Calendar's Centre Of Oscillation RE: Reference Year Displacement

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Calendar's Centre Of Oscillation RE: Reference Year Displacement

Karl Palmen

Dear Michael and Calendar People

 

I comment below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 13 February 2017 16:25
To: [hidden email]
Subject: Re: Reference Year Displacement

 

 

 

On Mon, Feb 13, 2017 at 8:36 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Here is my attempt to explain what I meant by DR in my guess at what Michael meant by calendar’s centre of oscillation.

 

...except that a guess wasn't needed, because I clearly stated what i was referring to.

I'll say it just one more time:

I was referring to, and said at the time that I was referring to, the center (midpoint) of the oscillation an SEL's calrendar date (including time of day), from one leapyear to the next.

 

KARL REPLIES:  Is this the same as the date of the SEL with the calculated displacement subtracted from it as I have demonstrated?

If not, how would you go about measuring it?

Also this cannot be a calendar’s centre of oscillation. It can be a SEL’s centre of oscillation in a calendar. My guess was different also for that reason.

 

Michael has mentioned a reference year and this reference year has a length, which he sets his calendar mean year (Y) near to. Unlike Y, the length of the reference year changes slowly from year to year, because of changes in Earth’s rotation, precession rate etc.

 

and planetary perturbations.
 

 

The reference year displacement (DR) is reckoned in the same way as the calculated displacement (DC), but instead of using Y, one uses the exact length of the reference year for that year.

 

Not practical for use with a civil-calendar leapyear-rule.

 

KARL REPLIED: I never stated that is was practical for a civil-calendar leap year rule. However one could use the difference between it and the calculated displacement to determine how much the civil calendar is off. It is this difference that was my guess and it applies to the calendar rather than a single SEL.


 

 

I put this DR in my guess rather than actual displacement, because Michael referred to this centre of oscillation being used to calculate how far off the calendar is (with respect to its reference year).

 

...due to Y being different from even the initial value of the length of an SEL's tropical-year. I wasn't interested in gradual change in the actual length of the reverence-year, over the milennia. I was interested in the initial difference between Y and the length of some SEL's tropical year. 

...such as you'd have if you used one SEL's tropical year, and were concerned about the calendar-date of a different SEL.

But yes, it goes without saying that later gradual change in the actual length of the reference year (whose assumed length is represented by Y) will cause additional drift.

That isn't controversial, and I never said otherwise. It just wasn't what I was talking about. I was talking about the relatively large and immediate drift resulting from the use of one SEL's tropical year, when one is looking at another SEL's calendar-date constancy.

KARL REPLIES:  One would also get drifts in the SELs, if one were to use a Y near a mean tropical year, but over a precession cycle, the maximum drift, would be about half the maximum drift that would occur if one were to use Y near the tropical year of one SEL. This drift can be seen clearly if one subtracts the calculated displacement from the date of each SEL.

At present, the March equinox is about 186.4 days before the September equinox. This is 3.8 days more than half a tropical year (of about 182.6 days). After about 11 thousand years, when the perihelion and aphelion have swapped their SELs, this interval will be 3.8 days less at about 178.8 days. So if Y is kept near the mean tropical year, both equinoxes would drift about 3.8 days in opposite directions, but if Y were kept near the tropical year of one equinox,  the other equinox would drift about 7.6 days. I chose the equinoxes as an example because the perihelion is currently near halfway between equinoxes. One can apply the argument to any SEL and its opposite, from the time the perihelion is halfway between them.

Karl

16(06(18

 

Michael Ossipoff

 

 

 

 

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Re: Calendar's Centre Of Oscillation RE: Reference Year Displacement

Michael Ossipoff


On Tue, Feb 14, 2017 at 11:21 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

I comment below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 13 February 2017 16:25
To: [hidden email]
Subject: Re: Reference Year Displacement

 

 

Karl:

 
 

I'd said:

 


I was referring to, and said at the time that I was referring to, the center (midpoint) of the oscillation an SEL's calrendar date (including time of day), from one leapyear to the next.

