I see you on the verge of yawning. Don't do it! I'm telling you...don't. Okay. Fine. Yawn. But I'm telling you, this topic is very important in developing a realistic science fiction novel.
Most science fiction books are symbolic of a resulting consequence of societal, government, and cultural decisions happening today. Even if you're going to write a chick-lit/romance/light-hearted science fiction story you have to get the basics down to attract the science fiction peeps.
And the Sci-Fi masses love the "I told you so, People" moment. That second where, when they turn the last page, they look at the nearest person and say, "Ah ha! That's why I said we shouldn't genetically mix birds and whales! I knew it!"
...All right, that last sentence kinda detoured into a weird place. Let's just step out of AR's la-la land and get back on topic.
Governments are a main driver of societal change, whether it's City, County, State, or Country level. They start a society, trigger the end of a society, and drive the rebirth of a society. In writing, you can stay with today's current balance of governments but two things: one, it's boring and two, it's unrealistic.
Come on people! We're talking about a huge solar system...universe depending on how far in the future you're going. There's no way the G5 can maintain and sustain that kind of territory. Nor would the cultural and social framework thrive in such a widening of distance and expect to abide by detached government structures.
Look at history. As we evolved and spread out from Africa - or from hybrid chambers on some space ship where we were then "planted" onto Earth and given a send off kiss...whichever - our societies started to seed, spread, and split. It's like a drop in the water; the ripples go on until it dilutes back.
Your space frontier group will be separated. Their society will evolve to thrive within its new infrastructure, which will change its values, moral, and ethics. This will all be flexed off the government that oversees their ethical boundaries.
As a result, the society's culture will evolve and break off to some extent from the society they left and create a new (really recycled) government body. Then, when the various new societies throughout the solar system grow and start to bump hips, their conflict and dynamics will flex and strain once again. This will kick the cycle back around, merging, dividing, and remolding them. Humans and their governments are always similar to the analogy of "something new from the ashes".
So use the imagination to see the historical cycle of society and human development starting over again. Look back to go forward. Just make sure you've really thought out the details or the story will bite you in the rear and the least opportune moment.
Here's a couple links to get started on the various government systems/bodies.
Forms of Government from Scholastic (don't knock the elementary lessons, man. Have you seen "Are You Smarter Than a Fifth Grader"?)
Government Systems and Political Ideology
Types of Government
Nations: Forms of Government from the History Guy
Good writing all!