Most accurate calendar

November 18, 2011 3:13 PM

I am looking for the most accurate calendar. With even increments and no exceptions(leap years).

I am trying to find a method of measuring time that does not have exceptions(leap years) and is highly accurate. This system would preferable have the same amount of "days" in each "month", use a 10base system(like metric), or use increments that are even fractions of other increments.

Of course the system would be based off of the rotation of the earth, the position of the earths path around the sun, and the moons position around the earth as well.

Does such a method of measuring time exist, and if not, then what is the closest recorded method developed?

posted by digdan to Science & Nature (19 answers total)

No such method can exist, because the number of rotations of the Earth (days) in a revolution of the Earth around the Sun (year) is not an integer.
posted by madcaptenor at 3:16 PM on November 18, 2011 [2 favorites]

I think that's why "days" is in quotation marks?

I'm not sure of any calendar system that does not use a standard 24-hour day, though.
posted by Holy Zarquon's Singing Fish at 3:22 PM on November 18, 2011

Of course the system would be based off of the rotation of the earth, the position of the earths path around the sun, and the moons position around the earth as well.

The problem with this is that those are not integer multiples of each other. The Earth goes around the sun once in the period it take Earth to rotate 365.25 times. If you want to keep a year analogue that contains one full cycle of seasons, and a day analogue that contains a full day-night cycle then you'll always end up with this problem.

If you got rid of months and made a week 5 days long then there would be an integer number of weeks in a year. Number each week. You'd still have leap days and leap seconds though.
posted by atrazine at 3:24 PM on November 18, 2011

I agree with madcptenor. More explicitely, you have to fudge one relationship or another - either your clock-day won't match your solar-day, or your calendar-year won't match your solar year.

We chose the second one, because having a shifting day is more confusing than having a shifting year. BUT, you are free to pick the first one, if you so choose. Depending on how precise you want to be, the earth takes roughly 8766 hours to go around the sun. Divide that how you like. Or if you want to avoid the possibility of leap-seconds start from how many nanoseconds the average revolution takes.
posted by muddgirl at 3:26 PM on November 18, 2011

Hmm. Well, there is technically Unix time. It's quite accurate as long as you get rid of the concept of minutes, hours, days, weeks, months, years...

Well, not so accurate for older computers on old-style January 19, 2038 when every 32-bit Unix system will have a bad day.
posted by Fortran at 3:28 PM on November 18, 2011 [1 favorite]

The length of a day is not constant.

Nor is the length of a year.

If you measure these things by the number of vibrations of (usually) a caesium atom, you will find that attempting to define a standard 'year' is impossible. As a consequence, atomic clock times must be periodically adjusted to take into account these minute variations.
posted by fearnothing at 3:28 PM on November 18, 2011

I don't have an answer, but there's a more exact discussion of the problem here.
posted by coolguymichael at 3:28 PM on November 18, 2011

Of course the system would be based off of the rotation of the earth, the position of the earths path around the sun, and the moons position around the earth as well.

I'm not sure why you say 'Of course.' The speed of the rotation of the Earth, the revolution of the Moon around the Earth and the Earth around the Sun - these things change over time.

Frankly, what you want is the Unix Epoch, or something similar that counts the number of seconds from an arbitrary point in time; atomic clocks can measure this time to within very, very tiny fractions of a second. You can then divide this time up as much as you want, to make more human-scale time units - for example, One Megasecond roughly 12 days long. But all you're doing is marking off arbitrary blocks of seconds, which are the arbitrarily defined fundamental SI unit of time.
posted by Tomorrowful at 3:30 PM on November 18, 2011 [2 favorites]

Yep. Pick your fundamental unit of time based on your desired application and add SI prefixes. Want to make it the year? Well, a deciyear is 5.2 weeks or 36.5 days. A centiyear is 3.65 days or 87.7 hours. And so on. Or you could do the same with days or seconds.

