This document is part of the Martian Time Boneyard. It was originally located at http://www.virtualmars.net/Calendar.asp.
Author: Shaun Moss

     
Earth/Luna (UT)

Mars


The Areosynchronous Calendar

Credits/References

This calendar was constructed using contributions from the following people:

If you have, or know of, a brilliant idea that you think should be a part of the Areosynchronous Calendar, please email me.

Terminology

There are two terms used in this document which may be unfamiliar:

sol = Martian solar day. This term was first used by the NASA JPL Viking mission team in 1976 and is now widely accepted within the Mars community. It is a precise unit of time equal to 88775.244 seconds (24 hours, 39 minutes, and 35.244 seconds), which is the average length of the Martian solar day. A sol is thus only fractionally longer than an Earth day. This is one of the most compelling reasons for colonization of Mars, as humans and other Earthly organisms that have evolved with a biological cycle of 24 hours should have little difficulty adapting to the Martian day/night cycle.

Other new terms can easily be derived from 'sol', for example: 'tosol', 'yestersol', and 'holisol'.

mir = Martian year. This is a new term I've introduced in absence of a widely accepted existing term. As we may refer to a tropical year or calendar year, so may we refer to a tropical mir or calendar mir. I adopted this particular word for several reasons:

  • in remembrance of the famous and beloved space station
  • it sounds like a contraction of 'Martian year'
  • it means 'peace', 'commune' and 'world'
  • it's easy to remember

I use the terms 'month' and 'week' in the context you would expect. I've not defined new terms meaning 'Martian month' or 'Martian week', because I don't think it's necessary.

The word 'month' literally means 'moon', and originally meant the period of time between two new moons - a duration now referred to as a 'lunar month'. Because of the complex motion of the moon, lunar months vary slightly in duration, although the average length of a lunar month is known precisely: 29.5305888531 days (and getting longer by about 0.02 seconds/century). On Earth, the term 'month' is commonly understood to mean a 'calendar' month, or 'a fraction of the calendar year approximately equal in duration to a lunar month', and may refer to a period of 28, 29, 30, or 31 days.

The term 'month' is thus not a reference to an exact time unit, nor is it used in precise calculations, but primarily in determination of calendar dates. There is therefore little reason for invention of a new term meaning 'Martian month', as long as it is defined similarly to an Earth month, namely 'a fraction of the calendar mir approximately equal in duration to a lunar month'. A lunar month is equal to 28.74 sols, therefore I favour Martian months of roughly this duration.

The term 'week' is also not employed as a precise time unit. There is no known astronomical basis for the week - it evolved as a standard work-rest cycle (or the period between market days). Because the week is not used as a exact time unit, but rather as a definition of the work-rest cycle, there seems little reason to invent a new term for 'Martian week'.

Overview

The Areosynchronous Calendar has been created by adding original and imaginative names for seasons, months, and sols-of-the-week to the Darian Calendar, along with my own notes and commentary.

The numerical features of the Darian Calendar which combine to form an attractive solution are summarized as follows:

  • 7-sol weeks, parallelling Earth
  • Almost all months are of equal length and a whole number of weeks (28 sols, 4 weeks, or 2 fortnights)
  • Months are approximately the same length as Earth/Lunar months
  • Each month begins on the first sol of the week, and hence so does each mir
  • A mir is divided into 24 months, a number which makes it easy to divide the mir into 2, 3, 4, 6, 8, or 12 parts
  • A simple system of determining leap mirs

Mirs and Leap Mirs

The average tropical mir, used as a basis for calendar design, is equal to 668.5921 sols. A Mars calendar, however, needs to describe mirs that are whole numbers of sols in duration. The Gregorian calendar describes a combinination of years of 365 and 366 days to compensate for the fact that Earth's average tropical year is 365.242199 days long, and we may easily adopt a similar system for Mars by defining a pattern of mirs with 668 and 669 sols. To properly compensate for the fraction of 0.5921 sols, the calendar must specify a total of 5921 leap mirs per 10000. The Darian calendar (and some others) accomplishes this using the following simple rules, which are similar to those used to define leap years on Earth:

  1. If the mir is odd then it is a leap mir having 669 sols (an odd number). This rule accounts for 5000 leap mirs per 10000.
  2. If the mir is divisible by 10 then this also is a leap mir (in most cases - see following rules). This rule adds a further 1000 leap mirs per 10000, totalling 6000.
  3. BUT, if the mir is divisible by 100 then it is not a leap mir. This reduces the number of leap mirs per 10000 by 100, bringing us back to 5900.
  4. BUT, if the mir is divisible by 500 then it is a leap mir. This accounts for 20 more leap mirs per 10000, bringing us to a total of 5920.

