According to the Titius-Bode “law”, formulated by the German Johan Titius in 1766 and reiterated by his countryman Johann Bode in 1772, the radii of the orbits of the planets around the Sun would be in proportions given by a certain mathematical sequence: 0.4 (Mercury), 0.7 (Venus), 1.0 (Earth), 1.6 (Mars), 2.8 (??), 5.2 (Jupiter) and 10.0 (Saturn).
For the next planet, if it existed, it would be 19.6. In fact, Uranus’ orbital radius, discovered by William Herschel in 1871, is 19.2 times that of Earth. But to make the law work it was necessary to postulate the existence of an unknown planet between Mars and Jupiter, corresponding to the value 2.8. “Does anyone believe that the Founder of the universe would leave this space empty? Of course not.”, assured Bode.
In 1800, the German astronomical magazine “Monthly Correspondence” invited 24 astronomers on a systematic search for the mysterious planet. This group, which became known as the “Celestial Police”, actually encountered three large asteroids.
But the first, and greatest of all, was observed by the Italian priest and astronomer Giuseppe Piazzi (1746–1826) on January 1, 1801, even before receiving the invitation to join the Celestial Police. Piazzi called the new star “Ceres”, and published the discovery in the “Monthly Correspondence” in September of that year.
The finding could not be immediately confirmed by other astronomers, because in the meantime Ceres had become too close to the Sun in the sky to be observed. It would be visible again at the end of the year, but it was very difficult to predict where it would be after so long.
The situation was saved by the great mathematician Carl Friedrich Gauss, through a new method of calculating orbits that he developed in just two weeks. Using his calculations, the Celestial Police found Ceres in the sky on December 31st.
Gauss’s work, published in 1809, also contains the claim that he had been using the “method of least squares”, one of the main tools of scientific calculus, since 1795. This created a dispute with the Frenchman Adrien-Marie Legendre, who was the first to publish this method, in 1805.
The discoveries of Neptune and Pluto, which do not follow Titius-Bode, have ruined the law’s reputation. This story is left, a beautiful example of how solving concrete problems about the world around us leads to the discovery of powerful abstract tools, advancing mathematics.
