Cycles of the Moons

I'd like to pull some info together to help flesh out the cycles of the moons. For those that are scientifically inclined and for simplicity sake I will generally speak of synodic periods of the moon.  Sidereal periods will be more discussed below.  If you care to know more about the difference - Wikipedia is your friend.

Throughout history the phases of the moon have driven a number of things on Earth.  Time tracking and light at the night are some of the things that come to mind.  The world of Dark Sun has two moons revolving around its planet Athas.  Some people have wondered, what would this be like, what would their phases be like and how would it affect calendars and life in general on Athas. Unfortunately, the original authors of Dark Sun 2e never out right defined the orbital periods of these moons.  

When 4e came along, they also never specified the orbits or cycles of the moons.  This may be because this allows the DM to make them be what ever he or she wants them to be.  Which is fine, I always say DM > science.

I have seen others just ignore the this info; super convenient and easy to just make it whatever you what the phase to be for whenever, but sometimes people do care. Like those with the Draji Moon Priest that wants to know when he can next cast a certain spell and not have to rely on arbitrary DM decisions.  

The only semi-official source for moon periods is found in the Athas.org material in Trade Lords.  They decided to specify these as follows:

"Dune Traders and others that travel the wastes use the Two Moon Calendar to predict the moonlight on any given night. A quinth, meaning 75 days (a fifth of an Athasian Year), synchronizes Ral’s 25‐day phase cycle with Guthay’s 15‐ day phase cycle, and also coordinates the periods in which the moons rise and set."

The quinth is language and duration originally came from Lynn Abbey's book "Rise and Fall of a Dragon King". This appears to be an attempt to reconcile information presented in her book with official rules.  Although her books added depth to the Dark Sun world, many consider much of her writing to be non-canonical, as she wasn't always in the loop with what the game designers were writing.  I also find the math behind using these numbers problematic, discussed more below.  Therefore, I happen to ignore this decision to use a quinth and the moon phases at described in Trade Lords.  I prefer to use a Ral 33 day and Guthay 125 day period.  These periods were previously proposed by Agantyr and are found in his Merchant Calendar program

Although you can use whatever you want in your world for periods of the moons, here are a few things to consider that may sway you one way or another.

1) The Major Conjunction/Eclipse 

We know that there is a major conjunction that occurs every 11 years or 4125 days. this has been depicted as both moons being full when Ral crosses the face of Guthay. 

...Athas' two moons, Ral and Guthay, meet in the heavens, a major eclipse that occurs once every 11 years. (Dark Sun Campaign Setting pg 85) 

This means that when the duration of the phases of each of the moons are multiplied they will equal 4125.  The following combinations would also work:  33 and 125, 11 and 375, 25 and 165, 15 and 275, 55 and 75.  Using 25 and 15 day cycle result in  375 days. Or once every year.  However, if your are interested in using a quinth as a measurement of time for your Athas, I would tie it to the the phases of Guthay and put Ral at 55 days between phases.

2) A closer moon has a faster orbit

Troy Denning described the moon Guthay as being larger and Ral as being smaller. See The Crimson Legion chapter 13.  Brom's art depicted these two moons with the larger behind the smaller when seen during a conjunction. See that belgoi image with the moons behind it.  This infers that Guthay is the moon behind Ral and thus Guthay is further away.

In physics orbits are described with a an equation originally describe by Kepler.

Kepler's third law states that:   

Where "T" is the orbital period (or time in seconds to go around the planet one time)

"a" is the semi-major axis (think average distance between moon and planet)

"mu" - is a constant - don't worry about this for now.

Now just for simplicity sake think of it this way: as "a" gets bigger "T" will get bigger.  If "T" is relatively small number like 15 days it stands to reason that "a" is a certain distance for that moon.  When compared to a moon that has a 25 day period "a" will have to a larger distance as well.  What we get with Ral-25 and Guthay-15 puts Guthay in front of Ral, which doesn't square with Brom's art and Denning's description. Alternatively, if you decide that Ral is closer than Guthay it doesn't square with physics.  But again, you don't have to use science and can use whatever, and maybe your physics operates differently, or "magic" or you can just ignore this science-y stuff. 

3) Phases of the moons drive calendars

Calendars through out the history of the earth have largely been tied to the phase of our moon. ~29.5 days for our own moon.  We have months that are any where from 28 to 31 days.  Even the word month is derived from the word moon.  It stands to reason that month lengths and moon phases on Athas could possibly be related. A typical month on Athas is 30 days. Granted, 25 is close to 30 and 33 is closer.  But for argument sake let's look at both.  

If we allow 25 to be the period of Ral then the period of Guthay would be 165. (to get us to the 4125 days between eclipses) Likewise, if we allow 33 to be the period for Ral then the period for Guthay would be 125. The calendar presented in Dark Sun has one aspect to it that we should consider, that is the festival weeks that fall on every 125 days.  Which fits nicely for a Guthay-125 period. These festival being celebrated as Guthay waxes full and then culminates on the 125th day when the moon is 100% full. 

The Guthay-165 period doesn't appear to correlate to any other known or obvious calendrical events. ut again, you can use whatever alternate science/physics you want... if you like having all the math work out a Ral-33 and Guthay-125 works nicely.  

4) Sidereal period

There is one final aspect that could be considered in driving month length and in turn time between phases, and that is the sidereal period of the moons. If the synodic period is the time between full moons, the sidereal period is the time between positions in the night sky, (or the actual orbit of the moon; the time it takes make a complete orbit around Athas.) Think of it this way: When you look at the moon on a given night, certain stars will be near it or behind it.  Each night the moon will move to a different position with stars behind it.  The sidereal period tells you how long until the moon moves back to the same stars behind it. 

Our moon has a synodic period of ~29.5 days and a sidereal period of ~27.3 days

There is some complicated math to calculate this which boils down to the following equation:

Ts = 1/(1/Tm + 1/Tp)

Where "Tm" is the synodic period of the moon (~29.5) and "Tp" is the period of the planet (~365.25) which gives us ~27.3 days.

Doing this for a Ral-25 and Guthay-165 period gives us ~23.43 days and ~113.66 days sidereal periods respectively.  Nothing too remarkable about those numbers. This is even less interesting for Ral-55 and Guthay-75 periods.

However, when we do this for Ral-33 and Guthay-125 periods it provides more interesting results.  Ral's sidereal period turns out to be ~30.33 (close to almost exactly one month) while Guthay's sidereal period calculates to 93.75 or  exactly one quarter of a Athasian year.  This means that Ral will pass the same star in the sky every 30.33 days and Guthay will pass a given star every 93.75 days, making four complete revolutions around Athas in one year.  An Athasian could watch Ral move across the night sky each night and know that once it got back to the same point, about 30.33 days had passed or one month. 

5) The n-body problem and orbit resonance

If you are not familiar with the n-body problem for planetary bodies it's some pretty complicated physics.  I will only say that Ral-33 and Guthay-125 put the moons far enough away from each other so that one doesn't immediately get thrown off into space.  The sidereal periods of 30.33 and 93.75 put them at a ratio of 1:3.  Which happens to be stable orbits for the two moons. 

Anyway, those are my two extremely oversized ceramic bits and in the end it really doesn't matter, but if you like this stuff, well there it is. If you find it burdensome, then just ignore it and do what makes sense for you and your players.  I only dabble in this stuff a bit and it you happen to know more, I'd love to hear your input.