To summarize, a mir is a leap mir if it is odd or divisible by 10, unless it ends in 100, 200, 300, 400, 600, 700, 800, or 900. In general it will only be necessary to remember that if the mir is odd then it has an odd number of sols (669) and is a leap mir, and if it is even then it has an even number of sols (668) - except for those mirs divisible by 10 which will require closer examination of the rules.

What about the extra 1 leap mir per 10000, to total 5921? It is not necessary to over-complicate our leap mir system by trying to account for this one extra sol per 10000 mirs. After this length of time (about 18800 years), the length of the tropical mir will have altered slightly due to perturbations of Mars' orbit. Combined with the assumption that our descendants will have much more accurate astronomical tools at their disposal, and are likely to reform their calendar periodically anyway, we may safely conclude that it's unnecessary to build in this level of accuracy. There have been numerous calendric reforms and adjustments in our history and it is reasonable to assume that they will occur again, probably within the next 10000 mirs.

Where should the extra sol in a leap mir be inserted? The Darian calendar and many others place the leap sol at the end of the mir, which is logical, and has the advantage that sols identified by counting from the beginning of the mir (e.g. the 200th sol) always fall on the same date.

Seasons

I have chosen to adopt the names of the seasons proposed by Peter Kokh (author of the Mars Pulse Calendar and Prospector Pete's Mars Pages). The problem with using the familiar terms 'Spring', 'Summer', 'Autumn', and 'Winter' is that these terms refer to a different time of year in the Northern versus the Southern hemisphere - for example, it is Spring in the North while it is Autumn in the South and vice-versa. Peter has invented new names for the Martian seasons that can be used planet-wide. Note that the term 'Vernes' is used in place of 'Spring' - this is the Latin equivalent from which the word 'vernal' is derived, as used in 'vernal equinox'.

Name Meaning Introduced by Approximate length
Vertum Northern Spring (Vernes)/Southern Autumn Vertum Equinox
(Northern Vernal/Southern Autumnal Equinox)
194 sols
Sumwin Northern Summer/Southern Winter Sumwin Solstice
(Northern Summer/Southern Winter Solstice)
177 sols
Tumver Northern Autumn/Southern Spring (Vernes) Tumver Equinox
(Northern Autumnal/Southern Vernal Equinox)
142 sols
Winsum Northern Winter/Southern Summer Winsum Solstice
(Northern Winter/Southern Summer Solstice)
156 sols

I don't know if Peter knew this when he made these names, but Vertumnus was the Roman god of seasons.

As you can see, Mars' seasons are not of equal length - this is because of Mars' elliptical orbit.

How does a mir align with the seasons? Although the Gregorian calendar does not begin on a seasonal marker (that is, a solstice or equinox), the convention in both astronomy and astrology is to mark the beginning of a year with the Northern Vernal Equinox. This approach has naturally been popular in the design of Martian calendars too, and as there are no reasons to oppose this choice, the Areosynchronous Calendar also begins each mir with the Vertum Equinox.

Month lengths

The system of month lengths described by the original Darian calendar offers several compelling features, the most important of which is that it is easy to understand: A mir of 668 sols is divided into 4 quarters of 167 sols, each of which is further divided into 6 months - 5 months of 28 sols plus one month of 27 sols. The number of months therefore totals 24. In a leap mir the final month has an extra sol, totalling the usual 28.

Here are the advantages of this system:

  • Each quarter is the same length of 167 sols, except for the final quarter in a leap mir which has 168 (compare with Earth/Gregorian where quarters may be 90, 91 or 92 days).
  • All months have a consistent length of 28 sols, except for 3 or 4 per mir which have 27. These 'clipped' months are evenly spaced and always occur at the end of a quarter.
  • 24 is a useful number of months, as it then becomes simple to divide a mir into 2, 3, 4, 6, 8, or 12 equal parts.
  • 27 or 28 sols is approximately the same duration as a Gregorian calendar month (27.25 .. 30.17 sols) or Lunar month (28.74 sols). Considering future interplanetary commerce between Mars, Luna, and Earth, it will be useful for a month to mean approximately the same thing on each world. Months of this length are also more harmonious with the female menstrual cycle.
  • The extra sol in a leap mir is the last one of the mir. This is more convenient, and after all, if you want an extra free sol, New Mir's Eve would be the best time to have it!

This arrangement of months is expressed diagrammatically below, along with their names.

