Tag Archives: calendars

The Hum Calendar

With work on the next issue of the Frontier Explorer happening, it’s taking me a bit longer to get to these posts than I had hopped but progress is being made. And I haven’t yet fallen behind.

Today we build the calendar system for Hum, the humma homeworld in the Fochrik system, which we have been detailing in the previous posts (part 1, part 2) in this series.

The Data

image credit – JPL

In the first part of this series, we established the following facts about Hum:

  • From Zebulon’s Guide to Frontier Space
    • Rotational period: 30 hours (we’re going to refine this a bit later on)
    • Surface gravity: 0.9g (which we increased the precision on to 0.91g)
    • 3 moons: Kran, Gluk, & Clud
  • From our calculations:
    • Orbital Distance: 1.23 AU
    • Orbital Period: 11323.3 hours
    • Density: 5.43 gm/cm3
    • Mass: 0.8139 Earth masses
    • Radius: 5,991.93 km

Of those parameters, we won’t be using the surface gravity, radius, or orbital distance in this analysis but we will be using the rest.

The Moons

I ignored the moons in the early parts of this series but now they become important so we need to detail them out a little bit more. Just as the orbital period of the Earth’s moon defines the concept of a month for us, given that this is the humma homeworld, the orbital periods of Hum’s moons would probably play a roll in defining their calendar system as well. So lets figure out the data on Hum’s moons.

All we really have to start with is the fact that there are three moons and their order (assuming the first one listed is the closest). Beyond that, we can really do whatever we want. That said, we have a few considerations to keep in mind.

First, Hum is smaller than Earth (about the size of Venus) and so has a smaller gravitational pull. This just means that the larger the moon, the more it will cause the planet to “wobble” about their common center of gravity. So we may not want any moon to be too big. It also means that if the moons have to be too far away, they might have escaped the planet’s gravity well. This latter point shouldn’t be an issue but is something to keep in mind.

Second, the moons will all mutually interact gravitationally. Which means if we have strong orbital resonances (orbital periods in small integer ratios), or if they have very close passes (with “close” depending on their relative sizes) as they orbit, the moon system may be unstable and not have survived to the present day.

So while we can pick anything we want, we should keep those ideas in mind. Now ideally, after picking the parameters for the moons and their orbits, I would generate orbital data for them all and run them through several hundred thousand or several million years of orbits to confirm stability but I didn’t do that. So we’ll just hope what we come up with something that makes sense and works.

The other thing to consider is what role we want to attribute to the moons in regards to the calendar system. This will have an impact on the orbital periods we pick.

Kran

From here on out we’ll be calculating time in hours and using the Galactic Standard Hour (which equals one Earth hour) as the value. In truth, there is no real reason for the humma to have an hour (or minutes or seconds for that matter) that correspond to that but it as useful measure to discuss the topic. There’s only so much new information you can wrap your mind about.

Kran is the innermost moon of the system. It will have the shortest orbital period of the three. As such, I decided that this moon would also be the smallest and associated with the “week” concept on Hum.

Since I want the “week” to be something on the order of 5 to 10 local days, and as I have no real reason to prefer one value of another, I’ll just roll 1d6+4 to get the value. I rolled a 5 so a Hum week is 9 local days long. Since the local day is 30 hours (from Zeb’s Guide), the week is 270 hours long. I want the orbital period of Kran to be something near this value so I just rolled four d10s to refine the number. The first one, I subtracted 5 from to get a number to add or subtract from 270, and the next 3 were just read as digits to represent the first 3 digits after the decimal place.

I rolled a 5 for the first die which meant no offset and then I got a 6, a 10(0), and a 4 so the orbital period of Kran is 270.604 hours. I realized later in the process that I should have probably given a bit more range the the +/- die but it’s fine as it is.

We’re also going to want to have a mass for the moon as that will have a small impact on its orbital distance. Since I wanted this moon to be small but still basically spherical, I just arbitrarily picked a size that was near to the size of the asteroid Ceres. I rolled some dice to pick exact values (although now I don’t remember exactly the rationale behind what I rolled) and came up with a value of 0.0125 times the mass of the Moon.

