If months are based on the moon, then why are the months longer in the Gregorian calendar than lunation?

  • What I have always thought / known is that:


    Days are based on the period of rotation of the earth.


    Months are based on the moon.


    Year is the time taken by the earth to make one revolution around the sun.


    But if we take a look at the lunation it takes on average 29 days, 12 hours, 44 minutes, and 28 seconds. Why is it that the months then in the Gregorian calendar have 28-29 / 30 / 31 days?


    I'm unsure if this is the correct site to ask this question. I was unable to find the calendar tag.

    Your question is fine here. I think that questions on the astronomical basis of a calendar are perfectly on-topic. Timekeeping and calendar regulation have been an important part of astronomy since ancient times.

    @PM2Ring Tho I agree with you, and I enjoy the great answers below, this kind of question might attract some interesting perspectives in the history of math and science SE.

    Obligatory (and absolutely brilliant) suggestion for another calendar reform that "makes more sense" https://youtu.be/vunESk53r5U

    "If months are based on the moon, then why are the months longer in the Gregorian calendar than lunation?" The logical, no-astronomy-needed answer is that therefore the months **must not be** based on the Lunar cycle.

    How many moons per year? Answer that question and the rest falls into place.

    @RonJohn, true but ... neither days should be based on observations of the Sun. Then, in which unit and how many of them should we break down a large period such as a Year? Before we knew that time-keeping consistency must rely on sub-atomic observations, what else could our ancestors do? I think they did quite well. The fact is that we agree (almost worldwide) to use a common, and admittedly imperfect, calendar.

    @NgPh only the last paragraph needs answering, and that's been answered hundreds of times before.

    @RonJohn, and because it apparently is well-accepted that there had been a misconception, that we have to look at, not only the last paragraph, but the entire statement of problem, with a different perspective (ignoring the numbers): if this is so obviously wrong, why is this taught that way? Myself had been ingrained at school that "month", "moon", "lunar" have the same root and a Year is divided into 12 months. Paraphrasing Galileo, if I may, "and yet, there seems to be linkage", between Month and Moon ...

    @NgPh sure they "have the same root", but words -- being human creations, not mathematical laws -- can change meanings.

  • Ancient Egyptians and Mesopotamians came up with “administrative” calendars of 30 days, that were easier to calculate than “real” lunar months of sometimes 29, sometimes 30 days. At the end of the 12 months, they added five days of religious observances, sometimes positive, sometimes negative.


    When Julius Caesar conquered Egypt, he knew about the very regular Egyptian calendar and appointed his mathematicians and astronomers (if we can really call them that, as Roman science wasn’t very developed) to discuss with their Egyptian peers and devise a better calendar for the Roman Republic (reminder that Caesar was not the Emperor; the first one was Augustus, his [adoptive] son, and not right away).


    Eventually, it was decided in Rome that, in order to follow with the seasons, the already-existing Republican Roman calendar was to be modified. It contained 10 months of 29 and 30 days plus a “winter” of 59 days, which became divided in January and February. As Julius Caesar was the one who brought this change, he was “honored” by having a month renamed from Quintilis (“Fifth”) to Julius (our July)—and that month was given 31 days, as well as a few others. Also, the beginning of the year was shifted (at this point or later; it’s not clear) to January, making the “numbered months” off with their new rank—e.g. “October” is not eighth (“octo”) anymore.


    Caesar’s reform was not well applied, and eventually, Augustus had to enforce the new calendar, and he was also “honored” with a 31-day month, right after Julius’, so that’s how Sextilis (“Sixth”; and it had 30 days) became Augustus (with 31 days).


    The rest is basically adjusting here and there to make it a total of 365 days at the end of the year, someone sometime having the “brilliant” idea of alternating 30- and 31-day months (a little like nature “alternates” between 29- and 30-day lunar months).


    Side note… In some languages, the word for Moon and the word for month is the same—it’s already quite similar in English! For example, Romanian has “Luna” for both, and Korean has ”dal.”


    Thank you for the great answer. If I understand correctly the problem with calendar design is that there are no whole number of days in a lunation. Nor whole number of days or lunations in a year. So we basically end up adjusting days / months to get the year correct?

    Yes, basically. Add to that politics and human emotions, and you get a mess like what we have today!

