WELL THAT WAS A WASTE OF FIVE MONTHS...

      A ways back, I got my hands on a gravity simulator program and I was really excited to use it. Y'see, when I was in school ensuring my status as an outcast and inspired by Star Wars, Star Trek, Babylon 5, and even the old PC game Nova 9, I tried my hand at creating planetary systems. They were initially crude but I would refine them as I learned new things like how to properly calculate an orbital period*, how to properly calculate gravity at a defined surface**, among other things. But the one thing I could never know was if the orbits I assigned the planets and especially the orbits of the moons were stable. I could only hope.

      As I progressed, I created a cursory society along with an outline of its history on one of these worlds and part of that culture and history was dependent on this world having two moons. Now, in my blissful ignorance, I assigned these moons names, masses, and orbital periods. The orbital periods were supposed to have some cosmic importance to the people below forming the basis of a complicated lunar calendar which would later be replaced by a simpler solar calendar making one wonder why I was even bothering to figure this all out in the first place. My only justification is that it actually is fun to try to get things to work out and that lunar calendars were important to early man on Earth and still exist in Jewish and Muslim calendars. But I figured the lunar calendar would have cultural significance and produce an alien way of thinking about time which is important when you want to create societies that aren't merely humans whose only noticeable difference from Earth humans is that they are wearing different hats.

      Yes, they're humans because I guess like Star Wars which takes place in a different galaxy a long time ago...given enough star systems, it's bound to happen again, right? The world "my" humans live on has a slightly stronger gravity, slightly thinner air, and such so they would be adapted to that. See? They're different! ;-)

      Anyways, I originally gave the moons of this world a 3:2 orbital resonance which means that the inner moon makes three orbits for every two made by the outer moon. I did this because I read somewhere that resonances like these help stabilize orbits and they do exist. The Galilean satellites of Jupiter orbit like that with Io completing four orbits for every two by Europa and for every one by Ganymede. I didn't want to go with 2:1 because it seemed both "too perfect" and offered little dynamicism so I went with 3:2 even though I've read that 5:3 and 7:4 are also stable. I assumed the moons would regularly eclipse each other because unlike Earth's moon, they would have formed from the same cloud of material the homeworld formed from. Ideally I wanted the cycle to take three solar years to complete and seven total cycles to bring everything back to the beginning where the moons eclipse each other in the new phase and probably produces a solar eclipse too for added effect.

       With the gravity simulator program, I could see if my ideas held any water. Right away there were problems. The orbits of the moons immediately destabilized and either crashed into each other or the outer one would be ejected from the system. I played with the distances but those orbits too would destabilize. My thoughts were that the moons were too massive so I reduced their masses by making their original radius in miles, their new radius in kilometers and adjusting their masses accordingly. I even stumbled upon a ratio of distances that seemed to be working but I wanted the simulation to run for a minimum of ten million simulated years before even considering the arrangement and then working out a lunar calendar from it even though there would be no chance it would resemble what I had hoped for. At this point, a stable set of orbits is the goal. It really is amazing the subtle interactions each object has with each other over the simulated years. The planets are stable (If I leave out the moons, I can run the simulation really fast. Even after 100 million years, the system remains as is), but finding an acceptable solution to this three-body problem has been maddening because it will all really just come down to a lucky guess.

       I almost made it, but like some tease, the simulation failed somewhere between 9.8 and 9.9 million years. It took me five months of letting my computer calculate all day while I was doing my web surfing and while I slept. The outer moon got ejected from the system. Small instabilities had built up to a critical point. And the trouble is, even as the worlds you set up deviate from the paths you give them doesn't mean something is ultimately wrong. These simulators reveal grand cycles you could not have imagined...even with our own solar system. The orbit of the planet Mars is affected by both Jupiter and Earth causing it to go from nearly circular to a highly eccentric orbit and back again over tens of millions of years. The same thing happens to two of the worlds in this particular star system of mine. So I noticed variations in the orbits when I'd check in on them over time, but how was I to know if this was merely some variance or the slow build-up to escape velocity? I guess if I were a real astrophysicist, I probably would have seen it coming sooner. I guess the simulation failing at that point shows that I'm on to something but it is frustrating to have to start over. I'm gonna keep the reduced masses since that's produced better results than before. I'm gonna keep the inner moon where it is since its orbit is ridiculously stable.

       Back to the drawing board....

ADDENDUM: I tried moving them around but to no avail so I'm gonna reduce the moons' masses again on the assumption that, like last time, their respective gravities are too much for the system to handle stably. I wish me luck...

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* p² = ka³ where p is the orbital period in years; a is the average distance from the object orbited in astronomical units (92,956,000 mi. [149,566,000 km]) and k is a constant which is the [Mass of the Sun ÷ Mass of the Object] (in consistent units). The mass of the Sun is 1.9895 x 10³³g for this calculation.

** g = [GM] ÷ r² where g is the surface gravity in meters per second squared (Earth's gravity for comparison is 9.797 m/s²); r is the radius of the object in meters; M is the mass of the object in kilograms; and G is the gravitational constant valued at 6.6667 x 10^-11 m³/kg∙s².