Bode's Law
The TitiusBode Law is rough rule that predicts the spacing of the planets
in the Solar System. The relationship was first pointed out by
Johann Titius in 1766 and was formulated as a mathematical expression
by J.E. Bode in 1778. It lead Bode to predict the existence of another
planet between Mars and Jupiter in what we now recognize as the
asteroid belt.
The law relates the mean distances of the planets from the sun to
a simple mathematic progression of numbers.
To find the mean distances of the planets, beginning with the
following simple sequence of numbers:
0 
3 
6 
12 
24 
48 
96 
192 
384 
With the exception of the first two, the others are simple twice
the value of the preceding number.
Add 4 to each number:
4 
7 
10 
16 
28 
52 
100 
196 
388 
Then divide by 10:
0.4 
0.7 
1.0 
1.6 
2.8 
5.2 
10.0 
19.6 
38.8 
The resulting sequence is very close to the distribution of
mean distances of the planets from the Sun:
Body 
Actual distance (A.U.) 
Bode's Law

Mercury 
0.39 
0.4 
Venus 
0.72 
0.7 
Earth 
1.00 
1.0 
Mars 
1.52 
1.6 


2.8 
Jupiter 
5.20 
5.2 
Saturn 
9.54 
10.0 
Uranus 
19.19 
19.6 