Astronomers had calculated orbits and trajectories in accordance with Newtonian physics in the day. In Newtonian physics, they, even, could predict objects – such as stars and exoplanets – without observing. Neptune was predicted because of anomalies in the orbit of Uranus although there was no other evidence or observation.
Like once detected in the orbit of Uranus, astronomers found a discrepancy in the orbit of Mercury. The point in which a planet’s orbital ellipse gets nearest to the Sun is known as the perihelion. And, Mercury’s perihelion instigated the prediction of Vulcan in the solar system. The reason is as follows. “As time passes, Mercury’s perihelion gradually rotates relative to the background of fixed stars. In effect, the entire orbit slowly pivots with the Sun at its focus; the technical term is precession. A mathematical result known as Newton’s theorem of revolving orbits predicts this effect as a consequence of perturbations by other planets. However, when Le Verrier plugged the observations into this theorem, the resulting numbers were slightly wrong. Newtonian theory predicted that the perihelion of Mercury should precess through 532’’(seconds of arc) every hundred years; the observed figure was 575’’. Something was causing an extra 43’’ precession per century. Le Verrier suggested that some undiscovered planet, orbiting closer to the Sun than Mercury, was responsible, and he named it Vulcan, after the Roman god of fire(1).”
But we know now, the discrepancy between the observation and Newtonian prediction is not caused by an undiscovered planet named Vulcan; it is about Newtonian gravitation itself. In general relativity, there is no discrepancy or an unknown planet but gravitational waves. Gravitational waves create an extra gravitational force on Mercury hence Mercury’s perihelion precession.
(1) Stewart, Ian. "The Clockwork Cosmos." Calculating the Cosmos: How Mathematics Unveils the Universe. London: Profile Books, 2017. 68-69. Print.
Figure - 64.1 https://blog.briankoberlein.com/image/precession.jpg