Month names

For the month names I have adopted the Rotterdam system (recommended reading) by Frans Blok (author of Frans Blok's Earth2Mars pages). Frans has invented original names for the Martian months using clever patterns of vowels and consonants, and I perceive this to be the least culturally-biased and most creative proposal:

# Name Number of sols Quarter Season
1 Adir 28 First Vertum
2 Bora 28
3 Coan 28
4 Deti 28
5 Edal 28
6 Flo 27
7 Geor 28 Second
8 Heliba 28 Sumwin
9 Idanon 28
10 Jowani 28
11 Kireal 28
12 Larno 27
13 Medior 28 Third
14 Neturima 28 Tumver
15 Ozulikan 28
16 Pasurabi 28
17 Rudiakel 28
18 Safundo 27
19 Tiunor 28 Fourth Winsum
20 Ulasja 28
21 Vadeun 28
22 Wakumi 28
23 Xetual 28
24 Zungo 27, or 28 in leap mirs

There are a number of patterns contained within the arrangments of letters used to make each name. These are described better on Frans' website, so please take a look, but here they are in brief:

  • Each month begins with a consecutive letter of the alphabet (only Q and Y are omitted). This means that if a month comes later in the alphabet, it comes later in the mir. Also a month can easily be abbreviated to a single letter, which is very convenient for writing dates.
  • The last letters of each month follow a pattern of 'R', 'A', 'N', 'I', 'L', 'O'. This means that you can always tell what position a month is within a quarter-mir by looking at the last letter. A clipped month always ends in an 'O'.
  • Odd months end in consonants, even months end in vowels.
  • If a month name other than Deti contains a 'D', then it's the first in a group of four.

The names also correspond to Mars' variable-length seasons:

  • Names containing a 'U' (Neturima to Zungo, 11 months), indicate a Tumver or Winsum month.
  • Names of 3 or 4 characters (Adir to Geor, 7 months) indicate a Vertum month. The regular months of 28 sols have 4 letters and 2 syllables in their names, the clipped month, Flo, has 3 letters and 1 syllable.
  • Names with 5 or 6 letters, not containing a 'U' (Heliba to Medior, 6 months) indicate a Sumwin month. The regular months have 6 letters, 3 syllables, the clipped one, Larno, has 5 letters, 2 syllables.
  • Names with 7 or 8 letters (Neturima to Safundo, 5 months) indicate a Tumver month. The regular months have 8 letters, 4 syllables, the clipped one, Safundo, has 7 letters, 3 syllables.
  • Names with 5 or 6 letters, containing a 'U' (Tiunor to Zungo, 6 months) indicate a Winsum month. The regular months have 6 letters, 3 syllables, the clipped one, Zungo, has 5 letters, 2 syllables.

Week lengths

The 7-day week dates back to ancient Mesopotamia, however, there have been several attempts by different leaders to introduce weeks of different lengths (anywhere from 4 to 10 days). These attempts have all been eventually abandoned due to lack of acceptance. For some mysterious reason, human society seems to naturally prefer a 7-day work-rest cycle.

The 7-day week is used worldwide, and, as this is one of the few aspects of society that almost all humanity agrees on, many designers of Mars calendars have felt it prudent to similarly define a Martian week to be 7 sols. Another minor advantage to implementing a 7-sol Martian week is that the term 'fortnight', meaning 'fourteen nights', will continue to equal two weeks.

Names for sols-of-the-week

After examining the many different Martian calendars, I hadn't found a set of names for the sols that I really liked, so I've opted to make up my own. Before naming the sols in the Martian week, it is worthwhile to investigate how our current days of the week got their names.

According to several sources, including this informative web page, the days of the week were named by Persian astrologers for the 7 known celestial objects - the Sun, Moon, and the five planets known at that time. The Egyptians also adopted this system, followed by the Hebrews, Arabs, Indians, Tibetans, Burmese, and Japanese. Here we have yet another curious mystery surrounding the week - not only the system of 7 days per week, but the system of naming them was adopted almost unanimously by vastly different cultures worldwide. Even the order in which the days were named was preserved - the first day named for the Sun, followed by the Moon, Mars, Mercury, Jupiter, Venus, and Saturn.

This system of assigning the days of the week to celestial bodies is still accepted worldwide and, similarly to the 7-day week, there aren't valid reasons to deviate from it. Therefore, I've also adopted an astrological approach and named each sol of the week after the 7 most astrologically significant celestial objects in the Martian sky - the Sun, the two Martian moons, and the 4 planets closest to Mars: Earth, Venus, Mercury, and Jupiter.

Sol name Named for
Heliosol the Sun
Neriosol Nerio (formerly Phobos)
Libersol Liber (formerly Deimos)
Terrasol Earth
Venusol Venus
Mercusol Mercury
Jovisol Jupiter

One of the advantages of this set of names is that they each begin with a different letter, which makes for easy abbreviations. [If you're wondering where the new names for the Martian moons came from, please read The Renaming of Mars' Moons.]

Weekends

The story goes that "the LORD made the heavens and the earth, the sea and all that is in them, and rested on the seventh day; therefore the LORD blessed the sabbath day and made it holy". The Hebrews were instructed by Moses that it was forbidden to work on the Sabbath, the last day of the week, which was to be set aside for religious observances.

