The planet Mars has a day that is slightly longer than our own, but a year that is much longer. When people start living on Mars, what arrangements will they make for keeping track of time, in a fashion that relates to the natural cycles of their new home?
A Martian day is the time Mars takes to rotate on its axis to face the Sun once again. Because Mars orbits the Sun, there is a difference between conventional time and sidereal time, just as there is on Earth, but this difference is smaller because the Martian year is longer.
From this site, we learn that a Martian day is 88775.260726 seconds long, which is 24.659794646 hours, or 24 hours, 39 minutes, and 35.260726 seconds, or 1.027491443588 Earth days of 86,400 seconds each. Of course, the occasional use of leap seconds on Earth means that an Earth day is really slightly longer than 86,400 seconds, as if things weren't complicated enough.
The Mars novels of Edgar Rice Burroughs described the appearance of a Martian timepiece, and the units of Martian time. But these descriptions were inconsistent and illogical in some respects. For example, a Martian watch was described as having three hands, but then in at least one instance (in Llana of Gathol, where the tal that is one-fourth of a xat is explicitly given) the markings on it, and the units of time they represented, were such as to lead to all three hands always pointing in the same direction.
The day was divided into ten zodes, and began at the time we would call 6 AM by our system of timekeeping. Each zode was divided into fifty xats, and each xat was divided into either two hundred or into four tals. The face of a Martian watch showed ten zodes, divided into fifty xats, and each divided into four tals, by the markings on it.
If one tries to reconcile the various references, keeping only those which are reasonable, however, one can arrive at something that makes sense.
Let each xat be divided into two hundred tals; this shorter tal is used on several occasions in the novels (it features directly in the plot of The Warlord of Mars, and is given explicitly in a table of Martian time units in The Gods of Mars). But on the face of a Martian chronometer, let the circle be divided into ten markings for zodes, with each of those ten markings being subdivided into five spaces by the markings for xats, and each of the areas representing a xat divided into four spaces by the markings for tals.
Then the zode hand makes a cycle once a Martian day, the xat hand makes a revolution once each zode, and the tal hand makes a revolution once each xat. The three hands would bear a relation to each other similar to that of the hour and minute hands on an Earthly timepiece; the minute hand rotates once an hour, and points to markings which subdivide the markings that indicate the hour for the hour hand.
Incidentally, note that the longer tal, four of which make a xat, is the two-hundredth part of a zode, which is likely what made the confusion possible. Given that, though, one could postulate that the Barsoomian word tal actually means "one two-hundredth part", and so the long tal would really be a tal-zode while the short tal would really be a tal-xat. This would be less arbitrary than choosing the word "tak" for one of the types of tal, as was done in one published glossary of Barsoomian terms.
Upon rereading Llana of Gathol, however, it turns out that John Carter wrote "A tal is about eight-tenths of an Earthly second" in Chapter 10 of Book 4 (Escape on Mars) within that novel, immediately preceding Chapter 11, which contains the table that is the only source in the series for the long tal. Since the length given in Chapter 10 is only consistent with the short tal, one two-hundredth of a xat, the conclusion that the long tal is no more than a slip of the pen seems inescapable.
This represents one extreme. For novels of an alien society on Mars, it makes sense that the author Edgar Rice Burroughs would present a system of timekeeping that originated independently of the one we use on Earth. But it is unlikely that people from Earth, living on Mars, would seek change for the sake of change, even if watches telling time in that system might someday become a popular novelty item there.
Although one could fondly imagine a Mars divided into two groups of people, one group which divides the day into zodes, xats, and tals, and the other which uses a similar system based on the centisol (one-hundredth of a Martian day, and hence one-tenth of a zode) and the millicentisol (as the thousandth part of a centisol, and hence the ten-thousandth part of a zode, that would equal a short tal).
And one can probably guess what the names of the centisol and the millicentisol would be shortened to when Universal Pictures wasn't listening: that is, Mars would be divided between Edgar Rice Burroughs fans and Battlestar Galactica fans.
