented in a way that I have mentioned before.

If we take the Indian National Calendar, described here:

https://en.wikipedia.org/wiki/Indian_national_calendar

and shift the month lengths by one month about once every 1800 years, then we can adjust the calendar for the relative lengths of the seasons over the anomalistic cycle.  We can see how as the 31 day months make 6 shifts over the course of about 10,800 years, they are following the course of the apehelion over half of its cycle. Thus, all the seasonal points will shift half a cycle relative to the aphelion and perihelion. 

Thus, in the present era, the northward equinox year has been relatively stable as the 31 day months have shifted across it, but that will change when the northward equinox occurs during the 30 day months, and we will see the northward equinox creep earlier and earlier in the Gregorian Calendar, as that equinox would be shifted from 30 day month to 30 day month in the Indian National Calendar under my shifting proposal.

 With my shifting proposal, the season points would occur very close to the beginnings of the months pf Chaitra, Ashadha, Ashwin, and Pausha over the entire period of the anomalistic cycle.

-Walter Ziobro
  


-----Original Message-----
From: Irv Bromberg <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Sun, Jan 15, 2017 2:32 pm
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Amos Shapir [[hidden email]]
Sent: Friday, January 13, 2017 02:52

The term "tropical" in astronomy usually means "pertaining to the seasons", so a tropical year has nothing to do with aphelion and perihelion.

Irv replies further:

The progressive tidal slowing of the Earth rotation rate is unavoidable, notwithstanding that the rate of slowing isn't constant and with present knowledge is partially unpredictable. Therefore, if one isn't "married" to a particular equinox or solstice for religious or other reasons, it makes sense to choose a calendar mean year that is currently equal to the shortest current solar mean year, at aphelion, and let it run until it eventually becomes the mean year at perihelion.

Presently, the aphelion mean year is very close to the mean year of the 327-year cycle (with 58 leap weeks or 79 leap days), whose mean year is 365+79/327 days = 365d 5h 47m 53+43/109s (approximately 53.4 seconds) = approximately 365.241590214 days, and, because of the current proximity of aphelion to the north solstice, it so happens that it is also an excellent leap cycle for approximating the current mean north solstitial mean year until beyond the year 12000 AD (depending on what happens to Delta T in the future).

For most calendar cycles there exist two distinctly separated "calendar seasons": the more stable primary season where the variation over the long term is quite small, and the less stable secondary season that has more variation over the long term. For example, see these charts for the 293-, 524-, 33-, and 400-year cycles:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-293.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-524.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-33.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-400.pdf

In the case of a calendar cycle having a mean year equal to that at aphelion, however, the primary and secondary calendar seasons are very close together, as can be seen in this chart for the 327-year cycle:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-327.pdf

This indicates that the 327-year cycle has extended seasonal stability for calendrical purposes, and will be essentially the longest lasting of any within-range cycle that could be picked today. Although it starts out currently having the shortest mean year of all points in the solar cycle, by the time that will eventually reach perihelion, all other points in the solar cycle will have shorter mean years, and after that it will go "out-of-range" (too long).

If one chooses a cycle having a slightly shorter mean year then the primary calendar season gets closer to aphelion, but the secondary season becomes quite unstable and shifts to perihelion.

Anybody who wishes to experiment with calendar seasons is welcome to download my freeware Excel spreadsheet "Find Solar Calendar Seasons" with macro that can compute and plot the calendar seasons for any desired leap cycle (and was used to generate the above calendar seasons charts):

http://individual.utoronto.ca/kalendis/leap/Find-Solar-Calendar-Seasons.xls

The 327-year leap week cycle is built into my freeware calendrical calculator, Kalendis, as an optional experimental alternative for the Symmetry454 or Symmetry010 or related leap week variants.

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/leap/
http://www.sym454.org/seasons/
http://www.sym454.org/kalendis/

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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Karl Palmen

Dear Walter, Irv, Michael and Calendar People

 

I understand the quote of Irv quite differently to the way Walter does.

 

I see it as an extreme form of my idea that any mean year that is in range of the tropical years starting at any solar ecliptic longitude will do, which maximises the lifetime of each successive arithmetic calendar. One does not change the arithmetic calendar until its mean year reaches the edge of the range, when it will be the perihelion tropical year. Then one changes the mean year to the other edge of the range, which is then the aphelion tropical year. There is one difference and that Irv has the epoch of the first leap calendar is today.

