Monday, January 11, 2021

Space, as Douglas Adams used to say, is big.

Traveller is a pretty funky little system for creating sci-fi universes, but, like any game, it has its limits. For one thing, the excellent mapping system designs useful game environs without much correspondence to our real galaxy. Here's one example: globular clusters.

A globular cluster is a stellar formation, some of which are probably remnants of other galaxies that were absorbed by the Milky Way millions or billions of years ago. I was curious this morning about what fraction of the total mass of our galaxy is constituted by its ~150 known globular clusters. I ran the numbers as best I could and the answer seems to be about one one-thousandth of the total mass of the galaxy is located in those clusters. But that's a rough guess, as only slightly less than half of the total documented clusters in the Milky Way have mass figures on wikipedia.

Then I got thinking about stellar density. In Traveller, starmaps are drawn at one parsec a hex, with each hex either containing a single star system or nothing. Thus a subsector (6 hexes by 8 hexes) can contain no more than 48 star systems and a sector (16 subsectors in a 4x4 array) will have no more than 768 systems. That's with every hex filled; 200-400 systems per sector is more common on official sector maps.

Let's compare that level of stellar density to Omega Centauri, the largest known globular cluster in the Milky Way (pictured above). Globular Clusters are, well, globular in shape, so a flat map won't really do well to represent one. (This is another problem with Trav: the galaxy is flat as a pancake, at least with respect to jumpspace routes. More on that here.) So instead we will imagine each "hex" of space is a hexagonal prism on parsec thick.

With that assumption in place, Omega Centauri can be imagined as a series of stacked layers. The middle layer is about 27 hexes across. Above and below it are layers 53 hexes across. Above the top and below the bottom of that three layer sandwich are those two layers are layers 51 hexes across. And so one until this formation has a single hex sitting on top and at the bottom. If we assume each layer is itself hex-shaped, we end up with a thing that looks a bit like an eight-sided die, only the cross-section is a hexagon instead of a square. I guess you could make d12's that way, but they'd probably look way too much like a d10 to be useful at the table.

If the "north" pole of the cluster is a single hex, the level below
it would be three hexes across, followed by a layer five hexes across,
and so forth until you reach 53 hexes across, then reverse the process
until you get back down to one hex.

That's alot of total hexes. The middle, biggest layer would itself incompass 2,107 hexes by my math, or almost 3 standard Traveller sectors. The total space occupied by the cluster is 32,259 hexes. Wow! That's a little over 48 standard sectors, putting it in the ballpark of the original Traveller sector map, with it's 128 sectors.

At the parsec level, this map encompasses 98,304 hexes. There aren't nearly that many worlds on it, however. A lot of those hexes are empty. The Great Rift and Lesser Rift are very empty.

Okay, so the Omega Centauri cluster is 32,259 hexes. How many stars are packed in there? That's where this little exercise goes off the rails. Best estimate is that the cluster contains about TEN MILLION STARS. That averages to a fraction more than 269 stars per hex! That is to say, each 1-parsec hex of Omega Centauri could hold roughly as many worlds as are usually represented on a Traveller sector map. Of course, actual distribution will be less smooth than a flat 269 per hex. Stellar density in the cluster will be higher in the centermost hexes than out on the edges, probably following some variant of Zipf's law.

One thing I have to check at this point is how many solar systems can fit snugly in a single one-parsec hex, because part of me is doubting whether or not 269 systems can actually fit in a hex. (The other part of me knows that space is always bigger than I imagine it.) There are many ways to define the size of the solar system. I'm going to pick the heliosphere, which is the volume of space where the solar winds are more powerful than the insterstellar medium. I think. Maybe I should have mentioned earlier that I am not an astronomer. 

Anyway, I think that gives us a diameter of the solar system of 242 astronimal units (AUs). There are 206,264.806 AUs per parsec and by my math you could fit abut 9,930 spheres of 242 AU diameter into a hexagonal prism 206,264.806 AUs across and tall. Like Adams say, space is big. With nearly 10,000 spots available, finding room for 269 solar systems is a snap.

Does the existence of the Omega Centauri cluster and similar formation mean that Traveller astrography is rubbish? Not at all. The Traveller mapping mechanics produce useful, playable starchats for a universe of adventure. Still, I wonder what it would be like to play in a game universe where, instead of a Jump-1 drive being able to take you to your choice of up to 6 other worlds, it could take you to any one of a couple thousand possibilities. What would that look like, I wonder.


  1. It used to be thought that stars in a globular cluster would be unlikely to have planets because they are very old and thus have a low metallicity (i.e. abundance of elements heavier than helium). I guess that this idea has been questioned recently, since planets have been found around low metallicity stars. However, globular clusters (or other regions with a very high number of stars/cubic light year) are bad neighborhoods from the point of view of life. Orbits of planets can be perturbed by nearby stars, and planets can even be swapped between stars.

    1. Those are good considerations to keep in mind when developing a more realistic sci-fi universe. However, given 10 million stars in the cluster, it's just a matter of fine tuning the Drake Equation a bit to get a least some native lifeforms in the cluster. If you're playing something like Traveller already, there's probably already abundant life. And colonization from without opens up a lot of possibilities.

      Also, I think planetary migration might be a fun thing to explore in the setting. Planets aren't zooming around fast enough for it to directly impact in-play activities, but you could hide an ancient settlement by putting it in orbit around the wrong star.

  2. I always assumed Traveller maps didn't show every star. They show every star that has planets; i.e., places adventurers would want to go.

  3. I've played with home-ruled expansions to traveler world creation and I found if yuo add in a few more variables to the equation and roll honestly (no automatic occupied or occupied worlds) you get a whole lot of uninhabitable solar systems to anything but high tech groups.

    The more stars there are nearby the more likely some catastrophic star-related doom would burn away some adjacent civilizations and life itself as well.

    I feel it would be best to take the sub-sector maps of traveler as hyperspace maps of systems reachable by the technology in the game as opposed to a cataloging of every possible physical star in close proximity.