Observatories can be found by using a ship's scanner while on a planet, or are one result of the 'Ask For Directions' interaction with a NPC.
Observatories have short satellite dishes on top of their structures. Inside, the player will encounter a console that requests the next entry in a numerical sequence. If the player inputs a correct entry, the console will mark a nearby Ruin.
1092 - 0921 - 9210 - ?
In this puzzle, the order of the digits is shifted to the left by one with each successive element, with the leftmost digit being moved to the far right position. Therefore, the correct input will be 2109.
Sometimes, a lifeform at an Observatory will give the player a mission to destroy Depots. If the player accepts the mission, they will instantly get a five-star wanted level.