Precise Astronomical New Year

[publius]

The mechanics of astronomical time has always made me MEGLO, but yet I still want to know stuff. We have a local solar day defintion of new year, simply 12 midnight in our time zone at the Jan 1 transition.

However, the year can be precisely defined in terms of the earth's *orbit*. I once thought that precession of the spin axis would skew the year, and in 12,000 years or so, it would be cold in July , but then I learned that no, the defintion of the year takes precession into account -- it's got to do with where the earth's axis is pointing relative to the orbit. The US Naval Observatory has this down pat I'm sure.

So, the year has to do with completing one orbital cycle where the earth's axis "comes back to the starting point". Now, however that works out, the center of mass of the earth will be at some point at that time, and our rotational position on the surface is irrelevant.

Thus, I would declare the "real New Year's" would be this exact time, adjusted to our local time zone.

Now, when is that? I suspect that leap year considerations (the nasty fact that the orbital cycle is not an integral number of solar day cycles) can can skew that back and forth over the 4 year cycle, probably up to 3/4 of a day. And then when you add local time zone, it might well occur on Dec 31st, all the way to Jan 2 or something.

-Richard

[grant hutchison]

I'm not sure there's such a thing.
It would have to be defined by the Sun passing through some particular southern latitude, corresponding to some agreed time interval after the December solstice which would represent the average time between solstice and the turn of the western calendar over some period of averaging, at some location. It seems like a clunky entity with no great purpose.
I think the solstices and equinoxes do the job you're thinking of, mapping out the return of the sun to the same position in the Earth's sky.

Grant Hutchison

[Kaptain K]

Am I the only one here who reads the BABBlog?

[publius]

I'm not sure there's such a thing.
It would have to be defined by the Sun passing through some particular southern latitude, corresponding to some agreed time interval after the December solstice which would represent the average time between solstice and the turn of the western calendar over some period of averaging, at some location. It seems like a clunky entity with no great purpose.
I think the solstices and equinoxes do the job you're thinking of, mapping out the return of the sun to the same position in the Earth's sky.

Grant Hutchison

Ah, I forgot about the that. The actual markers of the points of the tropical year cycle are the solistices and equionixes, but we unfornutately don't peg the roll over of our calendar on those days. *SIGH*

Winter solstice, around Dec 21st is the closest, but we'd have to say roughly 10 - 11 days after that to make any coincide with Jan 1. And then, if we wanted to be astronomical with that, we couldn't really use (solar) days, we need some defintion of how much the sun moved over that period......

So the best I can do is stick with the actual marker events, and celebrate "one seasonal cycle" at the winter solstice.

Whoever came up with this was crazy. But seriously, it may be the best we can do with what we've got, a dance of several cycles that affect day/night and the seasons which aren't integral multiples of each other. I doubt any other calendar we could come up with would really be any better.


-Richard

[hhEb09'1]

Winter solstice, around Dec 21st is the closest, but we'd have to say roughly 10 - 11 days after that to make any coincide with Jan 1. And then, if we wanted to be astronomical with that, we couldn't really use (solar) days, we need some defintion of how much the sun moved over that period......

You could use solar days if you like, it'd just be a conversion--unless you anticipate changing it each year, for some reason. And there are reasons, that I can think of.

Whoever came up with this was crazy. But seriously, it may be the best we can do with what we've got, a dance of several cycles that affect day/night and the seasons which aren't integral multiples of each other. I doubt any other calendar we could come up with would really be any better.

They've been working on it for a long time

PS: the actual time that the year takes to go around the sun, on average, is longer than 365.25 solar days, but our calendar treats the years as shorter than 365.25--that's why we don't have a leap year in years that end in 00 (with the exception of years like the one recently passed). That's good--otherwise, we might be forced to have a year with two leap days.

