On Earth calendars serve two basic functions :
- Agricultural and resource management - observing yearly cycles.
Administrative requirements just need any calendar - it's completely arbitrary when it starts or stops. The seasons do not matter. It's simply a day counting thing so we can e.g. set tax years, prison sentences, contract schedules, travel schedules.
Standardization is very important. It means everyone uses the same basis for their calendars and avoids problems in organizing everything in a complex world. Standardization can also use an arbitrary calendar, just so long as everyone uses the same one.
Which leaves us agriculture and food production. This is really why we need calendars and why they were developed. Administrators and standardization got bolted on later as useful, but the original purpose was to make sure we plant crops, harvest and so on at the right times. It was a disaster to get these wrong.
But in space colonies we're not going to be need to observe local seasons as they have no human purpose. The computers can track any important events better than we can and let us know, so we can ignore the only reason to lock a calendar to a local astronomical or planetary cycle.
We already have a very highly developed "home" calendar on Earth and we're going to export that. We'll define some arbitrary standard, using our computers to do the maths and our atomic clocks to do the ticking. Keeping things synchronized is more complex in the very long run, but that just means standard's committees invents and using leap-years, leap-days, leap-hours, leap-minutes and leap-seconds (which they already do, so it just keeps them employed :-) ).
The Saturnian calendar must:
"Must" ? Probably not.
be cyclical; while it doesn't have to use years per se, it must have some similar sort of cycle by which to measure large spans of time.
We'll use what we have already. It works.
Use Saturn, Jupiter, and Uranus as reference points.
Totally pointless, actually worse than pointless as it's useless to the humans involved. There's just no function to it, but it would create utterly pointless complications in dealing with other planets and moons and space stations.
The weather doesn't matter as we can't live in the local conditions without suits and ships and vehicles and completely enclosed buildings. The local day or night doesn't matter because humans have a very hard-wired biological clock and trying to work against this clock will damage the health (mental and physical) of a human very quickly. The Earth's day-night cycle is not optional.
So we'll be completely ignoring local basis for the calendar.
Have days. Humans still sleep.
Precisely : and they do it to a hard-wired Earth day-night cycle. I'd suggest trying not to work to anything else, except it will rapidly screw your health up, so don't even perform the experiment.
Not be an endless count up like Unix time or Mars mission sol counts.
So we use those well established human things : days, months, years, centuries. Don't fix if it ain't broken.
Incidentally almost everyone in the industrial world relies on their smart phone to tell them the date, time, etc. and that's using a Unix time and date system. It's here to stay.
Tick at humanly relatable intervals. If each cycle is defined as a Uranian year, that's just ridiculous.
So what's the problem again ? We use Earth-related calendars because that's what will work for the humans.
Oh, yeah, you said this :
Mars goes with the good old Darian calendar
No it doesn't. It's that simple.
For all the reasons I've stated (and more) there is no way an organized, financially connected, human populated system will be adopting an artificial calendar like the rather academic Darian.
In the real world Mars will be populated by people who have ongoing business with Earth, operate to a standard Earth calendar and in the majority won't care a fiddler's damn about the obscurities of Martian orbits or "weather". It's only weather when you see it and practically every "Martian" will be living in a world locked off and out of direct contact with the real Mars (or be dead).
So they'll standardize on what they need day-to-day, which is Earth's standard calendar for business and finance.
Forget the Darian calendar - it's drivel that keeps a very small number of people amused, but there's no practical reason for a real Mars colony to use it.
I can tell you one thing human history shows us : regardless of what army winds and how long an Empire lasts, the bloody standard's committee seems to survive forever. The Roman empire may be long gong, but their standards committee seems still to be alive and well and working in ISO-land. Likewise the British Empire and the French Empire. Standards have nothing at all to do with reality, but with the practicalities of business.
There is no useful purpose to the organizers and standard makers who need to sync with an Earth calendar in using a Darian calendar. It's not going to be anything other than an obscure concept if there ever is a real Martian colony.
Even if scientist and engineers started with Darian for some geek-crazed reason, the first wave of non-scientific settlers would rapidly say "what the heck for ?" and use what they know and relate to - Earth's calendar (which their relatives, friends, business links and politicians on Earth will be using).
The Saturnian calendar was designed recently and from scratch, so it's not quite as prone to historical weirdness as the Gregorian one.
This is not going to be possible. Planets may, on some superficial level, seem regular, but even Earth's calendar has ended up the way it does because there is no natural "all-integer" way to build an Earth calendar that wouldn't be rejected as being too different from (yes) The Standard.
So you're on different Moons of Saturn. What difference or use is a locally based calendar to you ? None. Just like Mars you need to exist in a human friendly bubble to survive. Saturn's cycles have no meaning for you, the ordinary dweller. You work e.g. in a a bank on a moon of Saturn. What's more important : the date on Earth (observed by all its financial markets) or the local Saturnian date ?
Long before your colonies become powerful enough to impose their own standards on Earth, the imported standards will be so established and have such a locked in inertia that no amount of flag waving would shift them. Again - the Roman Empire fell, but its calendar did not !
Even if Earth was destroyed, its main calendars would live on. With the standards committees.