To get the size of the moon given its mass, we need its density. Referring back to the possible densities of the planets from the original article, I wanted to pick something in the 2-6 gm/cm3 range. So I rolled a d4+1 for the integer part and some d10s to get two decimal places and came up with
a density of 2.71 gm/cm3 for the moon.

Okay, now we’re all set to calculate the final values. Determining the radius is straightforward, we’re just back to this equation:

Only we’re solving for that r in there instead of M. That gives us a radius of 432.51 km. Next we want the orbital distance which takes us back to this equation:

where we are solving for a. M1 is the mass of the planet, and M2 is the mass of the moon. Again I used this handy website but since you can’t actually solve for a, I had to try various distances until I got the period to match. So it might have actually been faster to do the math on my calculator but oh well. We end up with a result of 198,336.5 km as the orbital distance for Kran.

For reference the diameter of Earth’s moon is 3474.2 km, almost exactly 8 times bigger, and it’s orbital distance is on average 384,400 km, so Kran is nearly twice as close.

Gluk & Clud

I’m not going to go over every detail of the other two moons but suffice it to say I followed the same procedure for each of those. The only constraints I had was that I wanted Gluk to be the largest of the three moons and have it’s orbital period correspond to between 1/8 to 1/14 of a year to represent the month concept. Clud was going to be way out there and orbit only about 4 times a year to correspond to the seasons.

After working through all the math we get the following results for each of the moons:

NameOrbital Period (hrs)Orbital Distance (km)Mass (moon)Density (gm/cm3)Radius (km)
Kran270.604198,336.50.01252.71432.5
Gluk1,026.836483,757.20.52373.141,430.2
Clud2,826.842948,883.70.24133.461,069.5

This image shows the sizes of the moons relative to each other and to Earth’s Moon. The image on the left shows their actual physical sizes if they were all side by side. The image on the right shows their apparent sizes as seen from the surface of Hum (assuming the Moon was dropped in at the proper distance).

The moons are all physically smaller than the Earth’s moon by quite a bit and appear smaller in the sky. Also, notice that because Kran is so much closer than the other moons, although it is physically the smallest, it appears almost as big as Gluk and larger than Clud.

Hum’s Rotation Period

One more thing we need to establish is the actual rotation period of Hum. The information in Zeb’s Guide said it was 30 hours. However, I want to add a few more decimal places but still have it round to 30. So employing my usual method, I rolled d10-6 (to get a value between -5 and +4) and then two d10s for decimal places. I then added that to 30 to get the actual rotation period in hours. I ended up with 30.09 hours.

The Calendar

Now that we have all the physical data we need, we can get on to the actual purpose of this post, determining the calendar of the planet Hum.

Length of Year

The first thing to determine is the length of the year in local days. We have the orbital period of the planet (11,323.3 hours – about 30% longer than an earth year and 41.5% longer than the Frontiers’ Galactic Standard Year) and the rotation period of the planet (30.09 hours) so we just divide and find that the Hum year is 376.3144 local days long.

In local day terms, the year is only a bit longer than an Earth year, just 11 days more. It also tells us we’re going to need leap years, about every third year. We’ll come back to that.

In the previous sections, with the exception of the moon Kran, I sort of glossed over the relationship between the orbital periods of the moons as they relate to the length of the Hum year. Now let’s look at that in detail.

A Week on Hum

The inner moon Kran has an orbital period of 270.604 hours. Dividing this by the length of a day (30.09) hours, we get that Kran orbits every 8.993 days. That’s almost exactly 9 days. In fact, amazingly close to to exactly 9 days. Which is why I said above, I should have allowed for a bit more variation.