[Celestial Mechanic]

The Besselian Year might be what you are seeking as an "astronomical new year". Wikipedia gives the following definition:

The Besselian year is a tropical year that starts when the fictitious mean Sun reaches an ecliptic longitude of 280°. This is currently on or close to 1 January. It is named after the 19th century German astronomer and mathematician Friedrich Bessel. An approximate formula to compute the current time in Besselian years from the Julian day is:

B = 2,000 + (JD - 2,451,544.53)/365.242189

The equinox occurs when the Sun reaches ecliptic longitude 270 degrees, the addition of ten more degrees brings it close to January 1. This year is no longer in use.

[publius]

PS: the actual time that the year takes to go around the sun, on average, is longer than 365.25 solar days, but our calendar treats the years as shorter than 365.25--that's why we don't have a leap year in years that end in 00 (with the exception of years like the one recently passed). That's good--otherwise, we might be forced to have a year with two leap days.

The difference between those is the precession, I think. The earth's axis precesses every so slightly over each orbit and makes the tropical year defintion be slightly less that one actual orbital period. This is how precession is "automatically" taken into account. It's sort of the same thing as the sidereal day vs solar day.

Now, about the leap year cycle. That's the 100 year and 400 year cycle, right? You skip leap year every century marker, except for those that are multiples of 4 centuries. 2000 was a multiple of 400, so we hit that then.

And IIRC, that still will run out sync, but over a very long time, thousands of years -- so we will end up either adding an extra leap day, or subtracting one at some point, unless we want to add another 1000 or 4000 year cycle or whatever. It might take longer for the error to add up to a day, though, I don't know.

The way I think of it when I'm forced to is to imagine the little ball going around in the circle. Each year, we get ahead of ourselves in days by about 1/4 year. So every four years, we add an extra day to re-sync.

But, since the "extra" is slightly less than 1/4, we get behind ourselves a little bit every 4 years. After 100 years, that difference adds up to about 1 day, so we skip a leap year day.

But then there, it was a little less than a day, so every 100 years, we're getting a bit ahead of ourselves still, and after 400 years, we're back to a day there, so we don't skip that.

And that's where the official leap year cycle ends. But we're get a little behind every 400 years.............................*SIGH*

Anyway, if one is interested in doing it, just take the actual fraction of day 365.24nnnnnn. Take .24nnnnnn and mulitply by 4. That's slightly less that one, so take the difference with he remaining fraction is how much you're out of sync every 4 years, but of opposite sign. You'll see if you multiply that by 25 (100 years), you'll have a whole number again, but slightly greater than 1. That's the 100 year cycle. That less one give you 100 year error. Multiply that by 4 and you've got slightly less tha 1 again. Now, the remaining fraction is the error that we don't account for.

I absolutely despise calculations like that........

-Richard

[hhEb09'1]

The difference between those is the precession, I think. The earth's axis precesses every so slightly over each orbit and makes the tropical year defintion be slightly less that one actual orbital period. This is how precession is "automatically" taken into account. It's sort of the same thing as the sidereal day vs solar day.

Yes, the difference is the precession. And it's sorta the same thing in the day, but it's the difference between one sidereal day, and another!

I absolutely despise calculations like that........

You're going to love that link

[rudolpho]

"It would have to be defined by the Sun passing through some particular southern latitude, corresponding to some agreed time interval after the December solstice which would represent the average time between solstice and the turn of the western calendar over some period of averaging, at some location."

Posted by Grant

Maybe english is not my first language - and therefore this elegant sentence leaves me behind somehow

But then again - i did not understand the problem from the beginning...

[a1call]

The Georgian calendar while very accurate is not the most accurate calendar. It is based on approximating the actual length of a year (365 days, 5 hours, 48 minutes, 45.51 seconds). It does so by having a leap year if the year number is divisible by four but not 100. in other words a Georgian year has an average length of 365 days, 5 hours, 45 minutes, 36 seconds. This has an average error of 3 minutes, 9.51 seconds per year. Though very accurate it falls back 1 day (about) every 456 years. The most accurate calendar in the world is the Persian calendar which is synchronized on the Spring solar equinox. Persian new year is celebrated on the first day of Spring. It is said that Persians have celebrated the first day of Spring for the last 5, 6000 years.

