Johann Daniel Titius: Original Author Of Bode’s Law?

Even though he’s not a well known household name like Newton, did the astronomer and mathematician Johann Daniel Titius the original author of Bode’s Law?

By: Ringo Bones

It has since been rechristened as the Titius-Bode Law and in his honor, an asteroid – 1998 Titius -  and a crater on the Moon was named after him, the 18^th Century German mathematician and astronomer Johann Daniel Titius never became a well-known household name like the Englishman Isaac Newton. But nonetheless, Titius did make some important contributions to mathematics, physics, astronomy and biology during his lifetime.

Johann Daniel Titius (1729 – 1796) was born on January 2, 1729 in Konitz Royal Prussia – a fiefdom of the Crown of Poland – to Jakob Tietz, a merchant and council member from Konitz, and Maria Dorothea, née Hanow. His original name was Johann Tietz, but as was customary in the 18^th Century, when he became a university professor, he Latinized his surname to Titius. Teitz attended school in Danzig (Gdansk) and studied at the University of Leipzig (1749-1752). He died in Wittenberg, Electorate of Saxony on December 16, 1796.

Titius proposed his law of planetary distances in an unsigned interpolation in his German translation of the Swiss philosopher Charles Bonnet’s Contemplation de la nature (“Contemplation of Nature”). Titius fixed the scale by assigning 100 to the distance of the planet Saturn from the Sun. On this scale, planet Mercury’s distance from the Sun is approximately 4. Titius therefore proposed that the sequence of planetary distances (starting from Mercury and moving outward) has the form:  4,4 + 3,4 + 6,4 + 12,4 + 24,4 + 48,4 + 96,…

There was an empty place at distance 28, or 4 + 24 (between the planets Mars and Jupiter), which Bode asserted, the Founder of the Universe surely has not left unoccupied. Titius’ sequence stopped with the planet Saturn, the most distant planet then known. His law was reprinted, without his credit, by Johann Elert Bode in the second edition of his Deutliche Anleitung zur Kenntniss des gestirnten Himmels (Clear Guide to Knowledge of the Starry Heaven) in 1772. In later editions, Bode did credit Titius, but this mostly escaped notice and during the 19^th Century the law was usually associated with Bode’s name.

Titius published a number of works on other areas in physics, such as a set of conditions and rules for performing experiments and he was particularly focused in thermometry. In 1765, he presented a survey of thermometry up to that date. He wrote about the metallic thermometer constructed by Hans Loeser. In his treatises on both theoretical and experimental physics, he incorporated the findings of other scientists, such as the descriptions of experiments written by Georg Wolfgang Kraft in 1738.

As a confirmed polymath, Titius was also active in biology, particularly in classification of organisms and minerals. His biological work was influenced by Carolus Linnaeus. Lehrbegriff der Naturgeschichte Zum ersten Unterrichte, his most extensive publication in biology, was on the systematic classification of plants, animals and minerals, as well as the elemental substances: ether, fire, air, water and earth. The standard author abbreviation Titius is used to indicate Johann Daniel Titius as the author when citing a botanical name.

The Mysterious Mathematics Behind Bode’s Law: The Most Puzzling Law Of Science?

Often cited as the most productive – and most puzzling – scientific law at the same time, are there any “mathematical” mysteries behind Bode’s Law?

By: Ringo Bones

This rather “curious” scientific law was named after an 18^th Century German astronomer and mathematician named Johann Elert Bode, but contrary to popular belief, it was actually discovered by Johann Daniel Titius – a German mathematician – back in 1766. However, the empirical relation that gives the approximate distances of the planets from the Sun did not attract attention to the 18^th Century astronomical community until it was publicized by Johann Elert Bode – whose name has since then associated with it – back in 1772.

To the uninitiated, Johann Elert Bode (1747-1826) was an 18^th Century era German astronomer and mathematician who popularized an empirical law that was later named after him, which gives the approximate distances of the planets from the Sun. Bode was also famous for naming the planet Uranus that ended the confusion in the astronomical community at the start of the 19^th Century when the British astronomer William Herschel desired to name the then newly discovered planet as Georgium Sidius after King George III of England.

After examining the work of fellow German mathematician, Johann Daniel Titius, Bode noted that the distances of the various planets from the Sun fell into a curious mathematical sequence. Bode then published a paper which arbitrarily assigned numbers to the planets: 0, 3, 6, 12, 24, 48, 96, and 192. Thus the planet Mercury was numbered 0, planet Venus 3, planet Earth 6, planet Mars 12, and so on, each number being double the last one. When 4 was added to each of these numbers and the result is divided by 10, figures emerged which almost exactly equaled the planets’ distances from the Sun, measured in astronomical units. By the way, an astronomical unit is a unit of distance between the planet Earth and the Sun – which is around 93-million miles or 150-million kilometers.

The only trouble with the law was that back in the time when Bode published it in 1772, there were no planets found at positions 24 or 192. But astronomers searching in position 24 located the asteroids – around the start of the Nineteenth Century – i.e. the discovery of asteroid Ceres in 1801. The planet Uranus, which was discovered back in 1781, occurs at position 192 and conforms almost exactly to Bode’s calculations. Only the outermost planets – Neptune and the dwarf planet Pluto – failed to obey Bode’s Law. Although many attempts have been made to derive a physical explanation for the law, none has completely succeeded.  Today, many astronomers dismiss Bode’s Law as a coincidence and that Bode’s Law is not a rule governing planetary systems. Yet it remains one of the most mysterious statements of natural law formulated by man with the help of mathematics.