created by Mars Engineering

Clock and Calendar

by Shaun Moss

The primary resource used in preparing this aspect of VM was the Martian Time Website, by Tom Gangale.  Tom presented his timekeeping system, called the Darian Calendar, at the inaugural Mars Society convention in 1998.  It is an excellent, neat, well-defined calendar with many positive features, and is in many ways superior to the Gregorian calendar used by most people on Earth.  Tom goes into much more detail about Martian time on his website than I am currently prepared to do here, so if you want to delve deeper into this topic, I recommend his site.

Notes on the clocks

Just a couple of notes about the clocks:

• The standard format for a Martian date is orbit-month-sol, in line with the ISO-8601 standard for Earth dates, year-month-day. Thus it is currently orbit (Martian year) 13.
• The Earth/Moon clock uses UTC, Universal Co-ordinated Time, originally called Greenwich Mean Time.  UTC will probably be used on the Moon to provide a convenient day/night cycle for the humans living there. This is because the lunar day, also known as a lunar month, is 29.5 Earth days long - 2 weeks light and hot, 2 weeks dark and cold.

Introduction to Martian time:

One of the many good reasons why Mars is the ideal world for humans to colonise is that a Martian solar day is only fractionally longer than that of Earth's.  Whereas the length of the solar day on Earth is precisely 24 hours, the solar day of Mars is 24 hours, 39 minutes, and 35.244 seconds - only 2.75% longer.  This means that humans and other organisms from Earth should, in theory, have little trouble adapting to the night/day cycle on Mars (provided they can survive the extreme cold, thin air and isolation, that is).

You might be wondering why these figures I've just mentioned don't match up with the rotational periods given on the Mars and Earth page.  Consider Earth.  The reason the rotational period, also called the siderial day is slightly shorter than a solar day (the time it takes for the Sun to return to the same position in the sky) is because while the Earth is rotating on its axis, it's also moving along its orbit around the Sun.  Thus, after a full rotation, which takes about 23 hours and 56 minutes, the Sun is in a slightly different position.  The Earth must rotate slightly more, actually for about 4 minutes longer, before the Sun is in the same position as when the rotation started.  Similarly, the Martian siderial day, or rotational period, is approximately 24 hours and 37.4 minutes, whereas it's solar day is slightly longer at 24 hours and 39.5 minutes.

New term: The Martian solar day is called a sol.  This term was first used by NASA during the Viking 1 landing in 1976, and subsequently has been adopted by the Mars community.  It is also used in the famous trilogy by Kim Stanley Robinson, "Red Mars", "Green Mars", "Blue Mars" and in the Darian calendar.  The precise length of a sol is 88775.244 seconds - or 24 hours, 39 minutes, and 35.244 seconds.

The Martian year is 668.5921 sols long (686.98 Earth days).  Again, you might be wondering why this doesn't match the orbital period on the Mars and Earth page.  This is due to the precession of the equinoxes.  A year is in fact the length of time between equinoxes.

New term: In the absence of an existing term, I have dubbed the Martian year an orbit.  Although an orbit is slightly longer than the orbital period, as discussed, it is a convenient term to describe once 'round the Sun, and an easier-on-the-tongue alternative to "Martian year" or "M-year".

Orbit lengths:

Because there are 668.5921 sols per orbit, the calendar must describe a combination of regular orbits of 668 sols and leap orbits of 669 sols.  To properly allow for the fraction of 0.5921 sols, there must be 5921 leap orbits per 10000 orbits.  The Darian calendar accomplishes this using the following rules, similar to the rules for leap years on Earth:

1. If the orbit is odd or divisible by 10, i.e. ends in 0, 1, 3, 5, 7, or 9, then it is a leap orbit.  This alone would result in 6000 leap orbits per 10000 orbits.
2. But, if the orbit is divisible by 100, then it is not a leap orbit.  This brings us back to 5900 leap orbits per 10000 orbits.
3. But, if the orbit is divisible by 500, then it is a leap orbit.  This brings us to 5920 leap orbits per 10000 orbits.

Another, perhaps simpler, way to describe this system is to say that an orbit is a leap orbit if it ends in 0, 1, 3, 5, 7, 9 unless it ends in 100, 200, 300, 400, 600, 700, 800, or 900.

What about the extra 1 leap orbit per 10000?  One possible solution is to make any orbit ending in 9999 into a leap orbit - as we'll probably want the extra sol to celebrate 10 Martian millennia.  However, as Tom points out in the original description of this system, after 10000 orbits (about 18800 years), the length of the orbit will probably have changed anyway, (or possibly humans will have become extinct and replaced by robots who don't require approximated social time systems), thus this level of accuracy is unnecessary.