 

KARL REPLIES:  Is this the same as the date of the SEL with the calculated displacement subtracted from it as I have demonstrated?


No.

As I've been saying, when I spoke of drift of the midpoint of an SEL's calendar-date, I was referring to its drift due to a mismatch between Y and that SEL's tropical-year.

...at and soon after (certainly during the millennium of) the calendar's start. I wasn't concerned about future changes in the length of that SEL's tropical year. I was interested only in the closeness of Y to an SEL's tropical-year-length at the time of a calendar's epoch or adoption-date.

Drift refers to a unidirectional variation, and doesn't include any oscillations.


 

If not, how would you go about measuring it?


How would I measure the center of oscillation of an SEL's calendar-date, from one leapyear to the next?

Over the duration between one leapyear and the next, find the extreme values of the date of that SEL. Find the midpoint of those two dates. That's the center of oscillation of that SEL's calendar-date from one leapyear to the next.

But of course I was more interested in finding a Y value that would minimiize the drift of that center (by that Y being close to that SEL's tropical year), rather than measuring that drift.
 

Also this cannot be a calendar’s centre of oscillation. It can be a SEL’s centre of oscillation in a calendar.


That's what I said.

But of course the SEL's calendar-dates are dates that belong to that calendar, are part of that calendar,


 

 


  Quoting what I said, and then replying to Karl farther down:

 

...due to Y being different from even the initial value of the length of an SEL's tropical-year. I wasn't interested in gradual change in the actual length of the reverence-year, over the milennia. I was interested in the initial difference between Y and the length of some SEL's tropical year. 

...such as you'd have if you used one SEL's tropical year, and were concerned about the calendar-date of a different SEL.

But yes, it goes without saying that later gradual change in the actual length of the reference year (whose assumed length is represented by Y) will cause additional drift.

That isn't controversial, and I never said otherwise. It just wasn't what I was talking about. I was talking about the relatively large and immediate drift resulting from the use of one SEL's tropical year, when one is looking at another SEL's calendar-date constancy.

KARL REPLIES:  One would also get drifts in the SELs, if one were to use a Y near a mean tropical year, but over a precession cycle, the maximum drift, would be about half the maximum drift that would occur if one were to use Y near the tropical year of one SEL.

...a good reason to use the MTY as the reference-year.


 

This drift can be seen clearly if one subtracts the calculated displacement from the date of each SEL.

At present, the March equinox is about 186.4 days before the September equinox. This is 3.8 days more than half a tropical year (of about 182.6 days). After about 11 thousand years, when the perihelion and aphelion have swapped their SELs, this interval will be 3.8 days less at about 178.8 days. So if Y is kept near the mean tropical year, both equinoxes would drift about 3.8 days in opposite directions, but if Y were kept near the tropical year of one equinox,  the other equinox would drift about 7.6 days. I chose the equinoxes as an example because the perihelion is currently near halfway between equinoxes. One can apply the argument to any SEL and its opposite, from the time the perihelion is halfway between them.


So the MTY is the best choice for a calendar's reference-year.

I also considered letting Y be the arithmetic mean of the March equinox tropical year and the September equinox tropical year, on the assumption that people are particularly interested in the Vernal Equinox, in the north and also in the south.

A few questions:

That table whose March equinox times you quoted: Does it specify that it's referring to the time at which the center of the sun crosses the celestial equator, or, rather, to the time at which the center of the sun crosses the mean equinox (for which nutation, and our motion about the Earth-Moon barycenter are averaged-out)?

The changes over the millennia don't seem so important, because a millennium is a very long time.

A millennium ago, the Battle of Hastings hadn't happened yet.

As someone pointed out, it's unlikely that, if we adopt a calendar, it's unlikely to still be in use 1000 years later.

