The confusion in replacing the missing stars comes from the fact that the player is supposed to look through the telescope at the constellation in question, to see which two missing points (stars) need to be replaced --
-- but nothing I saw while playing indicated that the object in question was a telescope, let alone that I was supposed to look through it. Honestly, I thought it was an art-deco style railing post cap, in keeping with the general design style of the Clockwork City. Only after I saw someone use the object in a YouTube video, did I realize that it was actually a telescope meant for player use.