THE TITIUS-BODE "LAW"

The Titius-Bode "Law" is a mathematical curiosity, the result of an attempt to find a rhyme and reason to the distances of the planets from the Sun. Why is there a planet at 1.0 AU (Earth), and one at 1.5 AU (Mars), but none, for example, at 1.2 AU? If such a relation could be found, it could be used to predict the locations of other planets. Two mathematician/astronomers thought that they discovered such a relation in 1766. The procedure is as follows: In the first column, write a number four. In the first line of the second column write a zero, then a three in the next row, then double the entry in each row thereafter. Add the two columns, then divide by 10. That is the distance of a planet in AU from the Sun. Let's try it:

4
0
4 / 10 = 0.4
Mercury is at 0.387 AU
4
3
7 / 10 = 0.7
Venus is at 0.723 AU
4
6
10 / 10 = 1.0
Earth is at 1.0 AU
4
12
16 / 10 = 1.6
Mars is at 1.524 AU
4
24
28 / 10 = 2.8
?????? is at 2.8 AU
4
48
52 / 10 = 5.2
Jupiter is at 5.203 AU
4
96
100 / 10 = 10
Saturn is at 9.555 AU
4
192
196 / 10 = 19.6
Uranus is at 19.22 AU
4
384
388 / 10 = 38.8
Pluto is at 39.44 AU
4
768
772 / 10 = 77.2
??????? is at 77.2 AU

And so on. The Titius-Bode relation was much ballyhooed when asteroid Ceres was accidentally discovered at a distance from the Sun of 2.8 AU in 1801. However, the relation failed utterly to predict the position of Neptune at 30.11 AU in 1845. The Titius-Bode "Law" is a sterling example of an hypothesis that did not stand up to the test of predicting new discoveries. The relation was empirical in nature, so it was not explained, and it defied further attempts at explanation or modification, unlike Kepler's empirical Laws. The Titius-Bode relation has now been relegated to a mere mathematical coincidence, proving that, if you want to find something bad enough, you'll find it.

 
Updated 7/7/06
By James E. Heath
  
 
 
Copyright Ó 2006 Austin Community College