A quick review of these:
B: "ever more and more precise" is redundant and idiomatically incorrect. "Ever more" and "more and more" have approximately the same meaning, but these constructions can't be put together. Furthermore, in "scientists are hoping to enable them," the pronoun "them" can't grammatically refer back to "scientists," but the meaning of the sentence requires that it do so.
D: "with the purpose of making more precise measurements than ever" is suspiciously wordy (though not enough to rule out this choice except by comparison with others). The bigger problem is the "and" before "which" -- to what is "and" connecting the "which" clause? There's no other relative clause modifying "measurements," so this "and" is incorrect.
E: "more precise measurements than it ever did" creates a verb tense problem. The idiom "ever more precise" means that the measurements will become more and more precise as time goes by, while E suggests that the spacecraft's measurements used to be less precise, and will now become more precise. However, E lacks the sense of continuing improvement that the other answer choices contain.
Furthermore, the creation of a compound sentence (", and scientists are hoping...") eliminates the direct connection between the measurements and scientific understanding that is present in the original sentence.
On to C and A. I believe that A is the winner here.
The second problem with answer choice E also affects choice C. The compound sentence structure links two ideas that each function on their own as complete thoughts. Therefore, choice C creates a sentence containing two separate ideas:
#1) A spacecraft is going to make some especially precise measurements.
#2) Scientists sure hope that they will learn how the solar system formed.
Choice A creates a clear relationship between these two ideas; the measurements are what make it possible for scientists to understand the formation of the solar system.
Furthermore, the beginning of choice C is worded in an awkward and idiomatically incorrect way. In A, "to make" functions as an adverb modifying "moving." "For making" cannot function in this way; this modifier phrase will work like an adjective in the vast majority of cases ("his talent for making pancakes..." -- "for making" modifies "talent").