Michael Ossipoff









































 

Karl

16(06(18

 

Michael Ossipoff

 

 

 

 


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Re: Calendar's Centre Of Oscillation RE: Reference Year Displacement

Karl Palmen

Dear Michael and Calendar People

 

Thank you Michael for your reply. I reply below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 18 February 2017 22:04
To: [hidden email]
Subject: Re: Calendar's Centre Of Oscillation RE: Reference Year Displacement

 

 

 

On Tue, Feb 14, 2017 at 11:21 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

I comment below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 13 February 2017 16:25
To: [hidden email]
Subject: Re: Reference Year Displacement

 

 

Karl:

 

 

I'd said:

 

 

I was referring to, and said at the time that I was referring to, the center (midpoint) of the oscillation an SEL's calrendar date (including time of day), from one leapyear to the next.

 

KARL REPLIES:  Is this the same as the date of the SEL with the calculated displacement subtracted from it as I have demonstrated?

 

No.

As I've been saying, when I spoke of drift of the midpoint of an SEL's calendar-date, I was referring to its drift due to a mismatch between Y and that SEL's tropical-year.

...at and soon after (certainly during the millennium of) the calendar's start. I wasn't concerned about future changes in the length of that SEL's tropical year. I was interested only in the closeness of Y to an SEL's tropical-year-length at the time of a calendar's epoch or adoption-date.

 

Drift refers to a unidirectional variation, and doesn't include any oscillations.


 

If not, how would you go about measuring it?

 

How would I measure the center of oscillation of an SEL's calendar-date, from one leapyear to the next?

Over the duration between one leapyear and the next, find the extreme values of the date of that SEL. Find the midpoint of those two dates. That's the center of oscillation of that SEL's calendar-date from one leapyear to the next.

KARL REPLIES: That would oscillate by about 0.79 days for a leap week calendar.  So one must find the centre of that oscillation and so on. The result would then be very close to the SEL’s calendar date minus the calculated displacement, which is simple to calculate and measures the drift very well.

But of course I was more interested in finding a Y value that would minimiize the drift of that center (by that Y being close to that SEL's tropical year), rather than measuring that drift.

 

KARL REPLIES: One must measure the drift to verify that one’s choice of Y is good, given that the SEL’s tropical year length may vary in an irregular manner.

 

Subtracting the displacement is a good way of doing that. It is one good reason for defining the calendar rule in terms of displacement rather than by some other rule as Irv as done. The calculated displacement is a measure of the oscillation arising from the calendar leap year rule, so subtracting it removes that oscillation completely.


 

  Quoting what I said, and then replying to Karl farther down:

 

...due to Y being different from even the initial value of the length of an SEL's tropical-year. I wasn't interested in gradual change in the actual length of the reverence-year, over the milennia. I was interested in the initial difference between Y and the length of some SEL's tropical year. 

...such as you'd have if you used one SEL's tropical year, and were concerned about the calendar-date of a different SEL.

But yes, it goes without saying that later gradual change in the actual length of the reference year (whose assumed length is represented by Y) will cause additional drift.

That isn't controversial, and I never said otherwise. It just wasn't what I was talking about. I was talking about the relatively large and immediate drift resulting from the use of one SEL's tropical year, when one is looking at another SEL's calendar-date constancy.

KARL REPLIES:  One would also get drifts in the SELs, if one were to use a Y near a mean tropical year, but over a precession cycle, the maximum drift, would be about half the maximum drift that would occur if one were to use Y near the tropical year of one SEL.

...a good reason to use the MTY as the reference-year.


 

This drift can be seen clearly if one subtracts the calculated displacement from the date of each SEL.

At present, the March equinox is about 186.4 days before the September equinox. This is 3.8 days more than half a tropical year (of about 182.6 days). After about 11 thousand years, when the perihelion and aphelion have swapped their SELs, this interval will be 3.8 days less at about 178.8 days. So if Y is kept near the mean tropical year, both equinoxes would drift about 3.8 days in opposite directions, but if Y were kept near the tropical year of one equinox,  the other equinox would drift about 7.6 days. I chose the equinoxes as an example because the perihelion is currently near halfway between equinoxes. One can apply the argument to any SEL and its opposite, from the time the perihelion is halfway between them.

 

So the MTY is the best choice for a calendar's reference-year.

KARL REPLIES: That is one thing I intended to show. I also wanted to show the magnitude of the SEL drift over a precession cycle.

