From the Super Mario Wiki
The Observatory (Japanese: 幻想の部屋 Room of Illusion) is a room in Area Three of Luigi's Mansion.
After exiting the Astral Hall, Luigi enters the Observatory. He looks through a telescope and sees the Moon. After Luigi looks away, the walls fade away, allowing Luigi to enter a small balcony. Luigi sucks up a falling Meteor Ghost and shoots it at the Moon, allowing him to get Mario's Star.
The telescope is the only real object in the Observatory, apart from a small dresser with a globe on top near the door.