Vulcan

Vulcan was thought to be a planet in the solar system, in orbit around our Sun but inside the orbit of Mercury. As such it is the first instance of dark matter ever invoked by astronomers seeking to explain an observation inconsistent with physical law as they then understood it. With a better understanding of the physics of celestial bodies of tremendous mass, astronomers abandoned the concept of any such planet.

Theoretical background
Sir Isaac Newton first proposed his law of gravitation to explain Kepler's Laws of Planetary Motion: $$F = \frac{GMm}{R^2}$$

where F is the force of gravity, M and m are the masses of a primary and its orbiting body, respectively, and R is the radial distance between the orbiting body and the barycenter. Where M is much larger than m, the barycenter is at or very near the center of the primary. G, of course, is Newton's gravitational constant, later measured by Henry Cavendish.

Newton's equation assumes that M and m are both constant, irrespective of their absolute magnitudes, their proportion, or the value of R. For most of the satellites of the sun, this assumption is safe, and the Newton equation gives a good first-order approximation of the force holding any satellite of the sun in orbit around the sun. With this equation, astronomers could calculate the orbits of virtually all the then-known planets, from Venus on out, with great accuracy.

However, Mercury presented a problem. Mercury's orbit is significantly eccentric, and with each successive orbit, its perihelion, or point of closest approach to the Sun, will precess slightly. Though some precession is only to be expected on account of the mass of the other solar system bodies, Mercury's perihelion still precesses 43 arc-seconds per century more than Newton's equation would predict, after accounting for the masses of Mercury, the Sun, and the planets Venus and Earth.

A fudge factor
Astronomers sought to explain the anomalous precession by assuming other objects in the inner solar system that they could not see&mdash;in other words, the first dark matter, or matter that, though unseen and unobservable, nevertheless exerts a gravitational influence on other, observable matter. Some astronomers proposed a second, inner asteroid belt; others an additional planet; all agreed, however, that this matter, in whatever form, must lie inside the orbit of Mercury. If it were an asteroid belt, then the individual asteroids would be too dim to resolve against the Sun. If it were an additional planet, then that planet must always keep station on the far side of the Sun from the earth. Champions of the additional-planet theory commonly named this hypothetical planet Vulcan, after the Romanization of the Greek god of fire and of smithing.

Neither proposal was fully satisfactory. Inner asteroids, even if too small to resolve, would nevertheless occult fixed stars on occasion. An inner planet would have a period less than an Earth year and thus must be visible to Earth observers at various times or even have been known to the ancients. No such evidence was ever adduced from astronomical or other historical records.

Einstein solves the problem
Albert Einstein, in 1915, presented a solution that derives from his general theory of relativity. In this scheme, an object subject to gravity is no different from an object under acceleration. Therefore, its own mass will increase as if the object were accelerating at a rate equal to the gravitational acceleration. For Venus and the other planets further out, this acceleration is not enough to consider. But for Mercury, a second-order correction is clearly required.

Einstein made the second-order correction and found that he could account exactly for the 43 arc-seconds-per-century of precession of the orbit of Mercury. With the popularization of his solution, and of the theory behind it, astronomers no longer needed to assume that any additional matter existed in the inner solar system.

Implications for modern-day astronomy
Dr. John Hartnett reviewed the Vulcan controversy in his latest book, Starlight, Time, and the New Physics. He places the supposition about Vulcan (or an inner asteroid belt) in the same category as Ptolemy's eccentric, epicycles, and equants, concepts that Ptolemy invented to explain the motions of planets from Mercury outward that did not conform to a geocentric view of the universe. More to the point, he asserts that modern astronomers, and particularly Big Bang cosmologists, routinely invoke dark matter and dark energy to explain observations that their cosmology does not predict, and says that these astronomers, like those who once invoked Vulcan, are guilty of violating Occam's razor.