    Certainly, Julius Caesar wasn't an emperor, but he *was* the pontifex maximus, so one of his duties was "The regulation of the calendar; both astronomically and in detailed application to the public life of the state". Before the Julian calendar was adopted, things like the start of the year and the length of the months were decreed by proclamations of the pontifex maximus.

    @lunisolar It's actually not too hard to construct a regular lunisolar calendar (i.e., one that uses mathematics to determine the month lengths, rather than actual observation of the New Moon). But in order for such a calendar to correctly stay in sync with both the Sun and Moon the calendar needs to have leap *months*, not just leap days.

    I think the languages where the Moon and month are the same or related words are majority. In Europe, at least.

    So, initially the calendar had 29- and 30-day months, and only the "honor" of Caesar made one month 31-day—already away from lunar month, and this is where all the mess began. Right?

    @lunisolar, I suppose you could have the months track lunar months, but leave them free-running instead of locked to the year, like our weeks are now. (How useful those months would be, is another question.)

    @Ruslan No, the problem came from trying to have a fixed amount of months per year. This was all for _practical_ reasons, not to "honor" anyone. The older Roman calendar only had 10 months, and the rest of the year was _not_ divided into months. Julian calendar divided the year into 12 months instead, with no left-overs - and that meant having a few months that are longer than 30 days.

    @ilkkachu That's another approach that is still used to this day - instead of leap days, you get leap _months_ to put the calendar "back in sync". It's falling out of favour and mostly used for religious observances, though.

    @ilkkachu that sounds like a lunar calendar, problem with that I believe is that it would be difficult to tight it up with the seasons.

    You mean October isn't named for Octavius? /me ducks

    @Ruslan: The pre-Julian calendar had four 31-day months, eight 29-day months, and a variable-length leap month. Most lunar calendars have 29- and 30-day months, but the Romans had this idea about odd numbers being “lucky”.

    I am sceptical about this article. As I recall from Richard Parker's "The Calendars of Ancient Egypt", the 12x30 day months system (in say the Canopus decree) was not widely adopted. I don't think the Bablyonians ever adopted such a thing. 29/30 day months with roughly 7 additional months every 19 years was the rule. Nor do I think you are right about the Roman Republican calendar (see Agnes Kirsopp Michels's book). The departure from lunations was long in the past but Quintilis was a long month by then.

    Fasti indicate that the idea of not having Winter months was long gone by the time of the Caesarian reform (if it ever was).

    I have simplified greatly and made a (very!) long story (very) short. Yes, “winter” was divided before Caesar. No, the Babylonians did not use a “12 x 30 days” calendar “officially,” but for *administrative* purposes, one was used as early as 2,400 BCE (see e.g., https://www.britannica.com/science/calendar/Ancient-and-religious-calendar-systems or https://cdli.ox.ac.uk/wiki/doku.php?id=chronology).

    @fraxinus can you further clarify your claim? In Europe as far as I know only Germanic languages (I checked English and German) have similar words. Romance languages (Italian, French, Spanish) have totally different words (mese/mois/mes vs luna/lun/luna). According to automatic translation Greek also has a different words (φεγγάρι vs μήνας), and I don't know about Slavic languages (according to google translate, some - e.g. Russian or Polish - have different words, while others - e.g. Ukrainian - have the same). Why do you say that the majority has the same word?

    Slavic languages: Russian has two words for the Moon (луна / месяц), the second word is rarely used but pretty much legitimate and it is the month word as well. Same for my native Bulgarian and quite similar for Macedonian, Serbian ("месец" "месец дана" - lit. a moon worth of days), Ukrainian: "місяць" (a single word for both purposes).

  • Calendars can either be lunar or solar.


    A lunar calendar has months that match the phases of the moon but years that don't match the Earth's rotation around the Sun. It can't have both because the moon doesn't pass through an integer number of whole cycles in the year. The most common example of this kind of calendar is the Islamic Calendar in which dates move through the year as the years pass. On a given day in the Islamic calendar the moon will always be in the same phase, but the Earth will be in a different position in its orbit around the Sun.


    The Gregorian calendar in contrast is a solar calendar. It's years match (at least very closely) to the period of the Earth's rotation around the sun, and a given day - say 6th January - occurs when the Earth is in the same position in its orbit around the Sun, but the phase of the Moon will vary from year to year.


    There are also hybrid calendars which try to do both by, for example, adding an additional month every 2.71 years (like the Hindu calendar) to keep the days in a lunar calendar roughly, although not exactly, in sync with the rotation of the Earth around the Sun.