 

This has nothing to do with Walter’s proposed modification of the Indian National calendar, which the mean year would depend on, which month you start the year. Such a calendar could have much lower actual displacements over a precession cycle than anything Michael Ossipoff  has proposed, but is more complicated. I have looked into the behaviour of such calendars in past E-mails.

 

Karl

 

16(05(22

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 19 January 2017 04:59
To: [hidden email]
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 

Dear Irv, and calendar list:

Recently, Irv made the following statement in a discussion about Solar Calendar Design:

 

"Therefore, if one isn't "married" to a particular equinox or solstice for religious or other reasons, it makes sense to choose a calendar mean year that is currently equal to the shortest current solar mean year, at aphelion, and let it run until it eventually becomes the mean year at perihelion."

I find this statement rather interesting, and, if I understand it correctly, I believe that it can be implemented in a way that I have mentioned before.

If we take the Indian National Calendar, described here:

https://en.wikipedia.org/wiki/Indian_national_calendar

and shift the month lengths by one month about once every 1800 years, then we can adjust the calendar for the relative lengths of the seasons over the anomalistic cycle.  We can see how as the 31 day months make 6 shifts over the course of about 10,800 years, they are following the course of the apehelion over half of its cycle. Thus, all the seasonal points will shift half a cycle relative to the aphelion and perihelion. 

Thus, in the present era, the northward equinox year has been relatively stable as the 31 day months have shifted across it, but that will change when the northward equinox occurs during the 30 day months, and we will see the northward equinox creep earlier and earlier in the Gregorian Calendar, as that equinox would be shifted from 30 day month to 30 day month in the Indian National Calendar under my shifting proposal.

 With my shifting proposal, the season points would occur very close to the beginnings of the months pf Chaitra, Ashadha, Ashwin, and Pausha over the entire period of the anomalistic cycle.

-Walter Ziobro
  

 

-----Original Message-----
From: Irv Bromberg <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Sun, Jan 15, 2017 2:32 pm
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Amos Shapir [[hidden email]]

Sent: Friday, January 13, 2017 02:52

The term "tropical" in astronomy usually means "pertaining to the seasons", so a tropical year has nothing to do with aphelion and perihelion.


Irv replies further:

The progressive tidal slowing of the Earth rotation rate is unavoidable, notwithstanding that the rate of slowing isn't constant and with present knowledge is partially unpredictable. Therefore, if one isn't "married" to a particular equinox or solstice for religious or other reasons, it makes sense to choose a calendar mean year that is currently equal to the shortest current solar mean year, at aphelion, and let it run until it eventually becomes the mean year at perihelion.

Presently, the aphelion mean year is very close to the mean year of the 327-year cycle (with 58 leap weeks or 79 leap days), whose mean year is 365+79/327 days = 365d 5h 47m 53+43/109s (approximately 53.4 seconds) = approximately 365.241590214 days, and, because of the current proximity of aphelion to the north solstice, it so happens that it is also an excellent leap cycle for approximating the current mean north solstitial mean year until beyond the year 12000 AD (depending on what happens to Delta T in the future).

For most calendar cycles there exist two distinctly separated "calendar seasons": the more stable primary season where the variation over the long term is quite small, and the less stable secondary season that has more variation over the long term. For example, see these charts for the 293-, 524-, 33-, and 400-year cycles:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-293.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-524.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-33.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-400.pdf

In the case of a calendar cycle having a mean year equal to that at aphelion, however, the primary and secondary calendar seasons are very close together, as can be seen in this chart for the 327-year cycle:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-327.pdf

This indicates that the 327-year cycle has extended seasonal stability for calendrical purposes, and will be essentially the longest lasting of any within-range cycle that could be picked today. Although it starts out currently having the shortest mean year of all points in the solar cycle, by the time that will eventually reach perihelion, all other points in the solar cycle will have shorter mean years, and after that it will go "out-of-range" (too long).

If one chooses a cycle having a slightly shorter mean year then the primary calendar season gets closer to aphelion, but the secondary season becomes quite unstable and shifts to perihelion.

Anybody who wishes to experiment with calendar seasons is welcome to download my freeware Excel spreadsheet "Find Solar Calendar Seasons" with macro that can compute and plot the calendar seasons for any desired leap cycle (and was used to generate the above calendar seasons charts):

http://individual.utoronto.ca/kalendis/leap/Find-Solar-Calendar-Seasons.xls

The 327-year leap week cycle is built into my freeware calendrical calculator, Kalendis, as an optional experimental alternative for the Symmetry454 or Symmetry010 or related leap week variants.

