Hello everyone I just faced this question and cant decide whats the answer please help me.

There was an important reason to make such efforts: 5) .................. the moments a transit began and ended from different points on Earth, astronomers could use trigonometry to precisely calculate the distance from Earth to the sun.

5. a) having been recorded b) that recorded c) being recorded d) by recording e) recorded

I cant decide which one could be the answer I think ''a'' could be but ''d'' is more likely actually I dont know the usage of have+ing been v3.