Worldbuilt worlds will, by definition, have their own unique characteristics: rotation and revolution periods; axial obliquity; eccentricity variation; Milankovitch-style cycles; etc., all of which will contribute to making the place exotic and interesting.

One of the most-challenging-but-also-most-interesting aspects of a Worldbuilt world occurs 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. Holidays and birthdays will have different emphases. In a very real sense, time will have a different meaning.

When the presence or absence of companion objects such as moons or twin planets, 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.

One of the most-challenging-but-also-most-interesting aspects of a Worldbuilt world occurs 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. Holidays and birthdays will have different emphases. In a very real sense, time will have a different meaning.

When the presence or absence of companion objects such as moons or twin planets, 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**

Let’s try adding a planet to our own Solar system. We’ll call it Demeter (another name for Ceres, the dwarf planet which occupies pride-of-place in the Sun’s asteroid belt), and place Demeter on Ceres' known orbit of 2.76 AU. Further, let’s make Demeter 1.10 Earth masses and 1.04 Earth radii.

Its surface gravity, then will be:

Its surface gravity, then will be:

Demeter's orbital semi-major axis, being that of Ceres, is 2.76 AU; so, its period is:

This immediately gives us an exciting difference: Demeter’s “year” is over 4½ times that of Earth!

Note that we can use the short form here because the star is the Sun, so its mass value isM = 1.0, and at only 1.1 terran for the mass of Demeter, the planet’s mass is negligible.

If an inhabitant of Demeter 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:… or 26 hours and 24 minutes.

Remember that axial rotation periods areindependentof 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 (and in the other direction).

Here, again, an exciting distinction immediately appears. If your characters undertake a journey that comprises 8 Demetrian days, they will have travelled for more than 8½ days (8ᵈ 19ʰ 12ᵐ) terran.

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).

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).

So, how many

*Demetrian days*are in a*Demetrian year*?This can be collapsed into the singular equation:

Where:

8766 = (24)(365.25); hours in an Earth year;

What can we determine, then, about the sorts of months and weeks the Demetrians experience, and how they might organize, mark, and record time?

8766 = (24)(365.25); hours in an Earth year;

*κy*= the number of*local*days in the planet’s year;*P*= the planet’s orbital period in terrans;*ω**P*= the number of EARTH hours in one rotation of the planet.

What can we determine, then, about the sorts of months and weeks the Demetrians experience, and how they might organize, mark, and record time?

**Rudiments Of A Demetrian Calendar**

Let’s assume the dominant culture of Demetrians—the Naharesa—has a Medieval-level society without sophisticated astronomical observation and only a limited knowledge of advanced mathematics. Thus, they round their year up to 1523 full Demetrian days divide their day down into 26 equal periods (of 1 Earth-hour each).

No, there is no reason why the Demetrians should divide their rotational period into separate units each of which is one Earth-hour long—but we have to start somewhere, don't we?

Right off the bat, we have yet another challenge: 1523 is a prime number, and will not be evenly divisible by

One approach is to simply start dividing 1523 by whole numbers to see which quotients come out close to being a whole number.

*any*smaller numbers (including 26), so there is 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; I’ll leave it to the reader to check the math.)One approach is to simply start dividing 1523 by whole numbers to see which quotients come out close to being a whole number.

Dividing by 13 yields 117.154 days per month, but…. ewww.

Dividing the 1523 days of the Demetrian year into 19 months yields very nearly 80 Demetrian-days per month (80.158), but 19 is also a prime number, so there’s no convenient way to break a 19-Demetrian-day month into weeks.

Dividing the 1523 days of the Demetrian year into 19 months yields very nearly 80 Demetrian-days per month (80.158), 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.

A calendar with 39 months of 39 days has a certain symmetry to it; and, 39 is divisible by 3, though that results in a prime number 13….

Dividing by 40 results in months of 38.075 days, but

Using a value of 50 months is more promising:

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 the Naharesa, 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:

Dividing by 40 results in months of 38.075 days, but

*38 ÷ 2 = 19*, which is prime.…Using a value of 50 months is more promising:

- 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 the Naharesa, 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:

… still a full 2 days too long, though much closer to 1523.