Or switch to stardate (though you'd have to develop it first).
posted by supercres at 3:39 PM on November 18, 2011

It depends on which requirement is most important to you, because they are not all possible. Personally, I like a variation of the old Roman calendar (before the addition of July and August). Ten months of thirty-six days, with five days of festival at the end. Six days of festival on leap years.
posted by spaltavian at 3:47 PM on November 18, 2011

Many people have tried this (some are more famous than others.)

You can't get everything you want, which has frustrated every effort over the last two millenia I can think of, excluding the Julian-Gregorian switch (which took a very very very long time to get everyone to adapt to, and that's only if you're not picky about how you define "everyone.")

I'd say that of the calendars I'm familiar with, the Republican Calendar is the closest to the (frankly not very useful) metric concept, and I can't think of a system that attempts to stick to a solar year of some kind that doesn't have to deal with leap days. It's one of those "the universe was not built to adhere to your need for symmetry and order" things.
posted by SMPA at 4:09 PM on November 18, 2011

Response by poster: To my understanding, I would be better off trying to define two types of time measurement. One could be ... per say the radians in degrees the earth current position compared to the sun and the center of the galaxy, and a second one would be a constant measurement of time, like fractions of the speed of light?
posted by digdan at 4:17 PM on November 18, 2011

One could be ... per say the radians in degrees the earth current position compared to the sun and the center of the galaxy, and a second one would be a constant measurement of time, like fractions of the speed of light?

Well, we already have that to some extent. Days and years are a units based on celestial position, and seconds/minutes/hours are units based on physical constants (atomic clocks). The problem arises when you try to make a hybrid system.


(I don't follow the center of the galaxy part --- are you going to account for the fact that the solar system is revolving around the galactic center?)
See also: Sidereal time

posted by qxntpqbbbqxl at 4:51 PM on November 18, 2011 [1 favorite]

I am trying to find a method of measuring time that does not have exceptions(leap years) and is highly accurate.

There's always good old Unix Time, which measures the number of seconds since Jan 1st 1970 (~1321669100 as I post this). Doesn't meet your other requirements, though, and I'm not totally sure what it does with leap seconds.
posted by Leon at 6:19 PM on November 18, 2011

Just how bad would it be to let the day = 86400 SI seconds and the year = 360 days? The length of the year, 31104000 seconds, is easy to remember -- 2^10 * 3^5 * 5^3 seconds.

This definition of 'day' is pretty close to the current long-term average rotational period of the earth, differing by less than 1 second per year (<30 parts per billion). In the far future the earth's rotational period will become markedly different than 86400 SI seconds, leading to trouble with the definition. But in the next thousand years or so you won't have to worry that rules like "the sun is approximately overhead at noon" will become false. (this page suggests that two leap hours will be required the late 30th century and that 24 leap hours will be required by the 64th century)

What about the length of the year? To a first approximation, in a 360-day year the seasons will move by 6 1/4 days per year; if you're a farmer you'll want to refer to an almanac to find out when to plant crops. The seasons will move by about a half year every 29 years, so if Christmas in your youth was in the winter, it'll be a summer holiday for your own children. (by comparison, the celebration of Ramadan moves by about 11 days every calendar year, and this doesn't cause any great problems). You have lots of choices for the lengths of weeks and months, as the year is 2^3*3^2*5 days long—perhaps you'd like to have 12 30-day months, with each month divided into 5 6-day weeks.

You could also let the year = 365 days. This gives a year of 31536000 seconds, which takes away some of the small and pretty factors of the 360-day year and replaces them with the unlovable number 73: 2^7 * 3^3 * 5^3 * 73. Now, the seasons only move by 1/4 day per year, and a farmer who has learned what week of the year to plant his crops will only need to learn a new rule every 28 years or so, or just 2 or 3 times in his career. In 100 years, Christmas only moves something like 1/3 of a season, so there's no need in a human lifetime to think of a holiday as moving from one season to another. You don't have a lot of choices for the lengths of weeks or months, as the only numbers dividing the length-of-year-in-days are 5 and 73.