Added:
I looked up a leap year and forgot to mention if the year is divisible by 400 then it is a leap year this makes the average year length 365 days, 5 hours, 49 minutes, 12 seconds.This reduces the error down to +26.49 seconds. This way on the average Georgian Calendar will err 1 day every 3390 years. In practice though the error is already in. 30 years ago Spring Equinox would fall on 21st of March, nowadays it falls on the 20th (at least in the Eastern time zone).

[publius]

Added:
I looked up a leap year and forgot to mention if the year is divisible by 400 then it is a leap year this makes the average year length 365 days, 5 hours, 49 minutes, 12 seconds.This reduces the error down to +26.49 seconds. This way on the average Georgian Calendar will err 1 day every 3390 years. In practice though the error is already in. 30 years ago Spring Equinox would fall on 21st of March, nowadays it falls on the 20th (at least in the Eastern time zone).

Ah, so it will take ten 400 year cycles to err a day. That suggests simply a 4000 year cycle, where we skip a leap year on multiples of 4000. I'll let you figure out how many of those cycles it takes to get back to day. Wait a minute, we'd have to make sure that kept the error alternating sign as was the idea -- we might need to do it every 9*400 = 3600 years, or even 8 for 3200 years........

-Richard

[hhEb09'1]

Added:
I looked up a leap year and forgot to mention if the year is divisible by 400 then it is a leap year this makes the average year length 365 days, 5 hours, 49 minutes, 12 seconds.This reduces the error down to +26.49 seconds. This way on the average Georgian Calendar will err 1 day every 3390 years.

I don't know how you missed that, everyone was talking about it seven years ago.

In practice though the error is already in. 30 years ago Spring Equinox would fall on 21st of March, nowadays it falls on the 20th (at least in the Eastern time zone).

No, remember, the calendar accumulated error for 400 years--the leap day in 2000 corrected that. If there had been no correction, the equinox would be falling a day later. Now we're back on track.

[a1call]

One might think so but check this table.
Note that you will have to subtract 5 hours from UTC to get EST. And also note that any time zone to the west upto International Date line would be even earlier on 20th.

[hhEb09'1]

Here's another article, from space.com.

[grant hutchison]

No, remember, the calendar accumulated error for 400 years--the leap day in 2000 corrected that. If there had been no correction, the equinox would be falling a day later. Now we're back on track.

Well, a case might be made for saying that the calendar was corrected by the missed leap years in 1700, 1800 and 1900 as much as by the leap year in 2000.
The solstices and equinoxes progress steadily backwards through a sequence of Julian years (a strict alternation of three standard years with one leap year), because the tropical year is a little shorter than 365.25 days. The seasonal shift accumulates to the tune of 0.78 days per century. Skipping a leap year at the end of a century resets the accumulated error, shifting the seasons forward a day in the calendar; the overcompensation amounts to 0.22 days. After three such corrections, we arrive at our fourth century with the seasons lagging only 0.12 days behind the calendar: (0.22+0.22+0.22-0.78). So we let that one lie and have a leap year in the normal 3:1 pattern, as we did in 2000.
After 4000 years, the 0.12-days-in-four-centuries deficit adds up to 1.2 days, so in the year 4000 we might consider breaking the four-century pattern and having a leap year: that's one suggestion for the long-term correction of the Gregorian calendar.

Grant Hutchison

[SeanF]

Well, a case might be made for saying that the calendar was corrected by the missed leap years in 1700, 1800 and 1900 as much as by the leap year in 2000.

All the same thing, isn't it? A calendar of leap years every four years except in the 00 years is off by about one day per four hundred years, so excepting the exception in 2000 "corrected" that.

