Vulcan's analogue in Greek mythology is the god Hephaestus?.
At one point it was suspected that there existed a small planet that orbited between Mercury and the Sun, proposed to explain perturbations in Mercury's orbit from the path predicted by Classical Mechanics. This hypothetical planet was known as Vulcan. Albert Einstein's Theory of Relativity later explained these perturbations without the need for a third body, however, and so the possible existence of the planet Vulcan was discounted.