How many science points can be obtained through experiments in the whole solar system?

Infinitely much.

Each asteroid that is generated by the game is its own biome, and asteroid-centric research can be repeated for each of them, for full value each time.

Edit: In response to question edit:

It is possible to calculate the total amount of finite science points available, but it's:

• Meaningless. There is an infinite amount available.
• Extremely tedious work, which I expect is why you don't do this "simple calculation" yourself.
• So large a number that it might as well be infinite. An absolute lower bound exists. It's 209,444, and that is 0.90 and almost certainly missing a few edge cases even there.