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posted by Fnord666 on Sunday March 01 2020, @05:52AM   Printer-friendly
from the No-one-told-me-there-would-be-math! dept.

Over at The Conversation, a good explanation of the relation between solar system celestial mechanics and calendars.

Happy February 29! It doesn't come round very often, so make sure you enjoy it.

But why do we have these extra days? Well, if we didn't, the seasons would gradually move around the calendar. Rather than midsummer in the southern hemisphere falling around December 21, it would arrive in January, then February, and so on. After a few centuries, the Australian summer would end up be in July!

And Australians are confused enough as it is. Also, nice to talk about something not scaring the scaredy among us.

The sidereal year
The "sidereal year" is the classic classroom definition. It's the time it takes Earth to complete one lap of the Sun and return to exactly the same place in its orbit, judged by the position of the Sun relative to the background stars.

But one sidereal year doesn't take 365 days. Rather, it takes 365.256 days.

Then there's another problem. In addition to spinning on its axis (which gives us day and night), our planet also wobbles. More accurately, Earth's axis "precesses", spinning around once every 26,000 years or so, like a wobbling spinning top.

Then, there is this:

The tropical year
Fortunately, we have another way to define a year that can fix this problem. Instead of measuring the exact time it takes to orbit the Sun, we can instead measure the time between the vernal equinox of one year and the next.

The vernal equinox is the point in Earth's orbit where the Sun moves from the southern hemisphere of our sky to the northern one. Each year it falls on or around March 21.

The time between one equinox and the next is called the "tropical year", and is slightly shorter than the sidereal year. It comes in at 365.24219 days.

This difference is pretty small (about 20 minutes), but it equates to the amount that Earth's axis has precessed in that time - just under 1/26,000 of a full lap.

Article goes on to compare the Julian calendar, and the (modified) current calendar:

The Gregorian calendar
To fix this very slow drift, a new calendar was devised in the second half of the 16th century. Named after Pope Gregory XIII, the Gregorian calendar was released in 1582.

Of course, given relativity, a flat earth, and the administration's attitude toward science, oh, and Daylight Saving Time, we are lucky just to find lunchtime in any given day. Happy 29th!


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  • (Score: 4, Interesting) by maxwell demon on Sunday March 01 2020, @08:14AM (10 children)

    by maxwell demon (1608) on Sunday March 01 2020, @08:14AM (#964831) Journal

    It's an interesting article that finally cleared up the puzzle how the Gregorian calendar, making the average year a bit shorter is a better approximation to the real year than the Julian calendar, despite the exact length of the year being even longer than the Julian year. The solution is exactly that diferrence between sideral and tropical year that normally is never talked about.

    While I knew about the precession (for the facts that the polar star was not always above the pole, and the fact that astrological zodiac signs don't align with the astronomical apparent movement of the sun through the stars — a fact ignored by modern-day astrologers, and at the same time a mistake that astrologers of the ancient times would never have made because they still actually looked at the stars), I never thought about how it affects the length of the year.

    Having said that, there is another interesting question:

    If you look at the length of the year, you see that a much more regular calendar would be possible: Just have all odd months 30 days and all even months 31 days, except that February has only 30 days in non-leap years. So what made February end up with only 28/29 days?

    --
    The Tao of math: The numbers you can count are not the real numbers.
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  • (Score: 0) by Anonymous Coward on Sunday March 01 2020, @11:09AM

    by Anonymous Coward on Sunday March 01 2020, @11:09AM (#964856)

    Well, by the end of February everyone (except Antipodeans) is really tired of Winter and wants Spring to arrive.

  • (Score: 4, Informative) by Anonymous Coward on Sunday March 01 2020, @11:46AM (7 children)

    by Anonymous Coward on Sunday March 01 2020, @11:46AM (#964860)

    The original Roman calendar was lunar based. A year consisted of 355 days, which is about 12 lunar months. Using just straightforward math, this would have resulted in some months with 29 days and some with 30 days. However, even numbers were considered unlucky at the time, so instead they opted for seven months with 29 days and four months with 31 days. At that time, February was the last month of the year, so it ended up with remaining 28 days. When the calendar was changed to become solar based, February became the second month of the year and the extra 10 days required were inserted after February (not always 10 in each year - sometimes February was also truncated and a complete extra month was inserted). When Caesar decided to clean up this royal mess, he was less afraid of even numbers than his forebears were and spread the 10 extra days over the entire year. For what probably were culturally continuity reasons, he also decided to keep the still required periodic fudge factor at the same place of the year it had occupied all along. In addition, maybe February had a bit of an unlucky omen from having been the only even month so far, so it may have seemed appropriate to keep it as short as possible.

