I\'m going to make a space/trading/combat game that is completely procedurally generated. But, I know that storing all of the details of the whole galaxy in memory is unfeas
A random seed for each solar system is a viable solution but I have a feeling you're barking up the wrong tree here.
Can the player do anything to change what's there? (Say, build something, mine a depleatable resource etc?) If so, you'll have to save the state anyway.
Can the player look up what the place was like without actually having to go back there? (And if he can't, why not?!) Are you going to look it up or are you going to regenerate the entire solar system just to find out a piece of information about it? (the PRNG solution doesn't permit you to obtain only part of the solar system, you have to make the whole thing.)
Just how much detail is there anyway that you need to save?