## The Titius Bode Law

The Titius – Bode or Bode's law is a simple arithmetical relationship between the order of the planets moving out from the Sun, and the distances of those planets from the Sun. It was noticed by Titius of Wittenburg, but made more widely known by Johann Bode in 1772. At the time, the law held for all the known planets.

Starting with the numbers – which increase by a factor of two, apart from the first pair:

0, 3, 6, 12, 24, 48, 96, 192

add 4 to each number to give the list

4, 7, 10, 16, 28. 52. 100, 196

and divide by 10 to give the numbers

0.4, 0.7, 1, 1.6, 3.2, 5.6, 100, 19.6

Compare thes with the distances of the planets – and the asteroid belt - from the Sun given as multiples of the Sun – Earth distance. The Sun – Earth distance is equal to 1 A.U. Or 1 Astronomical Unit.

 Body True Distance Bode's Law Mercury 0.39 0.4 Venus 0.72 0.7 Earth 1.00 1.0 Mars 1.52 1.6 Asteroid Belt ∼3.2 2.8 Jupiter 5.20 5.2 Saturn 9.54 10.0

The asteroid belt was said to fit the law because it was supposed to be the remains of a planet and the discovery of Uranus in 1781 at a distance of 19.19 AU compared to a prediction of 19.6 Au seemed to confirm the law, as wll as the discovery between Ceres to add to the asteroid belt between Mars and Jupiter. Neptune and Pluto failed to satisfy the law, and it later fell into disuse.