Guest Author - Lea Terry

In 1772, German astronomer Johann Elbert Bode resurrected a nearly forgotten mathematical formula for measuring the distances of planets from the Sun. Though it was not his formula, and is not accurate, it was named for Bode and used for several years.

The formula was developed by German physicist and mathematician Johann Titius, who included it as a footnote in a book he translated in 1766. The book, and Titius, descended into virtual obscurity, so when Bode restated the formula, he received credit for devising it. Titius developed the formula after noticing a pattern in the distances of the known planets from the Sun. He found the distances followed a mathematical progression, described by the following formula: 0.4 + 0.3 · 2n

To calculate the mean distances of the planets from the Sun, you would start with the numerical sequence: 0, 3, 6, 12, 24, 48, 96, 192, 384. Aside from the first two numbers, 0 and 3, each number is twice the value of the number before it.

Next, you would add 4 to each number, to get the following sequence: 4, 7, 10, 16, 28, 52, 100, 196, 388.

You would divide these numbers by 10, for the following sequence: 0.4, 0.7, 1, 1.6, 2.8, 5.2, 10, 19.6, 38.8. According to Bode’s Law, these are the mean distances of each planet from the Sun.

There was no theoretical basis for the law, and some astronomers were initially skeptical, but the law at first seemed promising. In 1781, the planet Uranus was discovered precisely where Bode’s Law had predicted a missing planet. The formula gained credibility, even inspiring a team of astronomers to hunt down a “missing planet” allegedly located between Mars and Jupiter. The group, formed in 1800 and consisting of six German astronomers, was nicknamed the “Celestial Police.” They never found the missing planet, but other scientists, observing the same area of the sky, discovered an entire asteroid belt, including the asteroid Ceres. And that wasn’t the formula’s only failure: past the planet Uranus, Bode’s Law doesn’t hold up. Neptune and Pluto aren’t where the formula predicts, and modern astronomers believe it is merely coincidence that Bode’s Law accurately describes the locations of some planets. Bode’s Law isn’t a law in the strictest sense: it does describe a relationship, but poses no explanation for that relationship, and is not universal and invariant.