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/leap/
http://www.sym454.org/seasons/
http://www.sym454.org/kalendis/

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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Michael Ossipoff
Just a brief reminder:

If the mean-year (reference-year) of the calendar is the tropical year defined with respect to one particular (favored) point of the ecliptic, then the maximum displacement of the calendar, over a year, will be greater than it would be if the reference-year were the MTY of the mean of the lengths of the two equinox years.

(I repeat that the use of the mean of the lengths of the two equinox years is a suggestion of mine, intended as a compromise between the vernal equinoxes of the north and south hemispheres--in recognition of the importance of the vernal equinox to many people.)

But, as I've also said, it seems to me that there's much appeal to the use of the June solstice year as the calendar's reference-year, instead of minimizing year-round max displacement. If that were preferred, I wouldn't argue against it.

As for the matter of maybe changing to a different reference-year in 10,000 years, that's something that the people then will deal with, and needn't concern us now.

Michael Ossipoff




On Thu, Jan 19, 2017 at 8:32 AM, Karl Palmen <[hidden email]> wrote:

Dear Walter, Irv, Michael and Calendar People

 

I understand the quote of Irv quite differently to the way Walter does.

 

I see it as an extreme form of my idea that any mean year that is in range of the tropical years starting at any solar ecliptic longitude will do, which maximises the lifetime of each successive arithmetic calendar. One does not change the arithmetic calendar until its mean year reaches the edge of the range, when it will be the perihelion tropical year. Then one changes the mean year to the other edge of the range, which is then the aphelion tropical year. There is one difference and that Irv has the epoch of the first leap calendar is today.

 

This has nothing to do with Walter’s proposed modification of the Indian National calendar, which the mean year would depend on, which month you start the year. Such a calendar could have much lower actual displacements over a precession cycle than anything Michael Ossipoff  has proposed, but is more complicated. I have looked into the behaviour of such calendars in past E-mails.

 

Karl

 

16(05(22

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 19 January 2017 04:59
To: [hidden email]


Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 

Dear Irv, and calendar list:

Recently, Irv made the following statement in a discussion about Solar Calendar Design:

 

"Therefore, if one isn't "married" to a particular equinox or solstice for religious or other reasons, it makes sense to choose a calendar mean year that is currently equal to the shortest current solar mean year, at aphelion, and let it run until it eventually becomes the mean year at perihelion."

I find this statement rather interesting, and, if I understand it correctly, I believe that it can be implemented in a way that I have mentioned before.

If we take the Indian National Calendar, described here:

https://en.wikipedia.org/wiki/Indian_national_calendar

and shift the month lengths by one month about once every 1800 years, then we can adjust the calendar for the relative lengths of the seasons over the anomalistic cycle.  We can see how as the 31 day months make 6 shifts over the course of about 10,800 years, they are following the course of the apehelion over half of its cycle. Thus, all the seasonal points will shift half a cycle relative to the aphelion and perihelion. 

Thus, in the present era, the northward equinox year has been relatively stable as the 31 day months have shifted across it, but that will change when the northward equinox occurs during the 30 day months, and we will see the northward equinox creep earlier and earlier in the Gregorian Calendar, as that equinox would be shifted from 30 day month to 30 day month in the Indian National Calendar under my shifting proposal.

 With my shifting proposal, the season points would occur very close to the beginnings of the months pf Chaitra, Ashadha, Ashwin, and Pausha over the entire period of the anomalistic cycle.

-Walter Ziobro
  

 

-----Original Message-----
From: Irv Bromberg <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Sun, Jan 15, 2017 2:32 pm
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Amos Shapir [[hidden email]]

Sent: Friday, January 13, 2017 02:52

The term "tropical" in astronomy usually means "pertaining to the seasons", so a tropical year has nothing to do with aphelion and perihelion.


Irv replies further:

The progressive tidal slowing of the Earth rotation rate is unavoidable, notwithstanding that the rate of slowing isn't constant and with present knowledge is partially unpredictable. Therefore, if one isn't "married" to a particular equinox or solstice for religious or other reasons, it makes sense to choose a calendar mean year that is currently equal to the shortest current solar mean year, at aphelion, and let it run until it eventually becomes the mean year at perihelion.