Month lengths

The system of month lengths used by the Darian calendar is superior to the alternatives for a number of reasons.  First I'll describe the system, then outline some advantages.

An orbit has 668 sols, or 669 sols in a leap orbit.  An orbit of 668 sols is divided into 4 quarter-orbits of 167 sols, each of which is further divided into 6 months - 5 months of 28 days plus one month of 27 days.  Thus, the total number of months is 24.  In a leap orbit, the final month has the regular 28 days rather than 27.  Simple, isn't it!

Here are a few clear advantages of this system:

• Each quarter-orbit is almost always the same length of 167 sols.  Only in a leap orbit does the final quarter-orbit have 168 sols.  Compare this with Earth where quarter-years vary between 90, 91 or 92 days.
• All the months, except for 3 or 4 each orbit, have a consistent length of 28 sols.  The short months are evenly spaced and always at the end of a quarter-orbit.
• 24 is a very convenient number in which to divide an orbit, as it then becomes simple to partition it into 2, 3, 4, 6, 8, or 12 approximately equal segments, as required.
• 28 sols is approximately the same length of time as a lunar month (~28.7 sols).  Remember the word "month" comes from "moon" and in Sanskrit they are the same.  Considering there will most likely be humans on the Moon before Mars, with whom we'll probably have considerable trade and communication, this will be useful for estimating the time of month (er, day) on the Moon (remember that a lunar month is a lunar day - 2 weeks light, 2 weeks dark!).  This is also about the same length of time as the human menstrual cycle.
• The extra sol in a leap orbit is the last one of the orbit.  Much more convenient and logical (after all if you want an extra free sol, New Orbit's Eve would be the best time to have it!).

More advantages of these choices of month lengths become apparent later on when discussing "Weeks".

Month names

For the month names I have strayed from the names specified in the Darian calendar and opted for the Rotterdam system by Frans Blok.  He has invented totally new names for the Martian months using clever patterns of vowels and consonants, and I believe this is the least culturally biased and most creative solution.  Here are the month names:

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 orbit.  Simple!  Also a month can easily be abbreviated to a single letter, 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-orbit by looking at the last letter.  A short 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 is the first in a group of four.

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

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

Week lengths

Here's an interesting excerpt about the week:

WEEK   [formerly in the Web's Global Encyclopedia, now defunct]

Next to the day, the week is the most important calendric unit in our life. And yet, there is no astronomical significance to the week. Nothing cosmic happens in the heavens in seven days.  How, then, did the week come to assume such importance?

The first thing to understand is that a week is not necessarily seven days. In pre-literate societies weeks of 4 to 10 days were observed; those weeks were typically the interval from one market day to the next. Four to 10 days gave farmers enough time to accumulate and transport goods to sell. (The one week that was almost always avoided was the 7-day week -- it was considered unlucky!) The 7-day week was introduced in Rome (where ides, nones, and calends were the vogue) in the first century A.D. by Persian astrology fanatics, not by Christians or Jews. The idea was that there would be a day for the five known planets, plus the sun and the moon, making seven; this was an ancient West Asian idea. However, when Christianity became the official religion of the Roman empire in the time of Constantine (c. 325 A.D.), the familiar Hebrew-Christian week of 7 days, beginning on Sunday, became conflated with the pagan week and took its place in the Julian calendar. Thereafter, it seemed to Christians that the week Rome now observed was seamless with the 7-day week of the Bible -- even though its pagan roots were obvious in the names of the days: Saturn's day, Sun's day, Moon's day. The other days take their equally pagan names in English from a detour into Norse mythology: Tiw's day, Woden's day, Thor's day, and Fria's day.

The amazing thing is that today the 7-day week, which is widely viewed as being Judeo-Christian, even Bible-based, holds sway for civil purposes over the entire world, including countries where Judaism and Christianity are anathema. Chinese, Arabs, Indians, Africans, Japanese, and a hundred others sit down at the U.N. to the tune of a 7-day week, in perfect peace (at least calendrically!). So dear is this succession of 7 days that when the calendar changed from Julian to Gregorian the week was preserved, though not the days of the month: in 1752, in England, Sept. 14 followed Sept. 2 -- but Thursday followed Wednesday, as always. Eleven days disappeared from the calendar -- but not from the week!

