Explanation
Correct answer: A.
Choice A is the best answer. It’s the only choice that offers a form of the verb “acknowledge” that can go with the subject “International Astronomical Union” to make a complete sentence. This might seem like an odd use of “would,” but when speaking from a point of view in the past, we can actually use “would” to express something that happened later. That’s the case here: 200 years after Wang Zhenyi’s death, the IAU would finally acknowledge her contributions.
Why the other choices are wrong
Choice B
Choice B is incorrect. This choice creates a sentence fragment. There’s no main verb elsewhere in the sentence, so we need a form of the verb “acknowledge” that can go with the subject “the International Astronomical Union” and serve as that main verb. “To acknowledge” can’t do that.
Choice C
Choice C is incorrect. This choice creates a sentence fragment. There’s no main verb elsewhere in the sentence, so we need a form of the verb “acknowledge” that can go with the subject “the International Astronomical Union” and serve as that main verb. “Having acknowledged” can’t do that.
Choice D
Choice D is incorrect. This choice creates a sentence fragment. There’s no main verb elsewhere in the sentence, so we need a form of the verb “acknowledge” that can go with the subject “the International Astronomical Union” and serve as that main verb. The “-ing” form can’t do that.