You might be suspicious of how well these orbital periods line up. The exact values selected were not completely arbitrary. I picked approximate values based on what I wanted to see and then let the dice tweak them slightly. And then I also manually tuned them a bit more. For example, I actually rolled 30.06 hours as the rotational period of the planet but when working out the leap years, liked the values I got for 30.09 hours better and went with that. So it’s no coincidence that the numbers come out so close. Maybe too close.

But that’s fine, sometimes you get lucky. So we’ll define a week on Hum to be 9 days long. At some point the start of first day of the week corresponds to the full Kran on the meridian but since the cycles slowly drift, that only occurs every once in a while and the phases slowly move through the week.

Comparing Kran’s orbital period to the year, we see that it makes 41.84 orbits each year so a typical year is almost 42 weeks long.

A Hum Month

If we compare the orbital period of the moon Gluk to the length of day we see that it’s orbital period corresponds to 34.125 days. And comparing it to the planet’s orbital period, it makes 11.02737 orbits in a single year.

Since I’m going to tie the concept of a month to the orbit of Gluck, a nominal month is 34 days long and there are 11 months in the year. There might be some variation like on Earth but this works as a base line.

With eleven 34-day months, that accounts for 374 of the 376.31 days of the year, leaving 2 extra days in the calendar. I’m going to assign one of those days to one of the months making it 35 days long (in the spring) and the other will be a holiday celebrating the passing/new year and will occur at the end of summer which will be when the Hum calendar year ends.

A Seasonal Moon

That leaves us with Clud. It’s orbit is 93.95 days long and it orbits 4.006 times each year, completing one orbit every season. Since the timing of its orbit doesn’t quite line up with the planet’s orbital period, the timing of the full phase of this moon slowly shifts (by just over half a day a year) over the centuries but the humma have tracked this for millennia and know the pattern.

Leap Years

All that’s left is to deal with that pesky 0.3144 days left over after each year. Multiplying by 3 gives us 0.943 days, which is just enough to be considered another day. Thus every third year, the end of year holiday is a two day event instead of a single day adding an extra day on that particular year but not part of any month.

It’s not quite a full day though and so every 51 years, the deviations add up enough that the extra day is not added to the calendar, just like on Earth when we don’t add in the leap day on years divisible by 100.

Finally, there is one more minor correction and that occurs every 1530 years. On that year, which would normally be a year the extra day is skipped, the extra day is included (just like including the leap day here on Earth in years that are divisible by 400 as occurred in the year 2000). This has only occurred once since this calendar was established and the next one won’t occur for another 172 years.

The Final Calendar

So the final Hum calendar looks like this:

  • One week is 9 days long – in modern times it is a 6 day work week with a 3 day weekend
  • Each year has 11 months plus one holiday at the end of the year to celebrate the harvest and ring in the new year. This feast day/beginning of the new year corresponds to the end of the Hum summer (what we would call fall)
  • One month consists of 34 days, or nearly 4 weeks. The exception to this is the 5th month which is 35 days long. This occurs during the planting season giving one more day in that month.
  • Every three years there is a leap day, extending the harvest holiday into a 2 day event instead of a single day.
  • Except that every 51 years, the leap day is skipped and every 1530 years the day that would be skipped is included.

One more thing we need is to anchor this calendar with the Frontier standard calendar. To do that I’m going to say that the start of Hum year 2898 will coincide with FY60.124 and that year is a leap year so the end of year celebration (that starts on FY61.290) will last two days.

Last Thoughts

I realized as I was typing this up, that I didn’t account for the difference between sidereal and synodic periods for the moons. The orbital periods listed are really the synodic periods (as seen from the surface of Hum) but I treated them like the sidereal periods for computing orbital distances. Which means the distances are a bit off. The differences would be relatively small but that’s something I should revisit in the future. The rotation period for Hum is definitely the solar period (noon to noon) and not the sidereal period.

Otherwise, this is a pretty good description of Hum and its moons and a reasonable calendar for the system. I didn’t touch on Forge or Larg, the two other inhabited worlds in the Fochrik system. I’m assuming this calendar predates the humma’s space age and so is the foundation of any other calendar system on the other worlds. How it was adapted might be another article in the future but for now is left as an exercise for the reader.