 

I also considered letting Y be the arithmetic mean of the March equinox tropical year and the September equinox tropical year, on the assumption that people are particularly interested in the Vernal Equinox, in the north and also in the south.

A few questions:

KARL REPLIES: I see one question.

That table whose March equinox times you quoted: Does it specify that it's referring to the time at which the center of the sun crosses the celestial equator, or, rather, to the time at which the center of the sun crosses the mean equinox (for which nutation, and our motion about the Earth-Moon barycenter are averaged-out)?

KARL REPLIES:  Please visit the table I quoted to find such details. I believe actual equinoxes were used rather than any smoothed out variety.

 

The changes over the millennia don't seem so important, because a millennium is a very long time.

A millennium ago, the Battle of Hastings hadn't happened yet.

As someone pointed out, it's unlikely that, if we adopt a calendar, it's unlikely to still be in use 1000 years later.

KARL REPLIES: If so, then the advantage of using the MTY that we agreed earlier on, would not apply.

Karl

16(06(25

Michael Ossipoff

 

 

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Re: Calendar's Centre Of Oscillation RE: Reference Year Displacement

Michael Ossipoff

As someone pointed out, it's unlikely that, if we adopt a calendar, it's unlikely to still be in use 1000 years later.

KARL REPLIES: If so, then the advantage of using the MTY that we agreed earlier on, would not apply.

It seems to me that the benefit of that would apply right away, because, even if the length of the reference-tropical-year hasn't had time to change, there will still be relatively significant drift of the calendar date of an SEL due to a mismatch between Y and an SEL's tropical-year-lengsth.

Michael Ossipoff


On Tue, Feb 21, 2017 at 8:04 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

Thank you Michael for your reply. I reply below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 18 February 2017 22:04
To: [hidden email]
Subject: Re: Calendar's Centre Of Oscillation RE: Reference Year Displacement

 

 

 

On Tue, Feb 14, 2017 at 11:21 AM, Karl Palmen <[hidden email]> wrote:

Dear Michael and Calendar People

 

I comment below.

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 13 February 2017 16:25
To: [hidden email]
Subject: Re: Reference Year Displacement

 

 

Karl:

 

 

I'd said:

 

 

I was referring to, and said at the time that I was referring to, the center (midpoint) of the oscillation an SEL's calrendar date (including time of day), from one leapyear to the next.

 

KARL REPLIES:  Is this the same as the date of the SEL with the calculated displacement subtracted from it as I have demonstrated?

 

No.

As I've been saying, when I spoke of drift of the midpoint of an SEL's calendar-date, I was referring to its drift due to a mismatch between Y and that SEL's tropical-year.

...at and soon after (certainly during the millennium of) the calendar's start. I wasn't concerned about future changes in the length of that SEL's tropical year. I was interested only in the closeness of Y to an SEL's tropical-year-length at the time of a calendar's epoch or adoption-date.

 

Drift refers to a unidirectional variation, and doesn't include any oscillations.


 

If not, how would you go about measuring it?

 

How would I measure the center of oscillation of an SEL's calendar-date, from one leapyear to the next?

Over the duration between one leapyear and the next, find the extreme values of the date of that SEL. Find the midpoint of those two dates. That's the center of oscillation of that SEL's calendar-date from one leapyear to the next.

KARL REPLIES: That would oscillate by about 0.79 days for a leap week calendar.  So one must find the centre of that oscillation and so on. The result would then be very close to the SEL’s calendar date minus the calculated displacement, which is simple to calculate and measures the drift very well.

But of course I was more interested in finding a Y value that would minimiize the drift of that center (by that Y being close to that SEL's tropical year), rather than measuring that drift.

 

KARL REPLIES: One must measure the drift to verify that one’s choice of Y is good, given that the SEL’s tropical year length may vary in an irregular manner.

 

Subtracting the displacement is a good way of doing that. It is one good reason for defining the calendar rule in terms of displacement rather than by some other rule as Irv as done. The calculated displacement is a measure of the oscillation arising from the calendar leap year rule, so subtracting it removes that oscillation completely.


