Numbers in Space: the Titius–Bode law

No solid theoretical explanation underlies the Titius–Bode law, but so far this regularity remains one of most curious in Astronomy. Besides, it has a rather interesting story.

Strictly speaking, the first mention of a series approximating the Titius–Bode law was found in David Gregory’s The Elements of Astronomy published in 1715. In it he says, “…supposing the distance of the Earth from the Sun to be divided into 10 equal parts, of these the distance of Mercury will be about 4, of Venus 7, of Mars 15, of Jupiter 52, and that of Saturn 95…”

In 1766 German astronomer Johann Daniel Titius from Wittenberg also divided the distance from the Sun to Saturn, the last known planet at that time, but into 100 parts. In this case the distance from the Sun to Mercury was definitely 4, from the Sun to Venus 7 (or 4 + 3), to the Earth 10 (or 4 + 6), to Mars 16 (4 + 12). Titius revealed the following regularity: doubling the second number of the sum, we can get the distance to the planet, right up to Saturn, just with one exception: there was no planet at the distance of 28.

Johann Bode, an astronomer from the Berlin Observatory, was extremely interested in the theory of Titius and launched a whole campaign to find the missing planet behind the orbit of Mars. Due to his enthusiasm, this theory is now more often called the Bode law than the Titius–Bode law.

In 1800 several people in Germany organized a group to conduct systematic searches for the missing planet and took the name “The Sky Police”. They divided the area of the sky with the probable planet into several sections, and each was assigned its personal observer. However, on 1st January 1801 Italian priest and astronomer Giuseppe Piazzi from the Palermo Observatory got ahead of them. He discovered a “stellar object” that moved against the background of stars like a planet. Piazzi named it Ceres Ferdinandea after the Roman and Sicilian goddess of grain and King Ferdinand IV of Naples and Sicily. The location of this object corresponds to the Titius–Bode law, but it is too small. On 28 March 1802 “The Sky Police” discovered the second asteroid named after Pallas. Later, they found Juno and Vesta. In process of time the pace of discoveries had increased, and for today we know the orbits of more than 15 000 asteroids. Most of them are moving exactly on the Titius–Bode law distance from the Sun. However, scientists are still not sure whether this is really a law or a mere coincidence. And this regularity is not applicable to Neptune and Pluto.

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