Presently, the aphelion mean year is very close to the mean year of the 327-year cycle (with 58 leap weeks or 79 leap days), whose mean year is 365+79/327 days = 365d 5h 47m 53+43/109s (approximately 53.4 seconds) = approximately 365.241590214 days, and, because of the current proximity of aphelion to the north solstice, it so happens that it is also an excellent leap cycle for approximating the current mean north solstitial mean year until beyond the year 12000 AD (depending on what happens to Delta T in the future).

For most calendar cycles there exist two distinctly separated "calendar seasons": the more stable primary season where the variation over the long term is quite small, and the less stable secondary season that has more variation over the long term. For example, see these charts for the 293-, 524-, 33-, and 400-year cycles:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-293.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-524.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-33.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-400.pdf

In the case of a calendar cycle having a mean year equal to that at aphelion, however, the primary and secondary calendar seasons are very close together, as can be seen in this chart for the 327-year cycle:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-327.pdf

This indicates that the 327-year cycle has extended seasonal stability for calendrical purposes, and will be essentially the longest lasting of any within-range cycle that could be picked today. Although it starts out currently having the shortest mean year of all points in the solar cycle, by the time that will eventually reach perihelion, all other points in the solar cycle will have shorter mean years, and after that it will go "out-of-range" (too long).

If one chooses a cycle having a slightly shorter mean year then the primary calendar season gets closer to aphelion, but the secondary season becomes quite unstable and shifts to perihelion.

Anybody who wishes to experiment with calendar seasons is welcome to download my freeware Excel spreadsheet "Find Solar Calendar Seasons" with macro that can compute and plot the calendar seasons for any desired leap cycle (and was used to generate the above calendar seasons charts):

http://individual.utoronto.ca/kalendis/leap/Find-Solar-Calendar-Seasons.xls

The 327-year leap week cycle is built into my freeware calendrical calculator, Kalendis, as an optional experimental alternative for the Symmetry454 or Symmetry010 or related leap week variants.

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/leap/
http://www.sym454.org/seasons/
http://www.sym454.org/kalendis/


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Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

Michael Ossipoff
Typo:

I accidentally wrote:

"...the MTY of the mean of the lengths of the two equinox years."

I meant:

"...the MTY or the mean of the lengths of the two equinox years."

Michael Ossipoff



On Thu, Jan 19, 2017 at 3:49 PM, Michael Ossipoff <[hidden email]> wrote:
Just a brief reminder:

If the mean-year (reference-year) of the calendar is the tropical year defined with respect to one particular (favored) point of the ecliptic, then the maximum displacement of the calendar, over a year, will be greater than it would be if the reference-year were the MTY of the mean of the lengths of the two equinox years.

(I repeat that the use of the mean of the lengths of the two equinox years is a suggestion of mine, intended as a compromise between the vernal equinoxes of the north and south hemispheres--in recognition of the importance of the vernal equinox to many people.)

But, as I've also said, it seems to me that there's much appeal to the use of the June solstice year as the calendar's reference-year, instead of minimizing year-round max displacement. If that were preferred, I wouldn't argue against it.

As for the matter of maybe changing to a different reference-year in 10,000 years, that's something that the people then will deal with, and needn't concern us now.

Michael Ossipoff




On Thu, Jan 19, 2017 at 8:32 AM, Karl Palmen <[hidden email]> wrote:

Dear Walter, Irv, Michael and Calendar People

 

I understand the quote of Irv quite differently to the way Walter does.

 

I see it as an extreme form of my idea that any mean year that is in range of the tropical years starting at any solar ecliptic longitude will do, which maximises the lifetime of each successive arithmetic calendar. One does not change the arithmetic calendar until its mean year reaches the edge of the range, when it will be the perihelion tropical year. Then one changes the mean year to the other edge of the range, which is then the aphelion tropical year. There is one difference and that Irv has the epoch of the first leap calendar is today.

 

This has nothing to do with Walter’s proposed modification of the Indian National calendar, which the mean year would depend on, which month you start the year. Such a calendar could have much lower actual displacements over a precession cycle than anything Michael Ossipoff  has proposed, but is more complicated. I have looked into the behaviour of such calendars in past E-mails.

 

Karl

 

16(05(22

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 19 January 2017 04:59
To: [hidden email]


Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

 

Dear Irv, and calendar list:

Recently, Irv made the following statement in a discussion about Solar Calendar Design:

 

"Therefore, if one isn't "married" to a particular equinox or solstice for religious or other reasons, it makes sense to choose a calendar mean year that is currently equal to the shortest current solar mean year, at aphelion, and let it run until it eventually becomes the mean year at perihelion."