    Why exactly different cultures chose one or another is likely as much to do with historical accident as anything else, but there's some suggestion that cultures further from the equator tend more towards solar calendars. But that doesn't have much to do with Astronomy, the core Astronomical reason is simply that the Moon orbits the Earth in a number of days that doesn't exactly divide the number of days it takes the Earth to orbit the Sun.


    The Jewish calendar is also a well known lunar calendar.

    @Barmar There are many examples of all of these calendars, I am not attempting to provide a list.

    @Barmar: Lunisolar calendar. A pure lunar calendar (like the Islamic one) has a “year” of 12 lunar months ≈ 354.367 days.

    @dan04 It's actually more like the Hindu calendar, with leap months every 2-3 years.

  • What made calendar systems (any calendar, any civilization) "messy" is the belief that there is a magic cycle so that all repeating events observed can be described in integer number of this magic "base" period (month, day, hour,...), or at best in fractional numbers (and why in the decimal system by the way? After all, the Babylonians used the sexagesimal system, that we still use for dividing time into smaller units).
    Another wrong belief is that observed cycles do do not drift over years (everything must come back to the same "point", in a fixed time). Also, a wrong starting assumption is that the observer of the repeating events is in a fix reference, for example a "static" Earth. Even until today, not many people understand the difference between a solar day (86400 seconds) and a sidereal day (86164.0905 seconds).
    When we understand these wrong beliefs and wrong starting assumptions, we can understand why ancient and less ancient priests (and astronomers) were desperate in their quest of a "nice" celestial order. So, when you try to fit the Earth cycle to the Moon cycle, you will have problem in finding a "nice" mathematical solution.


    86400 seconds is only the *mean* solar day -- the actual solar day varies by almost a minute over the course of the year, i.e., we do not even have the described assumption of nice periodicity at this level.

    @Hagen, Indeed! Perhaps the interesting question is, for an astronomer, whether in other solar systems there could be physical mechanisms that "lock" various cyclic motions; something like our Moon being tidal locked. Put it in another way, is our difficulty in finding a "neat" calendar an exception or a norm?

    @NgPh Such mechanisms exist even in our solar system. They are called orbital resonances (see wiki). But they are not perfect - and the Earth doesn't participate in any useful resonance that would simplify the calendar.

    @fraxinus, Fascinating. Thanks! I will dig deeper into this.

    @NgPh, in the specific case of length of a solar day, it remains constant iff the planet has a perfectly circular orbital path, constant rate of rotation on its axis, and there is no axial tilt (obliquity to the ecliptic). That the Earth does not satisfy these criteria is what causes the real/apparent solar day to not be of constant length. The discrepancy between apparent and mean solar time is described by the so-called equation of time.

    @Jivan, Very informative. Thanks. I guess that this (cyclic) variation of a duration of a solar day did not bother too much ancient time astronomers, as long as the "mean" remains consistent year-by-year. One question springs on me: based on which observations people agree to split the mean day into smaller units? (I know that each culture has its own convention). A side note: it is only recently that we resolve to adopt the Cesium standard to measure time.

    @NgPh, ***"I guess that this (cyclic) variation of a duration of a solar day did not bother too much ancient time astronomers, as long as the "mean" remains consistent year-by-year.***" — Basically, yes; reading that wiki article, you will see that the discovery that the apparent solar day was not of constant length was only made when decently accurate timekeeping devices were in use. For a long time, people thought that their timekeeping devices were poor, rather than that the length of a solar day varied.

    @NgPh, ***"based on which observations people agree to split the mean day into smaller units?"*** — The history of timekeeping is long and tired. Most ancient societies used water clocks, and the Babylonians with their base-60 arithmetic decided to approximate the division of the day into two parts (day and night) of 12 hours each, further divided into 60 and 60. They thusly had to adjust the real length of day and night hours according to the time of year.

    @NgPh, ***"A side note: it is only recently that we resolve to adopt the Cesium standard to measure time."*** — Yes, the hyperfine transition periodicity of caesium is the basis for the atomic clock, and is what the BIPM now use to define the SI second for precision timekeeping, but the standardisation of the length of modern units (e.g. second, inch, meter, etc.) came much earlier. The standardisation of the second came in the mid-1500s.

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Content dated before 7/24/2021 11:53 AM