The Planet Vulcan
Table of Contents:
Introduction

Classical Observations of Mercury

Einstein and Relativity

Applying Relativity to Mercury's Orbit

Further Applications of Relativity

Bibliography

Around 1846 the French mathematician Urbain le Verrier, the German astronomer Johann Galle, and the English astronomer and mathematician John Couch Adams discovered the planet Neptune by observing how Uranus' orbit differed from its path as predicted by Kepler's Laws of Planetary Motion and hypothesizing that the deviance was due to the gravitational influence of another planet yet unobserved.
 
Mercury's orbit, like Uranus', had characteristics that could not be easily accounted for by the gravity of the known nearby planets.  In 1860 le Verrier proposed that a similar solution could be applied to the procession of Mercury's orbit.  He named the sunward planet Vulcan, after the Roman god of metal-smithing and volcanoes, appropriate for a world so close to the Sun's warm embrace. 

Over the following years there were many alleged sightings of Vulcan, either transits of an object in front of the Sun or fleeting glimpses of something reflecting light during a solar eclipse.  Most of those were too small to have enough gravity to do the job, or were only seen once and then never again.  Le Verrier suggested that Vulcan might be the largest in a belt of asteroids inside Mercury's orbit.

After 1915, and the publication of Albert Einstein's Theory of Relativity the majority of interest in searching for Vulcan waned.  Some photographic plates from an eclipse in 1970 showed an object between Mercury and the Sun, but that is currently believed to have been just a comet.  Interest in Vulcan still lingers in the occult community, as do things like Counter-Earth, Planet X, Lemuria and Mu, and all sorts of other hypotheses abandoned by science at large.
Close sun
Image source: https://www.boulder.swri.edu/~durda/paintings.html

Closer Sun
Image Source:http://www.technovelgy.com/ct/Science-Fiction-News.asp?NewsNum=359

Even Closer Sun
Image source: http://spaceart1.ning.com/photo/dying-world

Closest Sun
Image source: http://www.psi.edu/about/staff/hartmann/pic-cat/esplanets.html