Observing a planet inside the orbit of Mercury would be extremely difficult, since the telescope must be pointed very close to the Sun, where the sky is never black. Also, an error in pointing the telescope can result in damage for the optics, and injury to the observer. The huge amount of light present even quite far away from the Sun can produce false reflections inside the optics, thus fooling the observer into seeing things that do not exist.
The best observational strategy might be to monitor the Sun's disk for possible transits, but transits would only be seen from Earth provided the object orbits close enough to the ecliptic plane. A small, dark spot might be seen to move across the Sun's disk, as happens with transits of Mercury and Venus.
In 1915, when Einstein successfully explained the apparent anomaly in Mercury's orbit, most astronomers abandoned the search for Vulcan. A few, however, remained convinced that not all the alleged observations of Vulcan were unfounded. Among these was Henry C Courten, of Dowling College, New York. Studying photographic plates of the 1970 eclipse of the Sun, he and his associates detected several objects which appeared to be in orbits close to the Sun.[12] Even accounting for artifacts, Courten felt that at least seven of the objects were real.
Courten believed that an intra-Mercurial planetoid between 130 and 800 kilometres in diameter was orbiting the Sun at a distance of about 0.1 AU. Other images on his eclipse plates led him to postulate the existence of an asteroid belt between Mercury and the Sun.
None of these claims has ever been substantiated after more than forty years of observation. It has been surmised, however, that some of these objects—and other alleged intra-Mercurial objects—may exist, being nothing more than previously unknown comets or small asteroids. Today, the search continues for these so-called vulcanoid asteroids, which are thought to exist in the region where Vulcan was once sought. None have been found yet and searches have ruled out any such asteroids larger than about 6 km.[2] Neither SOHO nor STEREO has detected a planet inside the orbit of Mercury.[2][13]