What do you think of the calendar system presented? What would you have done differently? What do you like? Let me know in the comments below.

The Clarion Calendar

One of the things about sci-fi games that span multiple worlds is that each world has its own length of year and length of day that impact the way the planet operates. And while I’ve been pretty good about initially describing it for the worlds my on-line game has been set in, I’ve not been very good about keeping track of it during actual play.

I got to thinking about this some more as I was working on the Frontier Timeline. I needed an entry for a blank day and decided to make it the birthday of a notable person in the Frontier (Crown Princess Leotia Valentine Leotius of Clarion). And that got me to thinking about the time keeping on that planet.

Another thing that came out of this is the realization that so far, I’ve only really looked at this on planets that have really slow rotation periods. My online game has so far taken place on Pale in the Truane’s Star system which has a rotation period of about 55 hours and on Laco in the Dixon’s Star System which has a rotation period of about 60 hours. Clarion’s is 50 hours, 5 minutes. Which is funny to me since the length of a “Galactic Standard” day is only 20 hours. Maybe some day I’ll work on a system with a period close to that.

So this post is going to talk both about Clarion’s calendar and also about how I went about calculating it. We’ll start with what we know from published materials and work our way to a final calendar.

Stellar Data

From both the Expanded Game rules and the Warriors of White Light module, the star is described as a yellow-orange star. Zebulon’s Guide gives it a spectral type of F7 but that is a yellow-white star not a yellow-orange one. Yellow-orange would give it a spectral type of late G or early K so from notes I have in other places, I’ve assigned White Light the spectral type of K1.

This means that the star is about 72% the mass of our sun. The exact value I assigned is .72155 solar masses (actually I took it to a few more decimal places) or 1.43516×1030 kg.

Orbital Data

Orbital Distance

In the Warriors of White module there is this image of the White Light system:

Based on the scale on the image I estimated that the orbital distance of Clarion was about 93 million kilometers (for reference the Earth is about 150 million km from the sun). This makes sense for a K1 star that is less luminous than the Sun as a habitable planet would have to be closer. The exact value I gave for the semi-major axis of the orbit was 93,027,587 km. That was generated by simply rolling six d10s for the digits after 93. Had the first digit not been low, I might have rolled a d4-1 but I actually rolled a zero so I was happy.

Orbital Period

Now that we have the mass of the star and the orbital distance we can calculate the orbital period of the planet. This can be done simply by applying Newton’s form of Kepler’s Third Law of planetary motion:

Where we have the following:

  • P = the planet’s orbital period
  • a = the semi-major axis
  • G = the gravitational constant
  • M1 = the mass of the star
  • M2 = the mass of the planet (which we’ll ignore here as it is about half a million times smaller than M1)

I’m working in hours since I’ve decided that everyone in the Frontier uses that same unit of measure and it’s equal (for the convenience of us Earthlings playing the game) to an hour here on Earth. So an hour on Clarion is the same as an hour on Pale is the same as an hour on Gran Quivera (Prenglar system) is the same as an hour on Earth.

Plugging everything in in the correct units (left as an exercise for the reader) we get that the orbital period of Clarion around White Light is 5059.77 hours. This means that the “year” on Clarion is just under 253 Galactic Standard days; significantly shorter than the 400 Galactic Standard days in a Galactic Standard year (which is only ~91.3% of an Earth year). Compared to Earth, the year on Clarion is only 211 days long, about 58% of our year.

But we’re not quite done yet as we need to calculate that in terms of the local day.

Rotational Period

This one is easy. The Warriors of White Light module says that the rotation period of the planet is 50 hours and 5 minutes, with is just a little more precise than the 50 hours given in the Expanded Rules and Zebulon’s Guide so we’ll go with that number. I’m just going to leave it as is and not add any extra seconds on to it.

