Short answers, pulled from the story.
Charles Bonnet wrote the original text describing planetary distances in a textbook published in 1764. This work contained a sequence of numbers that matched the spacing of known planets from the Sun.
Johann Daniel Titius added two paragraphs introducing a specific mathematical pattern to Charles Bonnets work during his 1766 translation. These lines established a progression where each planet distance was roughly double the previous one.
Astronomers discovered Uranus in 1781, which fit into the series nearly exactly and transformed the hypothesis into a serious scientific tool. The discovery validated the predicted gap between Mars and Jupiter at 2.8 astronomical units.
The law failed because Neptune sat at 30.07 astronomical units while the formula predicted 38.8 astronomical units upon its discovery in 1846. Pluto appeared near the designated spot for Neptune rather than its own predicted location when found in 1930.
A study applied a generalized relation to 68 exoplanet systems containing four or more planets and showed that 96% of these systems adhere to the rule. This research detected five candidate planets from the 97 planets predicted for those 68 systems.