 

  Quoting what I said, and then replying to Karl farther down:

 

...due to Y being different from even the initial value of the length of an SEL's tropical-year. I wasn't interested in gradual change in the actual length of the reverence-year, over the milennia. I was interested in the initial difference between Y and the length of some SEL's tropical year. 

...such as you'd have if you used one SEL's tropical year, and were concerned about the calendar-date of a different SEL.

But yes, it goes without saying that later gradual change in the actual length of the reference year (whose assumed length is represented by Y) will cause additional drift.

That isn't controversial, and I never said otherwise. It just wasn't what I was talking about. I was talking about the relatively large and immediate drift resulting from the use of one SEL's tropical year, when one is looking at another SEL's calendar-date constancy.

KARL REPLIES:  One would also get drifts in the SELs, if one were to use a Y near a mean tropical year, but over a precession cycle, the maximum drift, would be about half the maximum drift that would occur if one were to use Y near the tropical year of one SEL.

...a good reason to use the MTY as the reference-year.


 

This drift can be seen clearly if one subtracts the calculated displacement from the date of each SEL.

At present, the March equinox is about 186.4 days before the September equinox. This is 3.8 days more than half a tropical year (of about 182.6 days). After about 11 thousand years, when the perihelion and aphelion have swapped their SELs, this interval will be 3.8 days less at about 178.8 days. So if Y is kept near the mean tropical year, both equinoxes would drift about 3.8 days in opposite directions, but if Y were kept near the tropical year of one equinox,  the other equinox would drift about 7.6 days. I chose the equinoxes as an example because the perihelion is currently near halfway between equinoxes. One can apply the argument to any SEL and its opposite, from the time the perihelion is halfway between them.

 

So the MTY is the best choice for a calendar's reference-year.

KARL REPLIES: That is one thing I intended to show. I also wanted to show the magnitude of the SEL drift over a precession cycle.

 

I also considered letting Y be the arithmetic mean of the March equinox tropical year and the September equinox tropical year, on the assumption that people are particularly interested in the Vernal Equinox, in the north and also in the south.

A few questions:

KARL REPLIES: I see one question.

That table whose March equinox times you quoted: Does it specify that it's referring to the time at which the center of the sun crosses the celestial equator, or, rather, to the time at which the center of the sun crosses the mean equinox (for which nutation, and our motion about the Earth-Moon barycenter are averaged-out)?

KARL REPLIES:  Please visit the table I quoted to find such details. I believe actual equinoxes were used rather than any smoothed out variety.

 

The changes over the millennia don't seem so important, because a millennium is a very long time.

A millennium ago, the Battle of Hastings hadn't happened yet.

As someone pointed out, it's unlikely that, if we adopt a calendar, it's unlikely to still be in use 1000 years later.

KARL REPLIES: If so, then the advantage of using the MTY that we agreed earlier on, would not apply.

Karl

16(06(25

Michael Ossipoff

 

 


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Re: Calendar's Centre Of Oscillation RE: Reference Year Displacement

Karl Palmen

Dear Michael and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Michael Ossipoff
Sent: 21 February 2017 16:48
To: [hidden email]
Subject: Re: Calendar's Centre Of Oscillation RE: Reference Year Displacement

 

As someone pointed out, it's unlikely that, if we adopt a calendar, it's unlikely to still be in use 1000 years later.

KARL REPLIES: If so, then the advantage of using the MTY that we agreed earlier on, would not apply.

It seems to me that the benefit of that would apply right away, because, even if the length of the reference-tropical-year hasn't had time to change, there will still be relatively significant drift of the calendar date of an SEL due to a mismatch between Y and an SEL's tropical-year-length.

KAERL REPLIES: Over 1000 years, the maximum and minimum tropical years (365.2428 & 365.2416 days) would diverge by about 1.2 days, so a maximum of 0.6 days would be saved by choosing a mean year halfway between them. This 0.6 days is much less than the 3.8 days mentioned earlier on and  in my opinion is hardly worth bothering with for a leap week calendar.

Karl

16(06(26

Michael Ossipoff

 

 

 

 

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