The discovery of Neptune is a well-known story, but what followed up may receive less attention. After the discovery of Uranus by Sir William Herschel in 1781, Alexis Bouvard calculated and published the astronomical tables of the orbit of Uranus in 1821. He soon found substantial deviations from the tables, so hypothesized that an unknown body was perturbing the orbit through gravitational  interaction. Between 1844 to 1846,  British astronomer John Couch Adams and French astronomer Urbain Le Verrier worked independently on the calculation of this new planet's orbit. Both asked their friends in observatory to look for the new planet following their prediction. However,  Le Verrier's friend Galle was a more skillful observer. With the help from a student,  Heinrich d'Arrest, in the Berlin Observatory, Galle identified it in the night sky in 1846, becoming the second human who found a new planet. It was named Neptune shortly after.     

Le Verrier's success aroused great enthusiasm among general news readers and even scientists. This illustrated the triumph of rationality, science, or Newtonian mechanics, echoing the optimism for humanity in the late 19th century.  Le Verrier, for sure, became very confident to this methodology.  By 1845, he had noticed unexplained peculiarities in Mercury's orbit. In 1859, he  predicted an unknown planet  existing between Mercury and sun, thus applying gravitational perturbation to Mercury.  Right after the prediction was made public, a physician who was an amateur astronomer claimed discovering the long sought after planet.  Le Verrier happily named the new planet "Vulcan".  Based on the observation, Le Verrier computed Vulcan's orbit, and more people joined the astronomic task to confirm its existence. Many observations had been made between 1859 to 1908. Before his death in 1877, each time Le Verrier received a report of observing the transit of supposed new planet over sun, he would use it to predict the time of next transit. However, none of the prediction was realized. As the existence of Vulcan could never be confirmed, Le Verrier began to suspect if the perturbation of Mercury's orbit was caused by something that could not be seen easily. He postulated that  a  series of asteroids- Vulcanoids- surrounding sun could apply the same degree of gravitational perturbation, but each one of them was too small to be observed from Earth.  Le Verrier created a hypothesis that allowed every kind of analysis but could never be proved.

In 1915 Einstein's theory of general relativity showed that the peculiarities in Mercury's orbit were the results of the spatiotemporal curvature caused by the mass of the Sun. This theory was empirically verified by Sir Eddington's observation during the solar eclipse of May 29, 1919. Most astronomers quickly accepted Einstein' theory, and also found that the corrected equation of gravity did not allow a large planet inside the orbit of Mercury.  So far to these days, space-based telescopes and the NASA Parker Solar Probe have detected no Vulcan or Vulcanoids between Mercury and the Sun.

Also after the discovery of Neptune, physicists found the deviation of Neptune from its predicted orbit. Every astronomer speculated that another farther object perturbed Neptune's revolution around Sun, so a race of discovering new planet began again. In 1894, a rich American, Percival Lowell, had founded Lowell Observatory in Arizona. In 1906, he started a project in search of a possible ninth planet, which he termed "Planet X".  Lowell and his staffs in the Observatory conducted search, using mathematical calculations made by Elizabeth Williams, until his death in 1916, but got nothing.  In 1929, Vesto Melvin Slipher, the observatory director, hired then 23-year-old Clyde Tombaugh to continue the search. After nearly a year, Tombaugh discovered a possible moving object on photographic plates taken previously. Soon it was confirmed that Tombaugh became the third person who discovered a new planet. It was later named "Pluto" following the suggestion from a 11-year-old British girl, Venetia Burney. 

It sounded another triumph of Newtonian mechanics. However, the size of Pluto was too small to disturb Neptune's orbit. Many astronomers speculated there were "a series of ultra-Neptunian bodies" or "many long-period planetary objects yet to be discovered" outside the orbit of Neptune, condensed from primordial solar nebula that formed solar system. In 1951,  Gerard Kuiper hypothesized that, early in the Solar System's evolution, the outskirt remnants formed a disc that condensed to generated many small bodies.  This hypothesis was further expanded to the prediction of "Kuiper belt"in 1980 by astronomer Julio Fernandez . However, no second Pluto-like object was found around and outside the orbit of Neptune.

In 1987, astronomer David Jewitt and his graduate student Jane Luu began to search another object beyond Pluto's orbit, as he told her, "If we don't, nobody will." Since then they have worked in the Observatories located in Arizona, Chile, and Hawaii, and introduced new technologies like charge-coupled devices (CCD), which becomes the basis for most astronomical detectors  nowadays. Finally, after five years of searching, Jewitt and Luu announced in 1992 the "Discovery of the candidate Kuiper belt object 1992 QB1". Six months later, they discovered a second object in the region. By 2018, over 2000 Kuiper belts objects had been discovered. 

In 1977, NASA launched Voyager 1 and 2 space probe. When Voyager 2 flied by Neptune in 1989, it sent back data that allowed more precise estimate of Neptune's mass. It was 5% more than the previous estimation. This correction made the "perturbation" of Neptune's orbit disappeared. That is, the discovery of Pluto was totally accidental, based on an incorrect analysis. However, it stimulated scientists' imagination and encouraged the exploration of boundary of solar system. Today, Kuiper belt is a well-built fact, and its concept greatly facilitates the theoretical development of solar system evolution.

I found the stories following the discovery of Neptune very inspiring. They reflect the nature of scientific research: experimental validation of a theory can lead to the rise of a paradigm, which guides the conceptual development of the follow-up studies. When a prediction fails, people want to amend the paradigm until they could not anymore. The failure of a prediction not only bring down a paradigm, but also urge people to think outside the box, eventually resulting in the new paradigm. This is really the unique beauty of science. 

No matter what, when a paradigm is established, scientists would get stuck with it for a while. During this period many new concepts might be ignored. The newest example was the development of RNA vaccine. This is also the reason that we should not read only papers published in so-called "high-profile" journals. We may get stuck in the current paradigm and miss the opportunity to do the paradigm shift by ourselves.