Because of the Sun, which is 400 times larger than the Moon, but also 400 times farther away from Earth, so both the Sun and the Moon have the same apparent size in the sky.Option Elimination -
(A) Because of the Sun, which is 400 times larger than the Moon, but also 400 times farther away from Earth, so both the Sun and the Moon have the same apparent size in the sky. - "Because of" introduces a prepositional phrase; we need some noun or action it modifies. But here we have "so," the coordinating conjunction. For what? Are we combining two independent clauses? No. I'm afraid that's not right.
(B) The Sun, which is 400 times larger than the Moon, is also 400 times farther away from Earth, so the Sun and the Moon have the same apparent size in the sky. Ok. We have an independent clause combined by "so" with another independent clause. Moreover, it conveys the effect of "The Sun, which is 400 times larger than the Moon, is also 400 times farther away from Earth."
(C) The Sun and the Moon have the same apparent size in the sky because the Sun, which is 400 times larger than the Moon, and also 400 times farther away from Earth. - "because" introduces a subordinate clause. But what do we have after "because" modifiers? Wrong.
(D) Four hundred times larger than the Moon and 400 times farther away from Earth, the Sun has the same apparent size in the sky as the Moon's. - Moon's what? Size?. The better way to represent that is
The sun has the apparent size in the sky as that of the moon - there that goes to the size.
Or, The sun has the same apparent size in the sky as the Moon - here we are comparing the size of the Sun and the moon. It's ok to omit "that of" to avoid repetition.
Or, The sun has the same apparent size in the sky as the Moon does - here, "does" refers back to the action or the state mentioned earlier, which is having "the same apparent size in the sky."
(E) Four hundred times larger than the Moon and also 400 times farther away from Earth, so the Sun in the sky has the same apparent size as the Moon. - We have a modifier, then we need a noun it modifies. Why "So"? Are we combining two independent clauses? No. I'm afraid that's not right. Also, avoid "and also" - it's redundant.