After 4000 years, the 0.12-days-in-four-centuries deficit adds up to 1.2 days, so in the year 4000 we might consider breaking the four-century pattern and having a leap year: that's one suggestion for the long-term correction of the Gregorian calendar.

Having a leap year in 4000 is part of the current pattern, though, so it wouldn't correct anything. We'd have to have one in 3900 or 4100, right?

Actually, wouldn't we be closest to exactly one day off in 3300, thus making that the best choice for re-including an omitted leap day?

[grant hutchison]

All the same thing, isn't it? A calendar of leap years every four years except in the 00 years is off by about one day per four hundred years, so excepting the exception in 2000 "corrected" that.

That was rather my point; you need the complete four-hundred year cycle of omitted and honoured leap-centuries to make the thing work. They were introduced together to do the work together.

Having a leap year in 4000 is part of the current pattern, though ...

My bad.
Of course I should have said that we'd break the Gregorian four-century cycle by omitting the scheduled leap day in 4000. That would undo one day of the accumulated 1.2 day deficit.

Grant Hutchison

[hhEb09'1]

Well, a case might be made for saying that the calendar was corrected by the missed leap years in 1700, 1800 and 1900 as much as by the leap year in 2000.

I would never dispute that, though. I was just addressing the comment that the 4000 year error was already in place.

[MAPNUT]

The equinox occurs when the Sun reaches ecliptic longitude 270 degrees, the addition of ten more degrees brings it close to January 1. This year is no longer in use.

What's ecliptic longitude? And can someone identify a star that's directly overhead at midnight on Dec. 31/Jan 1? There would have to be a quarter-degree leeway to allow for the leap days. In other words can the start of the year be fixed on a coordinate system in space?

[grant hutchison]

I would never dispute that, though. I was just addressing the comment that the 4000 year error was already in place.

Okay.
I chimed in because when you wrote:

the calendar accumulated error for 400 years--the leap day in 2000 corrected that.

it could be read as suggesting that the 2000 leap year was doing all the work on its own.

I guess what we're both saying to a1call is that looking back 30 years will always show up a shift in the dates of solstices and equinoxes, because the correction cycle operates over a longer period than that.

Grant Hutchison

[grant hutchison]

What's ecliptic longitude?

Angular distance measured along the ecliptic (the plane of the Earth's orbit) from the First Point of Aries (the position of the Sun at March equinox).

In other words can the start of the year be fixed on a coordinate system in space?

It can't, because the end of the calendar year isn't fixed relative to the solstice, and the solstice isn't fixed in space (it migrates slowly backwards around Earth's orbit).

Grant Hutchison

[a1call]

Perhaps some simplification is in order. Consider the upcoming Spring equinox. At the moment that it is delivered, there is a longitude on Earth along which it will be midnight. We will call this longitude A. For the sake of this argument we will set this longitude as international dateline. Additionally we will reset the calendar as year 0 and the date of the equinox delivery as Mach 21st. In other words the moment of the equinox will be March 21st all over the world. Note that with such an arrangement the points immediately to the right of the longitude A will be on 21st of March for the next 3398 years at the moment of Spring Equinox delivery, never once falling on 20th or 22nd. This is true for these points only and the error will increase for other longitudes. As an extreme the points immediately to the left of the longitude A and up to 5 hours, 48 minutes, 45.51 seconds in longitude will experience an error as early as year 1,meaning the next spring equinox will fall on March 22nd. This is because the Spring equinox of year 1 will be at 5:49 AM with respect to locales on Longitude A.
The point here is that it does not necessarily take many years for the Georgian calendar to accumulate errors into more than a day. Depending on where the international date line is, most points will have a head start.

In respect to the title of this thread: "Precise Astronomical New Year ", IMHO there is only one way of achieving this.
* The year has to be synchronized with a solar orbital event such as equinoxes or solstices (as it is with Persian or Baha'i Calendars)
* The international Dateline will have to reset each year to the longitude at which when the year is synchronized, a new calendar day is starting (In Western tradition that would be midnight.)

