I've never known Trek to use any numbering convention other than numbering planets outward from the star. This was a convention in science fiction long before Trek, inspired by the old system of numbering Jupiter's known satellites outward from the planet.
"Prime" may be an informal but widely-used designation.
I believe it originated with Giedi Prime in
Dune. I believe it's generally used to refer to the dominant or capital planet in an interstellar empire or civilization. Instead of indicating physical position around a star, it indicates a planet's dominant position in a political hierarchy.
Regarding letters, I thought that a binary star system's components were designated A and B.
Yes, and the first planet discovered around, say, George B would be George Bb, the next would be George Bc, etc. (The body itself is "a," so its first companion is "b.")
Side topic and note: I don't give a damn what anyone has done planet classifications, there are NINE planets in our system. Pluto IS a planet.
If Pluto is a planet, then so are Ceres, Eris, Haumea, Makemake, etc. Either there are eight planets, or there are dozens of planets. The whole reason the redesignation happened was because we discovered that Pluto was not unique, but was one of an entire class of similar bodies, so there is no logical reason to give it a different status from the others of its kind. Either none of them are planets or they all are. That's the part that always gets lost in the public controversy -- that it was never
just about Pluto. But that is by far the most important part, the only reason the redesignation happened at all.
It's bizarre how many people suddenly discovered they cared desperately about Pluto in 2006, when nobody'd given it much thought before. It was an afterthought, a footnote, an also-ran. Its biggest claim to fame was sharing the name of Mickey Mouse's dog. But try to change something people never cared about, and suddenly they get fanatical about keeping it the way it was, because nothing terrifies adults so much as having to learn something new.
The fact is, astronomers had never liked calling Pluto a planet, since it was too different from the four terrestrial and four giant planets. It was just what they called it for lack of a better category, but it was recognized that it was a poor fit. Some astronomers declined to call it a planet even before the 2006 redefinition (for instance,
the Internet Stellar Database no later than 2000). The discovery that Pluto was merely the first of dozens, possibly hundreds of dwarf planets -- the harbinger of its own distinctive category, rather than just a footnote among the planets -- was a
promotion, not a demotion. Suddenly we knew where Pluto really belonged. It's like taking a wrestler who was a failure in the middleweight class and reassigning them to the featherweight class where they should've been all along, allowing them to excel at last. It's an improvement.
But the idea that there are nine planets is as dead as the idea that there were seven planets once Neptune was discovered. Either there are eight planets and hundreds of dwarf planets, or there are hundreds of planets, most of which are dwarfs. Those are the only realistic options. Personally, I favor the latter. Dwarf stars are still considered stars, dwarf galaxies are still considered galaxies, so it's contradictory for dwarf planets not to be counted as planets. As I see it, Sol System has four giant planets (two gas, two ice), four terrestrial planets, and an as yet uncounted number of dwarf planets. None of them is "superior" or "inferior" based on their size, because science is not a bloody pumpkin-growing contest, it's a search for understanding.