Okay ... what if they divide the year into two halves of 25 months each? There are two 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 <1>? That would reduce the number of 31-day months to 23, and increase the number of 30-day months to 27, so they’d now have 27 months of 30 days each and 23 months of 31 days each, or:

Okay ... what if they divide the year into two halves of 25 months each? There are two 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 <1>? That would reduce the number of 31-day months to 23, and increase the number of 30-day months to 27, so they’d now have 27 months of 30 days each and 23 months of 31 days each, or:

… which works out perfectly!

Checking back to the table, you’ll note that an even better solution is 76 months of 20 days each, perhaps comprising four weeks of five days each, which would amount to 304 weeks per year. This would make each quarter of Demeter's year approximately 76 weeks, or 380.75 days long, with adjustments for the lengths of the seasons.

To calculate Demeter’s seasons, we’ll have to decide on an eccentricity for the orbit. Since we originally put Demeter on the same orbit as Ceres, let’s specify that it has the same orbital eccentricity, 0.076:

Checking back to the table, you’ll note that an even better solution is 76 months of 20 days each, perhaps comprising four weeks of five days each, which would amount to 304 weeks per year. This would make each quarter of Demeter's year approximately 76 weeks, or 380.75 days long, with adjustments for the lengths of the seasons.

To calculate Demeter’s seasons, we’ll have to decide on an eccentricity for the orbit. Since we originally put Demeter on the same orbit as Ceres, let’s specify that it has the same orbital eccentricity, 0.076:

*e*=*0.076**P*=*1674.81*Thus:

… and the seasons will be:

Alternatively:

Have you noticed what’s potentially missing from this scenario? What if Demeter has moons? How might a moon or moons affect the Demetrian reckoning of time?

**The Moons Of Demeter**

Let’s take the two moons postulated in the discussion of synodic periods and assign them to Demeter. We’ll make the outer one the larger of the two and call it Persephone and the inner, smaller one will be Kora (another name for Persephone) <2>. Looking back, we specified that these moons had orbital periods of 11.72 and 24.36 Earth days, respectively. These translate to 10.6545 Demetrian days for Kora and 22.1455 Demetrian days for Persephone.

Assuming the Naharesa round these up and down respectively to 11 and 22 Demetrian days, we immediately see that neither of these periods fits neatly into either a 30- or 31-day Demetrian month, or a 1523-day Demetrian year.

Such rounding

There would be approximately 76 such periods per Demetrian year (another good reason for using the 76-month alternative calendar system mentioned 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.

Assuming the Naharesa round these up and down respectively to 11 and 22 Demetrian days, we immediately see that neither of these periods fits neatly into either a 30- or 31-day Demetrian month, or a 1523-day Demetrian year.

Such rounding

*does*present a problem: 22 : 11 is a 2 : 1 mean motion resonance, which is not the actual case for these moons. 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 76-month alternative calendar system mentioned 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.

**Demetrian Clocks**

And what about Demetrian clocks? A Demetrian hour is 1.1 Earth-hours long (

We also have said nothing whatsoever about Demeter’s obliquity, so let's talk about that next.

*26.4 ÷ 24 = 1.1*), or 66 minutes, so a statement like, “We waited five-and-a-half [Demetrian] hours” means 6.05 Earth-hours (6ʰ 3ᵐ) transpired. 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 Demeter's Axis**

What if we set the obliquity of Demeter's axis to 30°? This would cause Demeter’s seasons (which on average will be 1.146 Earth years long) to have somewhat greater temperature variation than Earth’s seasons.

**Habitable Zones of Demeter's Star**

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.

I’ll revisit this in a later blog.

I’ll revisit this in a later blog.

## Notes

- Subtracting from the 25ᵗʰ and 50ᵗʰ months might at first seem more attractive, but in this scheme, the 50ᵗʰ month already has only 30 days, and subtracting a day leaves it with 29, which breaks an otherwise largely symmetrical solution—call me pedantic.
- 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.