    • (Score: 2) by maxwell demon on Sunday March 01 2020, @01:25PM (2 children)

      by maxwell demon (1608) on Sunday March 01 2020, @01:25PM (#964869) Journal

      Interesting. This also gives a possible explanation for the error mentioned in the article, that leap years initially were every three years instead of every four. If the lunar year was 10 days short compared to the solar year, that difference would up to 30 days, or an additional month, every three years. Maybe such a leap month rule was initially considered instead of the longer months and single leap day, and then by mistake that number three instead of the correct four was used in the leap day rule ultimately adopted.

      --
      The Tao of math: The numbers you can count are not the real numbers.
      • (Score: 0) by Anonymous Coward on Sunday March 01 2020, @02:30PM (1 child)

        by Anonymous Coward on Sunday March 01 2020, @02:30PM (#964890)

        Traditional Chinese calendar(s) use a leap month,
            https://en.wikipedia.org/wiki/Chinese_calendar [wikipedia.org]

        • (Score: 0) by Anonymous Coward on Monday March 02 2020, @12:44PM

          by Anonymous Coward on Monday March 02 2020, @12:44PM (#965441)
          The traditional Jewish calendar likewise adds a 13th month (Adar II) intercalated every two or three years in a 19-year cycle so that Passover always happens every spring in the northern hemisphere.
    • (Score: 1, Interesting) by Anonymous Coward on Sunday March 01 2020, @06:41PM

      by Anonymous Coward on Sunday March 01 2020, @06:41PM (#965008)
      The old Roman calendar had months named Quintilis and Sextilis, with 31 and 29 days respectively. Julius Caesar in his calendar reform had ten days to add to the original 355-day Roman lunar calendar, so he distributed the days to the months, with Sextilis gaining an extra day, so it became 30 days long. In Augustus's reign, he renamed Quintilis after Julius Caesar, giving us July, and he decided to rename Sextilis after himself, making it August, because it was the month of several of his greatest triumphs, including his conquest of Egypt. But that made his month shorter than Caesar's, so the story goes that he stole a day from February to give it to August. Other stories (more plausible) say that Caesar had already given Sextilis 31 days from the beginning of his reform. As a side note, several later emperors (notably Tiberius, Caligula, and Domitian) tried unsuccessfully to similarly rename September after themselves.
    • (Score: 2) by toddestan on Sunday March 01 2020, @07:08PM (2 children)

      by toddestan (4982) on Sunday March 01 2020, @07:08PM (#965028)

      Another interesting thing that a lot of people don't realize is that the numbers seven, eight, nine, and ten in Latin are septem, octo, novem, decem - hence September, October, November, and December. The names, of course, come from the original Roman lunar calendar when those months were the seventh, eighth, ninth, and tenth months, respectively. When the calendar was changed to the solar calendar, these months no longer were in the right place, but the names were never changed.

      • (Score: 2) by dry on Monday March 02 2020, @01:52AM (1 child)

        by dry (223) on Monday March 02 2020, @01:52AM (#965192) Journal

        I thought the new year was in March until fairly recently. OK, according to Wiki, the Romans did move the new year to Jan 1st but later during the middle ages, various nations moved new years day to various dates, Mar 1st, Mar 15th, Easter, September 1st and December 25th. Then with the Gregorian calendar, Jan 1st was once again standardized. Nice to learn something new.
        https://en.wikipedia.org/wiki/New_Year [wikipedia.org]

        • (Score: 0) by Anonymous Coward on Monday March 02 2020, @03:31AM

          by Anonymous Coward on Monday March 02 2020, @03:31AM (#965254)
          That's also the reason why tax time is in April. The new year used to be on March 25 in England (and all their territories, including the colonies that would later become the United States), until 1752 when they finally adopted the Gregorian Calendar. One week after the new year was time, April 6, and that remained even after calendar reform.
  • (Score: 2) by VLM on Sunday March 01 2020, @03:14PM

    by VLM (445) Subscriber Badge on Sunday March 01 2020, @03:14PM (#964912)

    A common programming mistake is trying to make small, yet inappropriate, abstractions. Then when they don't work the abstraction slowly becomes infinitely complicated and debugging is a nightmare.

    Or in summary, we should abolish the "month" along with the dreaded daylight savings time.

    We do pretty well with integer julian dates and "week of the year" type stuff.

    In the old days when a pony express stamp was five cents and the only calculation machine was a slide rule, it made sense to do all kinds of billing and stuff based on paper bills and paper checks and stamps every couple weeks. But in the modern era of hyper-financialization it makes more sense to provide everything as "prepay" or maybe some kind of daily magical "near free" micropayment infrastructure or just explicitly offer credit.

    My gut level guess is we'd see a bifurcation of accounting type balance tasks that used to be monthly be on the 00s (aka every hundred days) or "on the quarters" every 25 days, whereas billing would go its own way as per above.

    Also I suspect this is yet another example of legacy sunken costs where the entire world will use the new calendar system EXCEPT the USA and UK "we don't need no steenkin metric calendar".