Ships in the world of Iliad-07 get up to nearly the speed of light for extended periods of time. This tremendous speed cause time on board to slow down relative to time on Earth. Missions like Iliad-07 can operate nearly indefinitely without communications from Earth. And even those communications would lag by 45 years.
Earth calendars are a bodge to try to reconcile astronomical phenomena with the human sense of repeatability and order. I say "Calendars" plural. One has to be aware of several different record keeping systems for dates to properly interact with clients across the globe. And there are a bevy of Calendars that one is required to understand for properly dating historical records.
They Earth rotates on its axis every 23 hours 56 minutes and 4.1 seconds. But because we are orbiting a star, and our position relative to that star changes during that rotation. This gives us the sense that the Sun is at the highest point in the sky rises every 24 hours (86400 seconds +/-7 seconds). This noon-to-noon is what the ancients (and our calendars) mark as a day.
The moon Orbits the Earth every 27.32 days. But... because the Earth itself is moving relative to the Sun, the pattern of light and shadow that makes what we think of the Moon's phases happens at a different rate: 29.53 days. This happens roughly 12 times a year, and thus why the calendar has 12 Months.
Finally, Earth is orbiting the star Sol. The Earth completes an orbit (roughly) every 365.2425 days. We call that a Year. And yes, it gets quite a bit more complicated than that. But I'm already in the weeds.
Ships are crewed by people. People evolved on a planet that had seasons. We expect events to repeat year after year. Beyond the psychological need, the plants and animals on board will also likely have growth, behavior, and reproductive patterns that only make sense in the context of seasons.
In the mid 21st century it was realized that any vessel or station operating outside of Earth orbit was going to need its own calendar. It is understood that personell moving from one ship or station to another was going to need to acclimatize to that shifted time, much like an air traveller has to adjust to local time.
Rather than replicate the insanity of a 400 year Gregorian calendar cycle, shoehorning moon orbits into roughy 12 even periods, and never knowing what day of the week January 1 will fall on, it was decided to generate a mathematical calendar which exists solely to provide those on board with a rough sense of repetitive events.
For Earth, ships, and space stations there is a universally agreed upon clock system based on Julian Days. This is simply the number of noon-to-noon events since November 24, 4714 BC (in the Gregorian Calendar). This date was chosen mathematically, and barring some Earth shattering archeological find, means that every date in recorded history is a positive number. Time in this system is recorded as a decimal point for a day. Remembering that the day starts at noon.
The Julian Date for 00:30:00.0 UT January 1, 2013, is 2456294.521. The Julian Date for the last time this page refreshed is 2459275.561
Each ship and station then establishes a "Mission Year Zero" (MYZ). This is the Julian date at which they start all record keeping. From this time forward, all events on the ship are recorded in the number of seconds (measured by the ship's atomic clock) since MYZ. This calendar system is designed to replicate most of the features of an Earth-based calendar but using a mathematical relationship that can be tied back to an absolute number of seconds.
A day is 86400 seconds on the ship's clock. An hour is 3600 seconds. A minute is 60 seconds. Days start at midnight (00:00). The time selected for MYZ is usually on a 0.5 mark for Julian Day to account for the difference between tracking day changes and noon vs. midnight.
A week is 7 days. This goes back to at least the Hebrews. It probably goes back to the first record keeping systems in the Near-East. For all its quirks, it works. Weeks start on Sunday and end on Saturday. Most planned activity happens on Monday through Friday, with Saturday and Sunday (the weekends) designated as a time for recreation and socializing.
A quarter is 19 weeks. Each quarter starts with a week of Holiday, followed by 3 months of 4 weeks each. This makes each year exactly 364 days, or 52 weeks. And weeks in this system cannot span multiple years, nor can a week span multiple months.
A typical calendar would look like:
You'll notice that the holidays are mostly just spelling the name of the season they represent backwards. (With a little license on Autumn.) This system also encompasses the idea that people more or less lose track of working time on a Holiday. Where I live in the United States, you just don't bother scheduling anything for the last 2 weeks in December. Nor for the week before or after Easter (wherever that might fall.)
Rather than have two major holidays of two weeks in the year, it was decided to go with one week of holidays 4 times a year. This is designed to allow for as many people as possible to have that entire block of time free from work.
7 days is not a long time to have a shop closed. With some preparation, most engineering systems can be set up to run happily for 7 days with minimal staffing. Having 7 days of commodities set aside requires far less storage than 14 days, assuming that commodity will even keep for 14 days. (Think milk and eggs, because the shops will be closed.)
Some departments must be run, regardless of a holiday going on. These departments are staffed in such a way that they can operate effectively with 1/4 of their personell for 7 days at a time. This includes emergency medical staff, food service personel, first responders, and utility workers.
The law on board is that nobody works more than one holiday per year. Ships take holidays deadly seriously. Overwork leads to sloppy work. Failing to make time to maintain social connections leads to isolation and mental illness.
If humanity learned anything from the Spreadheet Revolution, it is that nothing is more expensive than chasing cost.