So if we take that value, it turns out that Clarion rotates 101.027 times every year. Or said another way, the year is 101.027 local days long. The fact that it was almost an integer number of days was a happy coincidence. I did not try to make that happen. I was pleasantly surprised when it did.

The Calendar

Okay, now we have everything we need to get the calendar set up. Well, almost everything. There is one more bit we need to do.

Clarion was settled by humans. Who we assume are somewhat like us Earthlings in that they work better on a 20-25 hour day than a 50 hour one. When the humans landed on Clarion, the decided to simply divide the long 50 hour diurnal period into two 25 hour days. They deal with the extra 5 minutes by adding in an hour the “night” period every 12 days and most people get a little extra rest that night.

Each of these 25 hour day periods are divided into a “day” period and a “night” period even though it may or may not be light or dark as one would expect by the name. Like the locals on Laco, they refer to the periods throughout a single diurnal cycle as “day-day” and “day-night” when the star is up and “night-day” and “night-night” when the star is down.

With this set up, there are 202.054 days in the year. They break it down as follows. (From here on out, unless specified, the term day refers to one of these 25 hour periods).

  • 1 week = 8 days (4 diurnal periods)
  • 1 month = 20 local days (10 diurnal periods)
  • 1 year contains 10 months with two special holidays occurring mid-year (between months 5 & 6) and on the last day of the year.
    • The mid-year day is Observance Day, set aside to remember and commemorate all those who have sacrificed for the survival and safety of the planet.
    • The end year holiday is Landing Day, commemorating the day the original settlers landed on the planet. In many ways it is also a celebration of the ruling Leotus family and is often the day for coronations of new monarchs or other events related to the ruling family.
  • Every 37 years, that 0.027 of a local day catches up with the calendar and they have a leap year. On that year, they add an extra day to both Observance Day and Landing day making each a 2 day holiday. The next such occurrence of the Clarion leap year occurs during FY 69.

Reckoning Age

One impact of the calendar is that people have a lot of birthdays. Because of the very short local year, and the fact that the rate that the settlers grow and mature is similar to us here on Earth, people on Clarion mature much slower than their “age” would indicate. A 16 year old Clarionite is only 9.25 Earth years old. You probably shouldn’t give them the keys to the hovercar.

Because of this, the early settlers established the age of 35 (in local years) as the age of majority on the planet. This roughly corresponds to someone that is 22.13 Galactic Standard years old (or 20.2 Earth years old). There has been a bit of a push in recent years to lower this to 30 local years but the movement has not gained much traction.

Crown Princess Leotia

Which brings me back to what started all of this in the first place – Crown Princess Leotia’s birthday. The Warriors of White Light module contains this little tidbit:

The current king, Leotus XIX, has ruled for 37 years and soon will no doubt abdicate in favor of his daughter, Leotia XX.

If you’re following along with my #SFTimeline posts on Twitter, and reading this on the day the post publishes (Jan 15, 2019), I’m going to spoil a timeline entry for next week:

FY60.017 – Leotia Valentine Leotus, crown princess of Clarion (White Light), celebrates her 32nd birthday (18.5 earth years) #SFTimeline

I’m taking the “soon” in the quote from the module to be within the next decade or so (GST) and have decided that it will probably occur during the 2-day Landing Day celebration in FY 69. I also want Leotia to be young but she will have had to reach her majority by then. So I decided that she is about to celebrate her 32nd birthday.

The abdication might have occurred sooner but by the time Leotia reaches her majority (which will occur on FY61.375, the Second Sathar War will be in full swing and Leotus XIX doesn’t feel that she’s quite up to that task at her young age and so decides to wait until the big celebration in FY69.

Final thoughts

I had a lot of fun working this out. I’ll probably be doing it for more of the Frontier worlds in the future, again probably tied to trying to tie a series of local events into my timeline project. Although I may go do Pale and Laco first as part of my game background.

Have you ever done this for any of your worlds? Do you think it adds to the verisimilitude of the game or is it just too much of a hassle? Is there anything I didn’t explain to your liking? Share your thoughts and ideas below.