A mathematical formula that gives approximations to the distances of the planets from the Sun starting with only the number in order of sequence. The relationship takes the form: D = 0.4 + 0.3×N where D is the distance in astronomical units AU and N takes the VALUES (0, 1, 2, 4, 8..., doubling for each successive planet. The relationship holds to within a few per cent for the seven innermost major planets as long as the value N=8 is taken to represent the largest asteroid, Ceres. However, it breaks down seriously for Neptune and Pluto. The formula was devised in 1766 by J. Titius and copied a few years later by J. E. Bode, who published it. At that time none of the asteroids had been discovered, and the gap at 2.8 AU, where the formula predicted that there should be a planet, convinced astronomers that a small planet would be found there, which indeed proved to be the case.