From a forum post on SyFy, I learned of Kethinov's commentary on the issue.
And I decided to write a response of how it could be solved.
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I have to agree with you. Having 12 planets in a single solar system is very implausible, there are some ways to resolve it but they are very improbable. There are three ways around.
1) One such trick would be with Trojan planets. You could pack multiple habitable planets within a single circle if you have a gas giant in that circular orbit, and the two habitable planets (Earth mass) being 60 degrees apart. Jupiter does it with populations of small asteroids in this solar system called Trojans and Greeks, there are no large bodies there but it's thought there could have been.
Where you see, in the first picture, the green (trojan and greek asteroids) and the orange (hilda asteroids) you could have larger bodies. Add 1 or 2 moons around the gas giant and you then have 5 habitable bodies. We're already rather contrived here, because while these configurations might be stable in computer codes, they have not been observed. Admittedly, we barely have the technology to do so if they were blatantly common and obvious and I don't believe much time has been invested in the effort.
You cannot, however, go from 5 to 12. Look at the picture from this solar system. Jupiter is very far out - behind the "snow line" and thus the inner planets like Earth can be in peace. Put it into the inner solar system and all the inner planets will likely fly out. You could try something clever liking having 2 planets at each Lagrangian point, or having, somehow, an extra inner planet even though there's a gas giant there bullying everything. I've already stretched credibility, so I'll stop at 6 planets.
To be fair, everything we've seen so far was a complete surprise. The technology to see the type of system I described here will be online within twenty years, at this rate, and thus if these kinds of configurations exist, we'll probably know by the time the next reboot comes around, assuming they don't shorten the time between reboots.
2) Another trick is a cross between a single star system and multiple star systems - binary stars. The sun is a single star - the nearest star is 4.3 light years away. Most stars, approximately two thirds of them, come in binaries. Sometimes they come in hierachial binaries, such that two stars orbit each other, and much further out you have a third star. Using this, you could get multiple habitable zones if these are wide binaries. Some binary stars, indeed it seems most, are relatively close to each other which makes most planetary orbits unstable. A system like the Tatooine system in star wars would have a high probability of instability, and indeed even if it's stable, there's a single habitable zone that's a ring with both stars in the middle. You want the stars far apart such that they both have their own separate habitable zone.
Alpha Centauri A & B, the nearest major stars, are themselves a binary, with a distance between them about double that between Earth and Pluto, and they're very similar to the sun, the smaller one is 0.8 suns, and the larger is 1.25 suns, if i recall correctly. People are currently looking for planets around the smaller one (it would be easier to identify) , you can read about it here:
http://seedmagazine.com/content/article/the_long_shot/
3) Globular clusters are dense agglomeration of stars, tens of thousands or more stars within a few cubic light years. You could hop from star to star in a relatively short time in such a system. I have not seen any speculation I can recall for habitable planets to abound in such systems.
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If you combine the first two tricks, you could potentially make it quite high up but again I still find 12 unlikely. On the other hand, what we've seen (gas giants super close to their star) was considered unlikely.
I do think there's a sociological appeal to these configurations. If you had so many planets nearby, there would be a drive to colonize them, and to develop exploration technology. A friend of mine speculated the other day that the space program in the USA would have done a lot better if Venus and Mars had been more "interesting", e.g. potentially habitable without tremendous technological efforts. Analogously, having a "brother" planet at a distance of 0.2 light years or something could drive us to develop FTL technology.
Why would they ever develop FTL technology and integrate them in half their ships if they were within a single star? It helps, but it seems unlikely.
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