Over the years, how many hypothetical planets have been searched for but not found?

Vulcan (1860-1916) In 1916, Albert Einstein published his General Theory of Relativity, which explained the deviations in the motions of Mercury without the need to invoke an unknown intra-Mercurial planet. In May 1929 Erwin Freundlich, Potsdam, photographed the total solar eclipse in Sumatra, and later carefully examined the plates which showed a profusion of star images. Comparison plates were taken six months later. No unknown object brighter than 9th magnitude was found near the Sun.

Mercury's Moon (1974) Two days before the 29 March 1974 Mariner 10 flyby past Mercury, one instrument began registering bright emissions in the extreme UV that had "no right to be there". The next day it was gone. Three days later it reappeared, and the "object" appeared to detach itself from Mercury. The astronomers first thought they had seen a star. But they had seen it in two quite different directions, and every astronomer knew that these extreme UV wavelengths couldn't penetrate very far through the interstellar medium, suggesting that the object must be close. new moon. The "moon" was eventually identified as a hot star, 31 Crateris. What the original emissions came from, the ones spotted on the approach to the planet, remains a mystery.

Neith ( Moon of Venus) (1672-1892) In 1887 the Belgian Academy of Sciences published a long paper where each and every reported observation was investigated in detail. Several observations of the satellite were really stars seen in the vicinity of Venus. Roedkier's observations "checked out" especially well -- he had been fooled, in succession, by Chi Orionis, M Tauri, 71 Orionis, and Nu Geminorum! James Short had really seen a star somewhat fainter than 8th magnitude. All observations by Le Verrier and Montaigne could be similarly explained. Lambert's orbital calculations were demolished. The very last observation, by Horrebow in 1768, could be ascribed to Theta Librae. After this paper was published, only one more observation was reported, by a man who had earlier made a search for the satellite of Venus but failed to find it: on Aug 13 1892, E. E. Barnard recorded a 7th magnitude object near Venus. There is no star in the position recorded by Barnard, and Barnard's eyesight was notoriously excellent. We still don't know what he saw. Was it an asteroid that hadn't been charted? Or was it a short-lived nova that nobody else happened to see?

Earth's Second Moon (1846 to present) In 1997, Paul Wiegert (et al) discovered that Asteroid 3753 has a very strange orbit and can be considered a companion to Earth, though it certainly does not orbit the Earth directly.