Vulcan was a theorized planet that some pre-20th century astronomers thought existed in an orbit between Mercury and the Sun.

Speculation about, and even purported observations of, intermercurial bodies or planets date back to the beginning of the 17th century. The case for their probable existence was bolstered by the support of the French mathematician Urbain Le Verrier, who had predicted the existence of Neptune using disturbances in the orbit of Uranus.

By 1859 he had confirmed unexplained peculiarities in Mercury's orbit and predicted that they had to be the result of the gravitational influence of another unknown nearby planet or series of asteroids. A French amateur astronomer's report that he had observed an object passing in front of the Sun that same year led Le Verrier to announce that the long sought after planet, which he gave the name Vulcan, had been discovered at last.

In 1915 Einstein's theory of relativity, an approach to understanding gravity entirely differently from classical mechanics, removed the need for Le Verrier's hypothetical planet. It showed that the peculiarities in Mercury's orbit were the results of the curvature of spacetime caused by the mass of the Sun. This added a predicted 0.1 arc-second advance of Mercury's perihelion each orbital revolution, or 43 arc-seconds per century, exactly the observed amount (without any recourse to the existence of a hypothetical Vulcan).

The new theory modified the predicted orbits of all planets, but the magnitude of the differences from Newtonian theory diminishes rapidly as one gets farther from the Sun. Also, Mercury's fairly eccentric orbit makes it much easier to detect the perihelion shift than is the case for the nearly circular orbits of Venus and Earth. Einstein's theory was empirically verified in the Eddington experiment during the solar eclipse of May 29, 1919 when photographs showed the curvature of spacetime was bending starlight around the Sun. Astronomers generally quickly accepted that a large planet inside the orbit of Mercury could not exist, given the corrected equation of gravity.

Today, the International Astronomical Union has reserved the name "Vulcan" for the hypothetical planet, even though it has been ruled out, and also for the Vulcanoids, a hypothetical population of asteroids that may exist inside the orbit of the planet Mercury. Thus far, however, earth- and space-based telescopes and the NASA Parker Solar Probe have detected no such asteroids. While three Atira asteroids have perihelion points within the orbit of Mercury, their aphelia are outside Mercury's orbit. Therefore, they cannot be defined as Vulcanoids, which would require wholly intra-Mercurian circular orbital trajectories, which none of them possess.

The death of Vulcan: Study reveals planet is actually an astronomical illusion caused by stellar activity   PhysOrg - May 29, 2024

A planet thought to orbit the star 40 Eridani A - host to Mr. Spock's fictional home planet, Vulcan, in the "Star Trek" universe - is really a kind of astronomical illusion caused by the pulses and jitters of the star itself, a new study shows.