1. Fluff wise, most games don't take place on Earth, or even in our Universe. This would take more legwork from a DM if a player wanted to play it because it would need to be adapted.
2. A lot of the grammar and writing is confusing and could be cleaned up. For instance, what is 'proficiency in Wisdom rolls' from Neptune? Proficiency in Wisdom ability checks? Saving Throws? Spell Attack Rolls?
3. Flat bonuses (especially to AC) are bad. IE, a Warforged Druid at level 14 could easily hit a static AC of 26 while in Big Bang, assuming no multiclassing and a Dex 14. Plus it gets a free shield to boost up to 31 when needed.
4. Really broken multiclass potential. Its not something you're supposed to worry about too much if the class is otherwise solid, but a Paladin (or Hexblade) will bust this wide open. Elliptical orbit and such isn't so bad on a chassis that's normally mediocre at melee combat, but if you drop two levels of Paladin it gets crazy. Resistance to BPS, Increased Crit Range (Smite), and Bonus AC are all particularly problematic.
I hate it when people say this to me but unfortunately I have to say it: I am a little confused on the wording. What do you mean by elliptical orbit prepared? Does that mean you can choose between those options. The problem with having multiple options like this is that you have to try to make them equal. Seeing what Ursus the grim said is that saturn is obviously the best. You get barbarian rage without worrying about not being able to cast spells. If you really want to keep it make it like heavy armor mastery which is that you subtract piercing, bludgeoning, and slashing damage by 3. For big bang because of the wording if they save on a spell that allows to save for half you will actually reduce the damage by 1/8. Just say resistance unless you want people to be able to stack it. Venus healing on a stick is a little worrying.
Also I could be wrong but the 6th level makes it seems like they are at will abilities. People think that healing spirit is already really good or broken but with at will healing you will beat that easily because you don't even need to use a spell slot. Which wizards get something like that at level 18 but basically you are giving the 18th level wizard ability at level 6. Oh nevermind just read that it is only in elliptical orbit. That isn't as bad I suppose so that is okay forget what I said.
So basically then work on the wording a little bit. Apparently I need help on that too because like 3-4 people have said that about my homebrew. Basically though for balancing though I think that saturn is too strong compared to the others. Either bring them up or push down saturn. With this many options I don't want to do a deep dive. Mercury for example looks kind of weak. So if you are a wood elf you basically get +5 movement when you could have resistance against weapon attacks? Also jupiter you changed from spell attack to spell damage don't know if that was on purpose.
I don't think the +4 AC is that big of a deal but it is actually +9 because it is shield on a stick. So actually pluto is almost as strong as saturn. I have played in campaigns where at mid level creatures had a +16 to hit. That would mean that they would need to get a 15 to hit you. However this does nothing to spells that affect saving throws. So my biggest thing to potentially nerf is saturn.