I'd like to try an experiment - building a world here, adding a new (hopefully interconnected) piece each week. I don't have a story in mind - that's sort of the point, seeing what emerges just from the creation of the world itself. At some point this is going to need a name, but that feels rather premature for the moment.

Over the moon

Our bigger-and-heavier-than-Earth planet orbits around its deadly star every 120 years. That's a looong time to wait for Christmas - almost two generations. It'd be nice if they had something else to look at in the meantime.

Satellites are important to a planet's health and not just from a spiritual or aesthetic perspective of the inhabitants. Orbiting satellites help prevent tidal locking - a planet being stuck with the same side always facing its sun, the way the moon always faces the same side to earth. A planet that's tidally locked to a sun will fry on one side and freeze on the other, becoming rapidly uninhabitable. Satellites also help protect a planet from passing comets and asteroids, by influencing the gravitational pull or even providing a physical shield (if we're lucky).

With a solar year of 120 years, I'd like to add a couple of moons in there - it'll help break up that 120 years with varying kinds of eclipses and alignments. And besides, multiple moons is a great ingredient for inventing religions and cultures.

I'm going to go with three:

• One small, dense and dark - possibly the remaining core of a destroyed planet
• One medium, reddish and Mars-like. Smaller than Mars, though.
• One large, white and not-so-dense (what's a good antonym for dense?)

Okay. What we want to know now is the orbital period of each moon - how long each takes to go around our planet, and the size of it when it appears in the sky. For simplicity's sake, and because the satellites are different sizes anyway, I'm going to do with the same mass for each of them - about a quarter the mass of the Earth. Yes, there's maths, here. If it's too scary, skip to the end. I'll signal when it's over.

How close can we get...

First, we're going to need to check that the distance we want to use is possible - if too large bodies get too close, beyond what's called Roche's Limit, the gravitational forces rip them apart. (Doesn't apply if it's held together by structural forces, like a space station.) Roche's Limit is dependent on the density, size and distance of the two bodies: (2.44 *planet radius squared) * square root(planet density / satelite density)

Our planet's density is it's mass divided by the cube of its radius. Using our Earth-relatives, that gives us:

• a planet with a density of .5.
• a dark moon one fifth of the eath's radius, density of 31.25, Roche's Limit of .7AU
• a red moon one third of the earth's radius, density of 9.26, Roche's Limit of 1.33AU
• a white moon two third of the earth's radius, density of 1.16, Roche's Limit of 3.75AU

How long is a month?

We're using the same maths as we did to work out the size of our planet and its orbital period: square root((distance cubed) / mass). I want the dark moon in as close as possible, so we'll go with the limit of .7AU (that's 70% of the distance form the earth to the sun...

• Dark moon: sqrt((.7AU^3)/.25) = 1.17 earth-years.
• Red moon: sqrt((.1.4AU^3)/.25) = 3.13 earth-years. Let's round that to 3.15, which will orbit 38 times in 120 years.
• White moon: sqrt((4AU^3)/.25) = 16 earth-years.

The sixteen year cycle of the white moon gives 7.5 revolutions per planetary year. I like the half, there; it's an opportunity for spiritual or mystical 'gaps' in the cycles. Let's round the dark moon's cycle to 1.2 and the red's to 3.15,  which both fit nicely in 120 years. It means the satellites are just a little further out than we've calculated, and I'm all for fudging if it makes things easier to work with later - 38 and 100 months is much easier than 39.445 etc.

Important dates

Each of these moons will cross paths with the other at a given point in time. To find out how often, it's a simple matter of finding a common multiple using our adjusted dates:

• Dark-Red - 3.78 earth years.
• Dark-White - 19.2 earth years.
• White-Red - 50.4 earth years.
• Triple Eclipse - 60.48 earth years.

Note that  the triple eclipse occurs every sixty years (give or take - as I said, we can afford to fudge a little for the sake of story) - which is half our planet's solar year. That wasn't intentional on my part, I'm not that good at maths. But it's a convenient coincidence for something so monumental.