Ah January... the first month of the year. Although given that the orbit of the Earth around the Sun is for all intents and purposes a circle and therefore doesn't really have a beginning and doesn't really care about one, we could have very well placed that beginning point anywhere. Also because it is a circle, we could have divided up the year into something other than 12 parts and it would have been absolutely fine.
It is by a very long series of historical accidents and improvements that we have come to sort of accept the Gregorian calendar as the universal civil calendar here on Earth. The year which is made up of 365 days and which has to be corrected by means of a leap year with an extra day every four years, also overlays twelve months in an almost arbitrary fashion and the idea that the year should begin on January 1 which is the date of appointment of some officers in the Roman Empire, is itself daft, hundreds of years after that empire has long since disappeared.
The most sensible notion would be to assign New Year's Day as one of the equinoxes; for at least then, it would be tied to some physically measurable phenomenon upon the Earth. As it is, January 1 isn't exactly a marker of anything in particular except the arbitrary marker of the beginning of the year which we have all agreed to.
The calendar with its January 1 beginning is a bit like Peter Pan's remark in JM Barrie's novel that "every time a child says 'I don't believe in fairies' there is a fairy somewhere that falls down dead." January 1 seems to me to be either a fiat date or a fiduciary date, in that it's all made up and only exists because we all believe that it does.
Naturally, our entire time system of days, hours, minutes, months and even the year itself, is utterly unsuited for use on any other planet; which all have their own year and period of rotation.
Actually, the whole idea of years and days which can be measured is kind of a nonsense on all but two planets in the solar system.
Mercury only has about 1½ days in its year. Venus has roughly 1.9 days in its year.
Jupiter has more than 10466, Saturn 24134, Uranus 42732, and Neptune 89728. All of the big gas giants spin amazingly quickly as well; with all of them spinning in less than an Earth day, and Jupiter especially taking less than ten of our hours.
Note that I have deliberately left out Mars. The dusty red plans of the fourth planet, might very well end up being the only other planet that humans ever end up visiting. It is also the only other planet which has anything resembling a sensible day or year relative to us.
Mars has a day which relative to the Earth is 24 hours and 39 minutes long. It's close enough that humans could actually get used to that because we've conducted experiments on people who work underground and have concluded that humans can function absolutely normally with a day as long as 29 hours long. An extra 39 minutes in the day relative to the Earth, would be perfectly acceptable.
Mars also has a year which although is longer, is at least sensible. Since we've already proven that the idea of a year and where it begins and ends is more or less arbitrary, then having a 668/669 day year, with New Year's Day being measured from the Spring equinox, is also perfectly fine.
A calendar which would have to be devised for Mars would need four leap years for every ten; which is actually insanely easy to wrap your head around. Leap years would be all years that are even numbered except for the ones ending in 0.
Of course this then brings into question the idea of how many days would be in a month and how many months there would be and in that respect, 23 months of 28 days and one of 24 days or 25 days, solves the problem. Or if you want to tack on all the days at once, every tenth year would be a leap year with the 24th month either being 24 for the other 9 and 28 every 10th year.
If there was a calendar of 668 days with four being added in the tenth year, then the best option for deciding weeks, is to adopt an 8-day week like the Romans used to have. I note that the Romans had a day exclusively set aside for shopping; which is kind of what a lot of people end up using their Saturday for now. The existence of a seven day week appears to have zero relationship to anything astronomical but is still one of the most stubborn and enduring aspects of our time keeping.
As for the names of the 24 months and the eight days of the week that end up being the most logical:
Viri - spring
Flavu - summer
Rubu - autumn
Cabu - winter
Green, Yellow, Red, Blue for the names of the four quarters.
Una, Duo, Tres, Quatra, Penta, Hexa.
15th Rubu-Hexa, MY53: would be the 15th day of the Sixth month of Autumn in the Mars Year of 53. (15/18/53).
I note that there is already a system for enumerating Mars years relative to the northern spring equinox which occurred on April 11, 1955. That equinox marked the beginning of Mars Year 1 (MY1). That means that we would be in Mars Year 35 (MY35) on Mars.
As literally all calendars are made up and the rotation of the planets doesn't give a hoot about how we choose to number them, then any sensible system will work just as well. I am sure that the people playing in the Mars Football World Cup in MY135 will not even give us a thought.
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