Astrography

There are many contradicting models of the 'Verse and creator Joss Whedon has not published anything official. The closest thing to official is the "Complete and Official Map of the Verse" by QMX. But it is riddled with astronomical impossibilities. The companion piece, "The Verse in Numbers" is, in my opinion, even worse. The authors come up with some outlandish ideas to explain why all the planets have Earth-like gravity, days and seasons, etc.

I take a different approach. We only visit less than a dozen worlds in the entire series and movie. Maybe those worlds just happen to be Earthlike in gravity. And of those worlds, only a handful are visited long enough to get some idea of how long their day and night are. None of them are visited long enough to have any idea at all how long their seasons or local year are. Gravity between 80% and 120% of Earth's and days between 20 and 28 hours long might not be significant enough to neccesarily depict in a TV show.

So I have my own version of the map of the 'Verse, based on the map by QMX and taking some info from TViN, but a little more astronomically possible. I won't say it's not highly unlikely, but it's a little more possible. The map does contradict the show and movie frequently, but when it comes to travel times, I think the script places a location for plot convenience. So my map does contradict the show here and there. But, it's internally consistent, which is important for a campaign.

Using the World Generation Rules for Classic Traveller and GURPS Traveller, I created the summary charts on the pages below. The Traveller Universal World Profile lets me look at a world's entry and have an idea of the world, the Universal World Trade Number and Trade Classifications let me look at two worlds and calculate how much commerce passes between them.

Update
I just read The Verse in Numbers 2 and I see that they have addressed some of my issues, among them the positioning of habitable planets too close or too far from a star. Again, they have come up with some ideas which might work in a super science fiction setting, but which I feel are excessive for the Serenity setting.

Overview

The 'Verse consists of FIVE major stars (White Sun, Kalidasa, Georgia, Red Sun and Blue Sun) and a couple dwarf companion stars orbiting some of the primary stars. In order to get the number of habitable worlds listed in the series, some habitable worlds circle a primary star, others a dwarf companion and some are moons of a gas giant that is close enough to its primary that those moons are habitable.

White Sun is the largest and central star. Georgia and Red Sun orbit White Sun on opposite sides at 68 AU (astronomical units, the distance from the Sun to Earth. Neptune is about 30 AU for comparison). Kalidasa is further out at 121 AU and Blue Sun is even further at 181 AU.

If you looked at the picture of the system from a distance, you would think it was normal; a star with four planets. Except those "planets" are stars themselves, with planets of their own. Here's another chart which is easier to use for plotting travel times.

The various sources sometimes contradict each other on what is a planet and what is a moon, and the generic term world is often used. In my game, "world" refers to an inhabited body, whether it be a moon or a planet.