Dr. Robert Zubrin, who is responsible for a bold plan for humans to explore Mars, has suggested the opposite kind of time system. Let a Martian day be divided into 24 Martian hours, each of which is divided into 60 Martian minutes, each of which is divided into 60 Martian seconds.
This makes the most sense, it would seem, but there is one problem. The Earth second is one of the bases on which our system of measurements rests, along with the metre and the kilogram. So it would be confusing to always be using two kinds of seconds.
Because we know the distance of Mars from the Sun to high accuracy, we know the ratio of the Martian sidereal year to the Earth sidereal year to high accuracy. What is more difficult to determine, without an observatory on Mars itself, is the precise length of the Martian tropical year.
Thus, while the Martian sidereal year can be determined to higher precision, we only know (from this site) that a Martian tropical year is 686.97258 Earth days long, or 668.592018 Martian days long.
What kind of a calendar would people use on Mars?
Because the day on Mars is not precisely locked to the day on Earth, any determination of which day, in a cycle of seven days, is Sunday (or Saturday, or Friday) is intrinsically arbitrary. This will cause a problem for those whose religious beliefs cause them to take such matters very seriously indeed.
That is a problem I can see no obvious way to solve. 40 minutes a day adds up to a whole day in 36 days, so the Martian week would come into step with the Earth week about once every 250 days. The Martian synodic period, the time when Mars, on average, comes into a given relationship with Earth, is about 780 days. So, if the members of one such religious group only travel to Mars roughly at every eighth orbital opportunity, they can observe every seventh day on Mars continuing from the sequence on Earth and both observe every seventh day in their personal lives and be in agreement with the others of the faithful.
Of course, once a week on Mars is well established, any launch opportunity could be used by the simple expedient of switching the ships' clocks from Earth time to Mars time at different times during the voyage depending on the relationship between the Martian week and the Earth week.
What would people on Mars use for months? The Martian moons both have very short periods. Since Phobos orbits Mars three times in a day, even trying to use the recurrence of conjunctions between Phobos and Deimos at a given longitude wouldn't directly produce a cycle longer than Deimos' five and a half day synodic period.
Percival Lowell described dates on Mars relative to the Martian seasons in terms of the Earth calendar, dividing the Martian year into twelve months and those months into "days" as on Earth. This was useful for illustrative purposes, but is obviously not suitable as it stands for timekeeping.
Should the Martian year be divided into twelve, twenty-two, twenty-three, or twenty-four months?
Twelve months, each 55.7 Martian days long on average, would certainly conform well with our habits of dividing the year into seasons. Those months could simply retain the Earth names, and the year could be aligned so that the vernal equinox arrived about March 41st. Except for the longer month, then, dates would correspond to Martian seasons about the same way that they corresponded to Earth seasons on Earth.
Twenty-two months would each be 30.4 Martian days long. This would fit well with the Earthly habit of months being usually either 30 or 31 days in length.
Twenty-three months would be about 29 Martian days long each. But they would also be 29.9 Earth days long, whereas with twenty-two months, they would be 31.2 Earth days long. So twenty-three months would give the closest approximation to an Earth month. Since months are an important financial period on Earth, there is something to be said for synchronizing the Martian month with the Earth month.
In that connection, the Gregorian year is 365.2425 days in length, and so the average length of an Earth calendar month is 30.43685 Earth days, or 29.622485 Martian days. So, if one wished to maintain a long-term synchronicity between months on Mars and months on Earth, one could divide the Martian year into 22.57 months; that is, one could have a Martian year with 23 months for four years out of every seven, and with 22 months for the other three years.
Finally, twenty-four months would be 27.9 Martian days long. This would result in a neat and tidy division of the year into twelve equal parts; each one would be composed of two months. One could, for example, have twelve months with the Earthly month names alternating with twelve months named after the Zodiacal constellations, as I believe someone else has suggested. As one of my proposals is aimed at synchronizing the Martian month with the Earth month, one could use the twelve month names from the French Revolutionary calendar along with the Zodiacal constellations to form a pool of 24 month names distinct from those used for the Earthly calendar.