Asteroid 7785 was an asteroid in the Graveyard, the asteroid belt that formed from what remained of Alderaan after its destruction by the Death Star's superlaser.
A rumor, circulated by Darth Vader, claimed that the Royal Palace of Alderaan had been discovered intact on Asteroid 7785. He hoped this rumor would lure Leia Organa and any other of the survivors of the Battle of Yavin to Alderaan, where Captain Janus Bonn waited for them. Vader soon added a story that a survivor had been discovered in the asteroid who claimed to be Bail Organa. Vader even built a replica of the Palace inside the asteroid as a trap. Unfortunately for Vader, a group of Alliance agents intercepted the message from Hanos Darr and Zaz Kamiroz before it reached Leia Organa, and arrived at the asteroid before she did. Vader's trap was sprung, but not on its intended victims. Though the Palace had not actually survived intact, a tiny fragment of the Royal Palace's structure was indeed discovered in asteroid 7785.