In science, advances arise at the intersection of theory and real-world observation.

One of the great puzzles of the 1500s was how planets moved in an apparently retrograde fashion. This could either be explained through Ptolemy’s geocentric model (L), or Copernicus’ heliocentric one (R). However, getting the details right to arbitrary precision was something that would require theoretical advances in our understanding of the rules underlying the observed phenomena. (ETHAN SIEGEL / BEYOND THE GALAXY)

Our measurements reveal what does exist, but only theory can predict what should exist.

The theory of universal gravitation can explain the observed orbits of the planets, with Kepler’s 2nd law being derivable from that: that planets orbiting the Sun sweep out equal areas in equal times. (WIKIMEDIA COMMONS USERS RJHALL AND TALIFERO)

Throughout astronomy’s history, observations led the way, revealing the Universe for theorists to describe.

Although this is a modern, infrared view of our Solar System’s 7th planet, it was only discovered in 1781 through the serendipitous observations of William Herschel. (ESO)

That would change after 1781, following William Herschel’s serendipitous discovery of Uranus.

A very old orrery of the planets and moons in the solar system. An examination of this points to an origin in the first half of the 19th century: well after the discovery of Uranus and some of its major moons, but before the discovery of Neptune. (ARMAGH OBSERVATORY, COLLEGE HILL)

The other planets dutifully followed the laws of planetary motion, but Uranus appeared to violate them.

By tracking the motions of Uranus for years and then decades, scientists could evaluate whether it was following the laws of planetary motion or not. In a puzzling surprise, Uranus appeared to move in a fashion that violated those laws. (NASA / VOYAGER 2)

Breaking Kepler’s laws, Uranus moved too quickly for decades, then at the right speed, then too slowly.

For decades, Uranus was observed to move too quickly (L), then at the correct speed (center), and then too slowly (R). This would be explained within Newton’s theory of gravitation if there were an additional, outer, massive world tugging on Uranus. In this visualization, Neptune is in blue, Uranus in green, with Jupiter and Saturn in cyan and orange, respectively. It was a calculation performed by Urbain Le Verrier that directly led to Neptune’s discovery in 1846. (MICHAEL RICHMOND OF R.I.T.)

The observations weren’t easily dismissable, but their physical cause was unknown.

Uranus, shown at right, appeared to orbit in violation of the laws of planetary motion. Rather than suggest a modification to the laws of gravity, simply adding in an undiscovered mass with the right parameters beyond Uranus (like Neptune, at left) could explain the observed anomalies in its orbit. (NASA / VOYAGER 2)

An additional planet beyond Uranus, gravitationally tugging on it, offered a potential solution.

The orbital dynamics of the planets matched the law of gravity extremely well, with the relative newcomer, Uranus, providing the biggest outlier. Determining the mass, position, orbital distance and inclination of a potential planet beyond that caused these orbital perturbations was a herculean task. (NASA / JPL-CALTECH / R. HURT)

Determining the mass, orbital parameters, and location of an unseen world presented incredible calculational challenges.

Urbain Le Verrier, depicted here, was an extremely talented mathematician with an interest in astronomy. In 1845, the famed physicist François Arago compelled Le Verrier to take up work on the problem of Uranus’ orbit. By 1846, Le Verrier had a solution. (HENRI CHAPU (MONUMENT); HERBERT HALL TURNER (PHOTO))

On August 31, 1846, Urbain Le Verrier composed a letter detailing the hypothetical planet’s location.

From 1845 to 1846, British astronomer John Couch Adams, also working on the problem of Uranus’ orbit, proposed no fewer than 5 potential locations for a hypothetical new planet, but detection remained elusive due to mistakes on both the theorist’s and the observers’ ends. Le Verrier made his first and only prediction in 1846, which led to a near-immediate observational discovery. (J. LEQUEUX, LE VERRIER — MAGNIFICENT AND DETESTABLE ASTRONOMER (2013))

On September 23, the letter arrived at the Berlin Observatory.

The planet Neptune and its largest moon Triton, as photographed by the Voyager 2 space probe in August 1989. Although it requires a very strong telescope to be able to see Neptune’s largest moon, Triton, Neptune itself can be seen with an off-the-shelf pair of binoculars, if you know where to look. With 1846-level technology, discovering its presence was easy and unambiguous, once its location was known. (NASA / VOYAGER 2)

That evening, within 1° of Le Verrier’s prediction, Neptune was discovered.

Neptune was discovered way back in 1846, but was predicted by two men competing to discover it: John Couch Adams and Urbain Le Verrier. Today, the two main rings of Neptune are known as the Adams and Le Verrier rings. (NASA / VOYAGER 2)

For the first time, a new astronomical object was discovered through its gravity alone.

After discovering Neptune by examining the orbital anomalies of Uranus, Le Verrier turned his attention to the orbital anomalies of Mercury. He proposed an interior planet, Vulcan, as an explanation. Although Vulcan did not exist, it was Le Verrier’s attention and calculations that helped lead Einstein to the eventual solution: General Relativity. (WIKIMEDIA COMMONS USER REYK)

François Arago, who compelled Le Verrier to investigate Uranus’ orbit, lauded him as “the discoverer of a planet with the point of his pen.”