Engineers know Bode diagrams and Bode plots well, but do you know about Bode's Law? It has to do with the spacing of the planets of our solar system. According to Wikipedia, it was discovered in 1766 by Johann Daniel Titius and "published" without attribution in 1772 by the director of the Berlin Observatory, Johann Elert Bode, thus the name. However, some say
it was first proposed by Christian Wolff in 1724. Whatever the case may be, it was not the same Bode (Hendrik Wade Bode) that gave us our Bode plots. Today the astronomical 'law' is generally known as the Titius-Bode Law.
It says that the distance of a planet from the Sun is roughly given by:
D = 0.4 + 0.3N a.u., where N = 0,1,2,4,8,16…, i.e. integer(2^(n-2)) and n is the n'th planet from the Sun, counting in the largest asteroid (Ceres) as number 5. The unit a.u. is astronomical unit, the mean distance of Earth from the Sun.
Nobody knows why this formula (or 'law') works, but it does... up to a point. Read more by clicking this link . The page contains a downloadable PDF with lots of info.
Interesting Problem