Our system lets the year = 365.2425 days on average, or 146097 days per 400-years. 146097 = 3^3*7*773, so you do have some options about how to divide up this very long cycle—but as it's longer than a human life, nobody would really become familiar with the whole cycle if you do this. And none of the factors are particularly related to the year or lunar month: that big factor, 773, is about 2.12 years, so it wouldn't relate to anything like terrestrial seasons very well; neither is 3^3*7 very close to a half year, being about 3% longer. Likewise 3*3*3 is not particularly close to the length of a lunar month in days.

Anyway, those are the consequences if you keep the definition of the SI second and set the second, the day, and the year to all be related by simple whole multiples.

You could also define the day as 1 period of the earth's rotation, and define the civil second as 1/86400 day (or any other division that you prefer). Now, there will be no long term problem with the sun, but somebody will have to publish frequent (yearly?) numbers relating civil seconds to SI seconds. The relationship will be something like 1 civil second = 1.00000002 SI seconds now; in the far future the difference is likely to become bigger; very long term (and very suspect) calculations suggest that around AD 60000, we might have 1 civil second = 1.0000116 SI seconds. There are still the same problems with setting the length of the year in days, as discussed above. Far enough in the future, it might not even be practical to update the relationship between the SI and civil seconds as infrequently as once a year.

Of course, there's a rather drastic solution available to you: change the earth's rotational and orbital speeds so that you can establish the simple, fixed relationship between seconds and larger time spans that you desire. Particularly if the greenhouse effect continues, it seems plausible that you could move the earth out far enough to establish a 400-dayyear without making the earth uninhabitable. Change the rotational speed and the definition of 'hour' so that a day is 25 hours and now you've established a year of 10000 hours (you can also have the week of 4 days = 100 hours and the month of 40 days = 1000 hours = 1/10 year); divide the hours into further powers of 10 if you like, establishing a new second of 1/10000 or 1/100000 of a day. Instead of leap seconds, hours or days you'll just have to fire the engines at intervals determined by the world's smartest engineers. Of course, even with future tech rocket thrusters that can actually change the earth's motion this drastically, you'll need to spend at least centuries accomplishing this change so as not to cause an untenable number of excess earthquakes and other tectonic events.

I suspect that you will still not be able to both establish a lunar orbit that is a nice multiple of anything else in this system without giving up nice eclipses, which are improved by the relative parity of the apparent size of the sun and the moon. Instead, I'd modify the moon's orbit so as to give more frequent and striking eclipses without regard to how it fits into the calendar. (though you could just modify the moon's diameter so that it remains the right size while giving it an orbital period of e.g., 32 or 40 days) Similarly, the arbitrary motions of the planets are likely to remain an irritation, though maybe engineering in an even longer term can give them all nice round orbital periods as well.

You may find that it's easiest to abolish religion before undertaking this change in the earth's parameters; otherwise, there may be an undue amount of outcry about just how to determine when e.g., it is the sabbath day, when is it time to pray, when is it time to serve chocolate in the shape of a rabbit, etc.
posted by jepler at 6:53 PM on November 18, 2011 [8 favorites]

You couldn't measure time accurately even if you do not base it on the earth or the sun. The length of a year changes, the orbit of the earth is not circular. Everything slows down.

If you want to get really crazy and precise, you need to wrap your head around the fact that the flow of time changes depending on your location and speed. Satellites orbiting the earth measure time differently than clocks on the surface of the earth. Everything is relative and there is no absolute time.

Clocks and calendars work (in general) on human-scale because we don't care or notice the errors.
posted by blue_beetle at 7:17 PM on November 18, 2011

Modern time standards are all defined by setting a reference point in time and counting the number of reference periods that have elapsed since the reference time with a standardized clock. In addition, because of relativity, we have to choose a frame of reference for our clock.

