One of the challenging but most interesting aspects of a Worldbuilt world is when its "day" and "year" are different from Earth's. Differences in these two periodic cycles mean that civilizations on that planet would have their own unique calendrical systems. When the presence or absence of companion objects such as twin planets or moons, which will have their own periodic cycles, are added into the mix, it can get quite challenging to work out realistic calendrical systems, but also very rewarding and lend a great deal of verisimilitude to the milieu.
Demeter and Family
Its surface gravity, then will be:
Demeter's orbital semi-major axis, being that of Ceres, is 2.76 AU; so, its period is:
If an inhabitant of this world is 20 local (Demetrian) years old, then she is almost 92 years old in Earth years! In describing characters and historical time periods for this world, it will be absolutely crucial to be very clear that local timespans are different—or every timespan will have to be converted to familiar Earth-based ones.
As this planet is slightly larger and more massive than Earth, let’s give it a proportionally longer day, say one Earth day multiplied by the mass of the planet:
Remember that axial rotation periods are independent of orbital revolutionary periods (unless the body is tidally locked to a larger object, of course). Also, a planet's rotational period is independent of its mass, radius, density, etc. A good example is Venus, which is quite close to Earth in mass, radius, and density, but rotates on its axis much more slowly.
Just to get a sense of what we're talking about here, below is an illustration that graphically compares one Earth year with one Demetrian year (measured in Earth days).
Rudiments Of A Demetrian Calendar
Right off the bat, we have yet another challenge: 1523 is a prime number, and will not be evenly divisible by any smaller numbers (including 26), so there are not going to be a convenient number of weeks or months in the Demetrian calendar. (As it happens, 1522, though not prime, isn’t much better—do the math.)
Dividing the 1523 days of the Demetrian year into 80 months yields very nearly 19 Demetrian-days per month (19.0375), but 19 is also a prime number, so there’s no convenient way to break a 19-Demetrian-day month into weeks.
(From here on out, when I use "days", "weeks", and/or "months", assume I'm speaking in Demetrian units. I'll explicitly specify, otherwise).
Using a value of 50 months is more promising: for one thing, it permits subdivision into smaller units of 10 by 5, or 2 by 25; doing the division of 1523 by 50 results in 30.46 days per month, which is very close to the same average number of days-per-month we have here, on Earth, so a reader wouldn't have to keep a mental note of a "month" being longer than they're used to in real life.
Rounding a month down to 30 days per month gives 1500 days, 23 days short of a year; rounding up to 31 days per month gives 1550 days, which is 27 days over.
Perhaps they, like Earthlings, would develop a complex but regularized system of alternating month lengths? However, simply making half of the months 30 days and the other half 31 days doesn’t quite work:
Okay ... what if they divide the year into two halves of 25 months each? There are 2 extra days in the alternating calendar just postulated, so what if they subtract one day from the 1st month and one day from the 25th month ? They now have 27 months of 30 days each and 23 months of 31 days each, or:
In fact, a better solution is 76 months, comprising 4 weeks of 5 days each, which amounts to 304 weeks per year. This would make each quarter of Demeter's year approximately 76 weeks, or 380.75 days long. However, the discussion above is completely in keeping with a way to work out near-comensurability for non-Terran time systems.
The Moons Of Demeter
Assuming the Demetrians round these up and down respectively to 11 and 22 Demetrian days, we immediately see that neither of these periods fits neatly into a 30- or 31-day Demetrian month, or a 1523-day Demetrian year.
Such rounding does present a problem: it implies a perfect 2:1 mean motion resonance between the moons’ periods, which our earlier discussion showed is definitely not the case. It might happen then, that rather than basing time reckoning on either of the individual moons’ orbits, they might base a time unit on their synodic period, in Demetrian units, of course, which would be 20.53355 Demetrian days.
There would be approximately 76 such periods per Demetrian year (another good reason for using the alternative calendar system mentioned in the sidebar above). This synodic period of 76 Demetrian days would divide into two halves of 38 days each, or four quarters of 19 days. The 19.5413 Earth-years it takes these two moons to return to exactly the same point in the sky translates to 4.262 Demetrian-years, four cycles of which equal just a fraction over 17 Demetrian years (17.04706).
It might be that some other Demetrian culture would base their calendar on these periods, rather than the year, in much the same way that some Earth cultures use months as the basis for their calendar.
And what about Demetrian clocks? A Demetrian hour is 1.1 Earth-hours long (26.4 ÷ 24 = 1.1), or 66 minutes, so a statement like, “We waited five-and-a-half hours”—if those are Demetrian hours—means 6.05 Earth-hours (6ʰ 3ᵐ). And, anyway—as we said earlier—why would the Demetrians divide their day into 26.4 units each one Earth-hour long, and not into some other number of units that would make more sense to them?
We also have said nothing whatsoever about Demeter’s obliquity, so let's talk about that next.
Obliquity Of The Demeter's Axis
It is also worth noting that at 2.76 AU Demeter is 1.39 AU outside the Sun’s habitable zone, so we’d really have to put it into a stellar system of its own with a proportionately more luminous star in order for it to be habitable at all.
Building a Star for Demeter
However, if we set Demeter’s orbit as the optimistic outer habitable zone orbit instead of the nucleal orbit:
Note that we have not changed Demeter’s orbital period, so the length of its year is still the same, and our earlier calculations for its days, months, etc., remain valid. We have simply defined the optimistic outer habitable zone limit for this star system to be equal to Demeter’s orbit. We have built the star, Zeus, to accommodate the planet, Demeter.
The Spectral Class of The Star
Doing the math:
So, while it is good for you, the Worldbuilder to know these details, it is best that they are shared with the viewer in the form of the interesting and curious details they provide to the narrative.
2. Yes, I know there is already an asteroid named Persephone and a Jovian moon named Kore, but this is hypothetical. In any case, these aren't the names the Demetrians would give their moons.