Hi AdrianG,
Thank you for your question. Let's tackle this one problem at a time, and hopefully we can narrow things down to the right answer!
After a quick glance, it's clear the sentence is making a comparison. Whenever you see a comparison, the first thing to check is consistency or parallel structure. The sentence is comparing the theories of Galileo and Copernicus, which means each side of the comparison should be singular (Galileo's one theory vs. Copernicus' one theory). Let's see how each answer stacks up:
Galileo's theory that ours was indeed a solar system, in which Earth and other planets revolve around the sun, reinforced those of Copernicus.
A) ours was indeed a solar system, in which Earth and other planets revolve around the sun, reinforced those of Copernicus (singular/plural = WRONG)
B) ours was indeed a solar system, in which Earth and other planets revolve around the sun, reinforced that of Copernicus (singular/singular = OK)
C) our solar system was indeed solar for Earth and the other planets revolve around the sun, reinforced Copernicus' (singular/singular = OK)
D) our solar system was indeed solar, in which Earth and other planets revolve around the sun, reinforced those of Copernicus (singular/plural = WRONG)
E) Earth and the other planets revolve around the sun in our solar system reinforces that of Copernicus (singular/singular = OK)
We can rule out answers A & D because they compare Galileo's one theory to "those of" Copernicus, which is plural. Now, let's look at the answers we have left with the entire sentence intact and see if we can find the best answer:
B) Galileo's theory that ours was indeed a solar system, in which Earth and other planets revolve around the sun, reinforced that of Copernicus.
This is CORRECT because it uses parallel structure, and it keeps the modifier information between commas to show it's not vital information.
C) Galileo's theory that our solar system was indeed solar for Earth and the other planets revolve around the sun, reinforced Copernicus'.
This answer is INCORRECT because it uses the word "for" as a conjunction, but it doesn't have a comma before it. Therefore, this is a run-on sentence!
E) Galileo's theory that Earth and the other planets revolve around the sun in our solar system reinforces that of Copernicus.
This answer is INCORRECT because it changes the meaning of the sentence. Galileo's theory was that we live in a solar system, NOT that the Earth and other planets revolve around the sun (someone already came up with that...he just gave it a name).