All modern standards use the second as their reference period. The historical second was defined as 1/86400 of a solar day, but unfortunately the solar day is now known to not be a fixed period. The modern reference period is the SI second, the definition of which is currently derived from a fundamental and invariant property of nature (i.e. the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom). This is our modern standardized clock. As defined the SI second is close to 1/86400 of a mean solar day in about 1820.

Thus all modern time standards are derived in an elapsed number of seconds. For historical reasons modern time standards use a reference time based on 1 January 1977 00:00:32.184.

The modern calendar is derived from this time standard. We start with Geocentric Coordinate Time (TCG). TCG is equivalent to the time experienced by our standardized clock in a coordinate frame at rest with respect to the center of the Earth but is infinitely far from the Earth (i.e. a clock that performs exactly the same movements as the Earth but is outside the Earth's gravity well and therefore not influenced by the gravitational time dilation caused by the Earth). Of course, this is not practical for timekeeping on Earth.

However, based on TCG, we can define a time standard for Earth. Terrestrial Time (TT) is that standard. TT is a theoretical ideal, which real clocks can only approximate, and is not dependent on a particular realization. In relativistic terms, TT is described as the time of a clock located on the Earth at mean sea level. TT is approximated by observation, and in practice it is possible to make better estimates for TT based on reanalysis of historical data. Because it is awkward to use a time standard that results in past events retroactively occurring at new times as the realization of the standard is refined, we use yet another standard.

International Atomic Time (TAI) is that standard. Unlike TT, TAI is never revised once published, TAI is essentially the best estimate for TT at the moment at which it is measured. As such it is possible for errors in it to become known and remain uncorrected, TAI "wobbles" with respect to the idealized TT. However, the mean solar day is now slightly longer than 86400 seconds since the Earth's rotational speed is very slowly decreasing due to tidal deceleration (a day is currently approximately 86,400.002 seconds). Because of this TAI noon is slowly diverging from solar noon as the duration of the mean solar day increases. This leads to our next time standard.

Coordinated Universal Time (UTC) is the primary time standard by which the world regulates clocks and time (i.e. civil time). Coordinated Universal Time is based on TAI. The only difference between the two is that UTC is occasionally adjusted by adding a leap second in order to keep UTC noon within one second of solar noon. This leap second is added approximately every 500 days, but because the Earth's actual rotational speed varies on unpredictable factors such as tectonic motion, exactly when leap seconds become necessary is based on observation, not computation. UTC is adjusted so that our common experience of a day matches a standard day, the point at which the time standard begins to interact with traditional solar calendars.

The solar calendar we are most likely to be familiar with is the Gregorian calendar. The modern Gregorian calendar is based on UTC, but like UTC it needs occasional adjustment. The Gregorian calendar inserts a leap day occasionally in order to keep the calendar year synchronized with the rotation of the Earth about the sun. Because the astronomical year is not a whole number of days, a calendar that had the same number of days in each year would, over time, drift with respect to the event it was supposed to track (i.e. seasons would drift relative to the yearly calendar, Christmas would no longer be in Winter, etc.).

All of this is to say, modern calendars are essentially just a count of SI seconds (an arbitrarily chosen duration) since an arbitrarily chosen point of reference. Everything else layered on top is just adjustments to facilitate people's expectations (i.e. noon should be when the sun is high in the sky and Christmas should occur in winter).
posted by RichardP at 7:52 PM on November 18, 2011 [3 favorites]

The most accurate calendar is the POEE calendar from the Principia Discordia.

Five lovely months of 73 (50+23) days for 75% of the years, with St. Tib's day in the fourth year. I suggest you stay drunk and/or in a meditative trance for the entirety of St. Tib's day.
posted by Mad_Carew at 9:35 PM on November 18, 2011 [1 favorite]

Surprisingly, the Kodak corporation used the International Fixed Calendar until 1989. 13 months, each with 28 days. The extra month was named "Sol".
posted by Wild_Eep at 5:56 PM on November 20, 2011