TitiusBode

Titius-Bode Law, also known as Bode's Law, is an empirical relationship formulated by Johann Daniel Titius in 1766 and popularized by Johann Elert Bode in 1772. It describes the approximate distances of the planets from the Sun in a sequence that is now known to be a coincidence. The law states that the distance of a planet from the Sun, expressed in astronomical units (AU), can be approximated by the formula:

d = 0.4 + 0.3 × 2^n

where n is a whole number starting from -1 for Mercury and increasing by 1 for each subsequent planet. The sequence generated by this formula is 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, and 19.6 AU. This sequence closely matches the actual distances of the first seven planets from the Sun, with the exception of Ceres, which was later classified as a dwarf planet.

The Titius-Bode Law was initially seen as a strong evidence for the existence of a planet between Mars and Jupiter, which was later discovered as Ceres. However, the law has since been largely discredited due to the discovery of numerous objects in the Solar System that do not fit the pattern, such as Pluto and the Kuiper belt objects. The law is now considered a historical curiosity rather than a fundamental principle of planetary motion.