[hhEb09'1]

The point here is that it does not necessarily take many years for the Georgian calendar to accumulate errors into more than a day. Depending on where the international date line is, most points will have a head start.

Errors? I'm not convinced. The issues that you are describing have to do with time zones, and datelines, not the calendar.

[Kaptain K]

The international Dateline will have to reset each year to the longitude at which when the year is synchronized, a new calendar day is starting (In Western tradition that would be midnight.)

Like that's gonna happen!

[MAPNUT]

Angular distance measured along the ecliptic (the plane of the Earth's orbit) from the First Point of Aries (the position of the Sun at March equinox).

It can't, because the end of the calendar year isn't fixed relative to the solstice, and the solstice isn't fixed in space (it migrates slowly backwards around Earth's orbit).

Grant Hutchison

Still, if the Equinox can be matched to the First Point of Aries (whatever that is), there must be a similar point on the Zodiac that lines up with New Year's Day (plus or minus 12 hours, and not permanently) if I understand you right, Grant.

[grant hutchison]

Still, if the Equinox can be matched to the First Point of Aries (whatever that is), there must be a similar point on the Zodiac that lines up with New Year's Day (plus or minus 12 hours, and not permanently) if I understand you right, Grant.

Except it's a different point every year. The equinox is defined against the sun's position in the Earth's sky, rather than against the zodiac. So you could concoct a solar position that you called "official start of year", which would be when the sun passed through some latitude a little north of the Tropic of Capricorn. But since the New Year comes at a variable time after the December solstice, you'd need to do some sort of averaging, relevant to a particular time zone, over some long period, to produce a compromise solar position that would be wrong every year by some variable amount.
It just doesn't seem like a useful concept. I guess the problem (as I see it) is that the calendar doesn't operate to an astronomical schedule, except on average, over a timescale of centuries, so trying to tie it to a fixed astronomical event every year is always going to be a cludge of some kind.

Grant Hutchison

[Kaptain K]

...the First Point of Aries (whatever that is)...

The "First Point of Aries" is (by definition) the point where the Sun, moving north, crosses the Celestial Equator (vernal equinox). although (due to precession) it is no longer in Aries.

[a1call]

Like that's gonna happen!

A few points about IDL I did not know before today:
*As such the term ‘International Date Line’ is in fact a misnomer. Its exact course was never defined by any international treaty, law or agreement. At the end of the 19th century, George Davidson (1825 - 1911), the pioneer scientist and surveyor of the American West Coast, summed up the situation as:

“There is no International Date Line. The theoretical line is 180° from Greenwich, but the line actually used is the result of agreement among the commercial steamships of the principal maritime countries.”

*The IDL drawn on the map on this page and all other maps is now and always has been an artificial construct of cartographers—it is de facto (of fact). No international organization nor any treaty between nations has fixed the 'straight line' segments and their junctions. All nations unilaterally determine their standard time zones, which are applicable only on land and adjacent territorial waters. These national zones do not extend into international waters. Indeed, the 1884 International Meridian Conference explicitly refused to propose or agree to any time zones, despite 'common knowledge' that they did, stating that they were outside its purview. The conference resolved that the Universal Day (midnight-to-midnight Greenwich Mean Time), which it did agree to, "shall not interfere with the use of local or standard time where desirable."

* Most Calendars including the Gregorian calendar predate any proposals for an IDT.

* Should there ever be an "international" IDN, it is not likely to prevent anyone from inventing as of yet none existence calendar which chooses not to respect it in favor calendar accuracy.

* Annually reset IDL is the natural outcome of different locales synchronizing their calendars to an Orbital event and would not require any extra convention

[hhEb09'1]

* Annually reset IDL is the natural outcome of different locales synchronizing their calendars to an Orbital event and would not require any extra convention

You seem to be suggesting that the various locales define their year to have a fractional part of a day. As Kaptain K said, that's never going to happen