Sun-worshipping pagans, however, considered the 'day of the Sun' to be their holy day (holiday). The Roman Catholic church changed the Christian holy day to Sunday around 1000AD, as a means of marketing Christianity to pagan cultures. Many western religious groups have since followed suit.

Society is adaptable, and as we know, in modern times most people have both the first and last days of the week free. The system of having these two holidays per week is in widespread usage by people of all cultures, and I suspect most would be happy to continue this pattern on Mars. Hence, a typical Martian working week in the Areosynchronous Calendar is from Neriosol to Mercusol, and the weekend is Jovisol and Heliosol.

Synchronization of weeks and months

The choices made regarding month and week lengths result in an attractive feature that our Earthly Gregorian calendar does not have. Most of the Martian months contain 28 sols - exactly 4 weeks per month - therefore a month can easily and conveniently be divided into 2 fortnights or 4 weeks.

Imagine for a moment that every month in our new Martian calendar contained 28 sols - another useful advantage would emerge, namely that each month would begin on the same sol of the week. By starting a mir on the first sol of the week, the first sol of each month would therefore also fall on the first sol of the week. This would result in the useful situation that each calendar page would look pretty much the same (as will be presently illustrated).

Simplicity is a virtue in any system, and this is especially true in the case of a major societal system such as a global calendar. This kind of synchonization between the weeks and months means that determination of the sol of the week from the date becomes trivial. For example, if our Gregorian Calendar had this feature, the first day of any month would be a Sunday - as would the 8th, 15th, and 22nd.

However, we have an unresolved issue - not all months in the Darian calendar have 28 sols - every 6th month (except for Zungo in leap mirs) is a clipped month with 27 sols. Thus, if we maintained our familiar 7-sol cycle, we would lose synchronization by one sol per quarter-mir. The first 6 months would begin on the first sol of the week, the second 6 months would begin on the 7th sol of the week, the third 6 months would begin on the 6th sol of the week, and so on.

The Darian calendar proposes that, in order to take advantage of the benefits inherent in synchronization of weeks and months, we begin each month with the first sol of the week anyway, which means skipping the last sol of the final week in a clipped month. The final week of a clipped month therefore contains only 6 sols - a 'clipped' week.

Will this work? As we've noted, humans have historically not conformed to weeks of any length other than 7 days. Considering, however, that Martians will not be ordinary humans, but will in fact be highly adaptable and mentally acute people living in unusual conditions, I expect that this clipped week will actually prove to be one of the easier things for us to accept.

To summarize: the Darian calendar synchronizes the weeks and months in the following way - most months contain 28 sols, which is exactly 4 weeks of 7 sols, whereas the few clipped months per mir containing 27 sols are comprised of 3 regular 7-sol weeks and one clipped week of 6 sols. Hence, each month, and correspondingly, each mir, begins on the first sol of the week. This results in an extremely useful feature that an Earth calendar has never had - the name of the sol can always be easily deduced from the date, regardless of month or mir.

Here is the calendar page for any regular 28-sol month. Note the convenience of abbreviating the sol names to a single letter. Holisols are shown in light blue:

H N L T V M J
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28

Here is the calendar page for any clipped month of 27 sols. There is no Jovisol at the end of a clipped month, so Mercusol can be a holisol instead:

H N L T V M J
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27  

Written date format

The format for Martian dates is very important, because there exists the possibility of confusion. Fortunately, an international standard has already been established for the format of Earth dates, namely the ISO-8601 date format, that can easily be adopted for Martian dates. The format specifies year first, followed by month, followed by day, seperated by hyphens, for example: 2000-06-18. The year should never be abbreviated to two digits. If a month or day number is less than 10, then a leading zero is added to make 2 digits.

There are several important advantages of the ISO standard. Firstly, it favours neither the European convention of day-month-year, nor the American convention of month-day-year, thus it is a diplomatic choice. Perhaps more importantly, the most significant number (the year) is on the left and the least significant (the day) is on the right, in harmony with the rest of our numerical system.

Thus, it makes sense for Martian dates to be written mir-month-sol. Having a standard date format is even more important in relation to the Martian calendar, because the year is currently a low two-digit number and can easily be confused with the month or sol number. Because of this, I have prepended the mir with the capital letter 'M'. This both identifies which part of the date field is the mir, and also distinguishes Martian dates from Gregorian.

Although this is not specified in the ISO standard, I often spell out the month in letters, either fully or as an abbreviation, to further minimize any possibility of confusion. Because all months in the Areosynchronous Calendar begin with a different letter, we can conveniently abbreviate them to a single character when writing dates, for example: M13-A-18.



All contents of this website copyright Shaun Moss and Mars Engineering