Bode’s law states that there is a pattern in the way the planets are spaced from the Sun. Bode started with the number 0, then took 3, and began doubling: 0, 3, 6, 12, 24, 48, 96, 192, 384, 768. He then divided each number by 10 and added 4. The numbers that he discovered were similar to planetary distances from the Sun in astronomical units. According to Bode’s theory, there should be a planet between Mars and Jupiter.
The concept was devised and first published in 1766 by Johann D. Titius, a German mathematician and physicist, based on the six planets known at the time: Mercury, Venus, Earth, Mars, Jupiter, and Saturn. The German astronomer Johann E. Bode popularized the law in a book published in 1772, and it became associated with his name.
The law relates the mean distances of the planets from the sun to a simple mathematic progression of numbers. To find the mean distances of the planets, beginning with the following simple sequence of numbers:
0 3 6 12 24 48 96 192 384
With the exception of the first two, the others are simple twice the value of the preceding number.
Adding 4 to each number results,
4 7 10 16 28 52 100 196 388
Then dividing by 10
0.4 0.7 1.0 1.6 2.8 5.2 10.0 19.6 38.8