As it appears that having 7 days in a week is one of the few things that we humans agree on, it makes good sense to have 7 sols in a Martian week also.  Historically, attempts to introduce longer weeks have failed, although there is some evidence that shorter weeks would be more readily accepted, particularly by those students familiar with the one day on, three days off cycle :)

Fortunately we can have the best of both worlds (so to speak) with the Darian calendar, by having a 6-sol week at the end of each short month.  To explain - a regular month of 28 sols is made up of  exactly 4 weeks of 7 sols.  A short month of 27 sols is thus comprised of 3 regular weeks plus a short week of 6 sols.  Using the Darian calendar, we actually drop a sol from the last week in each short month.  This results in the excellent situation that the first day of each month is always the first day of the week.

Here lies the real beauty of the Darian calendar.  The name of a sol can always be determined by the date, regardless of what the month is.  The weeks and months are synchronised.

Sol names

After examining different Martian calendars I hadn't found a set of names for the sols that I really liked, so I opted to make up my own.  I've also adopted an astrological approach and named them after the Sun, the two Martian moons Phobos and Deimos, and the 4 planets closest to Mars:

One of the advantages of this set of names is that they each begin with a different letter, which makes for easy abbreviations.

Now we have the sol names, here's a typical Martian calendar page to illustrate the harmony contained within the Darian calendar:

For the short months, of which there are only 3 or 4 per orbit, the last Jovisol is dropped, and Venusol is free instead:

So the first sol of each month is Solisol.  The 19th of any month is Hermesol.  The 27th sol of any month is Venusol.  I'm sure you get the idea.  Very handy indeed.

The Clock

This is where my system differs from the system preferred by Tom Gangale, NASA, and JPL, which is a 24 hour, 60 minute, 60 second system, just like Earth.  In this clock, the Martian hour, minute and second are simply stretched slightly, by the same 2.75% that the Martian solar day is longer than Earth's.

I can see immediate problems with this approach, mainly one of confusion.  It is easy to imagine mix-ups between Martian hours and Earth hours, given that the difference is so slight.  I believe it is too risky to use a system like this.  Imagine a pilot flying from Earth to Mars - at the halfway point her clocks should automatically switch over to Mars time - how can she check her instruments and in a single glance, be sure this had happened?  What about the interplanetary Olympics being broadcast throughout the solar system - would the swimmers' or runners' times be displayed in Earth seconds or Mars seconds or both?  Considering that the readouts would be only fractionally different, there could easily be mixups.  A fraction of a second means a lot to a sprinter.

A metric clock is a better solution for various reasons.  The time units are clearly different to those of Earth, plus the format is clearly different, so a quick visual check of your chronometer will immediately remind you if it's set to Earth or Mars time.  My solution is to use the "millisol", literally one-thousandth of a sol, as being the basic unit for measuring the time of sol or time intervals of less than one sol.  One millisol is equal to 88.775244 seconds, and is conveniently abbreviated to "mil".

You can see from this comparison of Martian time units that metric clocks have been proposed before.  The millisol is in fact precisely the same unit of time as the "Martian minute" proposed by Tom Gangale in 1986 (although as mentioned, at that time he preferred the 24:60:60 system), and as the "milliday" proposed by Bruce Mackenzie in 1987 (the milliday was also abbreviated to "mil").  Both of these systems provided further units to correspond to the hour and the second, however I feel that this unnecessarily over-complicates things and would result in a system no better than Earth's.

Of course, I am looking at this from a programmer's perspective and, quite frankly, it simplifies things considerably if a single decimal number is used to express the time of day.  Calculations are made much simpler, even those as straightforward as tallying up your timesheet. 

One of the arguments against a metric clock is that it may be more difficult to learn than the 24:60:60 system that humans are used to.  However the colonists of Mars will need to be able to operate rovers, airlocks, computers and spacesuits.  I suspect they won't have too much difficulty learning how to tell the time of day as a number between 0 and 1000.  Colonists will probably adapt to this system within at most a few sols.

Keep in mind also that hours were invented as a unit of time for sundials, and minutes and seconds for the analog clocks that came later.  On Mars we will probably use precise digital clocks exclusively.

Formats:

The format for the clock is quite simple and illustrated in the Mars Clock.  The number of millisols is shown to a precision of microsols, i.e. 3 decimal places.  If necessary, the portion to the left of the decimal place is padded with zeroes until there are 3 digits.  Thus, the time of day is always represented by the format xxx.xxx, ranging from 000.000 to 999.999.

The format for the date 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 (I emphasize this point, having had hands-on experience with Y2K issues).  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 correspondence with the rest of our numerical system.  Finally, I can say as a programmer, although having a standard seperator character may seem like a minor thing, it makes things simpler when converting strings to dates.

Thus, Martian dates should always be written orbit-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.  The month may be spelled out in full, or abbreviated to a single character, for example, tosol is 13-A-18.

New term: tosol, the current sol - Martian equivalent of "today".