I will tell you how I opened the Gate, and flung away the Moon, and smiled as I did it.
-- Narrator (Prologue: Me, When I Was I)

Importance: When Hoa includes this statement in his prologue, it appears that he forced the Moon out of orbit because he was angry or spiteful. Even though Hoa and his fellow tuners had planned to use the Plutonic Engine to destroy Syl Anagist, Hoa threw the moon away from the earth to stop the fatal damage Father Earth had planned for the people.

The job you have to do is the easier of the two, you think. Just catch the Moon. Seal the Yumenes Rifting. Reduce the current Season’s predicted impact from thousands or millions of years back down to something manageable — something the human race has a chance of surviving. End the Fifth Seasons for all time.
-- Narrator (Chapter 1)

Importance: Essun believes that her job of bringing the moon back into alignment...