In 1846 French astronomer Frédéric Petit announced that he had discovered a second, smaller moon in an elliptical orbit around Earth. He was not the only astronomer to claim to have seen it -- on the evening of March 21, 1846 at least three other French astronomers reported sightings.
This was not too unusual; Petit was an expert on shooting stars, especially bolides, those meteors that flare or spark as they fall. However, when he calculated this one's trajectory, he concluded that it was not falling to Earth, but was in fact in orbit around it.
This was an interesting idea, and not entirely implausible, but his calculations showed it to be a body with a period of 2 hours 44 minutes 59 seconds, an apogee at 3570 km above the Earth's surface, and perigee at just 11.4 km above the Earth's surface -- well within the Earth's atmosphere. This of course, would explain why it flared so, but raised the question of how the orbit could survive, with the drag of the atmosphere applied every few hours.
The solution, of course, is simply that it could not; whatever Petit's moon may have been, it was not a moon... not for long, anyhow.
Petit did not give up on his theory, however, and over the years he received more reports of bolides that he believed to be minor moons; how many there might actually be, he did not know, only that there were clearly "one or more" smaller satellites in orbit about us. His theories did not catch on, but he was not discouraged. Although he learned not to refer to his bolides as satellites, it appears that right until his death in 1865 he continued to believe that we had small, flaring moons. He was not alone; while most professional astronomers did not accept his theories, they certainly captured the public's imagination. Many amateur astronomers continued to search for his moons after his death, along with other additional moons proposed by later astronomers.
Petit's moon also makes a brief appearance in in Jules Verne's 1869 novel Around the Moon, where it is used as a useful landmark, and treated as if it were a scientific fact known to all serious students of the night sky.