I find this statement rather interesting, and, if I understand it correctly, I believe that it can be implemented in a way that I have mentioned before.

If we take the Indian National Calendar, described here:

https://en.wikipedia.org/wiki/Indian_national_calendar

and shift the month lengths by one month about once every 1800 years, then we can adjust the calendar for the relative lengths of the seasons over the anomalistic cycle.  We can see how as the 31 day months make 6 shifts over the course of about 10,800 years, they are following the course of the apehelion over half of its cycle. Thus, all the seasonal points will shift half a cycle relative to the aphelion and perihelion. 

Thus, in the present era, the northward equinox year has been relatively stable as the 31 day months have shifted across it, but that will change when the northward equinox occurs during the 30 day months, and we will see the northward equinox creep earlier and earlier in the Gregorian Calendar, as that equinox would be shifted from 30 day month to 30 day month in the Indian National Calendar under my shifting proposal.

 With my shifting proposal, the season points would occur very close to the beginnings of the months pf Chaitra, Ashadha, Ashwin, and Pausha over the entire period of the anomalistic cycle.

-Walter Ziobro
  

 

-----Original Message-----
From: Irv Bromberg <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Sun, Jan 15, 2017 2:32 pm
Subject: Re: Solar Calendar Design RE: New Henry-Hanke calendar/website, old shortcomings

From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Amos Shapir [[hidden email]]

Sent: Friday, January 13, 2017 02:52

The term "tropical" in astronomy usually means "pertaining to the seasons", so a tropical year has nothing to do with aphelion and perihelion.


Irv replies further:

The progressive tidal slowing of the Earth rotation rate is unavoidable, notwithstanding that the rate of slowing isn't constant and with present knowledge is partially unpredictable. Therefore, if one isn't "married" to a particular equinox or solstice for religious or other reasons, it makes sense to choose a calendar mean year that is currently equal to the shortest current solar mean year, at aphelion, and let it run until it eventually becomes the mean year at perihelion.

Presently, the aphelion mean year is very close to the mean year of the 327-year cycle (with 58 leap weeks or 79 leap days), whose mean year is 365+79/327 days = 365d 5h 47m 53+43/109s (approximately 53.4 seconds) = approximately 365.241590214 days, and, because of the current proximity of aphelion to the north solstice, it so happens that it is also an excellent leap cycle for approximating the current mean north solstitial mean year until beyond the year 12000 AD (depending on what happens to Delta T in the future).

For most calendar cycles there exist two distinctly separated "calendar seasons": the more stable primary season where the variation over the long term is quite small, and the less stable secondary season that has more variation over the long term. For example, see these charts for the 293-, 524-, 33-, and 400-year cycles:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-293.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-524.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-33.pdf
http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-400.pdf

In the case of a calendar cycle having a mean year equal to that at aphelion, however, the primary and secondary calendar seasons are very close together, as can be seen in this chart for the 327-year cycle:

http://individual.utoronto.ca/kalendis/leap/Solar-Calendar-Seasons-327.pdf

This indicates that the 327-year cycle has extended seasonal stability for calendrical purposes, and will be essentially the longest lasting of any within-range cycle that could be picked today. Although it starts out currently having the shortest mean year of all points in the solar cycle, by the time that will eventually reach perihelion, all other points in the solar cycle will have shorter mean years, and after that it will go "out-of-range" (too long).

If one chooses a cycle having a slightly shorter mean year then the primary calendar season gets closer to aphelion, but the secondary season becomes quite unstable and shifts to perihelion.

Anybody who wishes to experiment with calendar seasons is welcome to download my freeware Excel spreadsheet "Find Solar Calendar Seasons" with macro that can compute and plot the calendar seasons for any desired leap cycle (and was used to generate the above calendar seasons charts):

http://individual.utoronto.ca/kalendis/leap/Find-Solar-Calendar-Seasons.xls

The 327-year leap week cycle is built into my freeware calendrical calculator, Kalendis, as an optional experimental alternative for the Symmetry454 or Symmetry010 or related leap week variants.

-- Irv Bromberg, University of Toronto, Canada

http://www.sym454.org/leap/
http://www.sym454.org/seasons/
http://www.sym454.org/kalendis/



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