This page explains how to complete the level 83 Endwalker quest "A Trip to the Moon".
This quest is available if you have completed the quest Gateway of the Gods.
Starting the Quest
Talk to G'raha Tia in the Nethergate (accessible via a gate in northwest Garlemald) to begin the quest.
Activate the Teleportation Device
Go to the quest icon and check on the Allagan Teleportation Device, and say Yes to proceed.
Speak with the Ancient Spirit
Go northeast and attune to the Aetheryte, then go to the quest icon on the map and talk to the Ancient Spirit to proceed. Defeat the three Lingering Grief that attack.
Speak with the Ancient Spirit Again
Talk to the Ancient Spirit to proceed. There will be a cutscene.
Survey the Destination
Go northeast from the Aetheryte and into the building. Go to the quest icon and check on the sparkling Destination to proceed.
Search the Watcher's Palace
Go northwest to the ramp and then go up the ramp that spirals upward. Go through the door at the top and talk to the Watcher to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to the Watcher to accept the next quest: Sea of Sorrow.