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The Titius-Bode "Law"
The Titius-Bode "Law" is a mathematical curiosity, the result of
an attempt to find a 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.
Its aim is to relate planet's order with its distance, in this being
similar to Zipf's law.
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. In this way...
| 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
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| 4 |
48 |
52 / 10 = 5.2 |
Jupiter is at 5.203 AU
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| 4 |
96 |
100 / 10 = 10 |
Saturn is at 9.555 AU
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| 4 |
192 |
196 / 10 = 19.6 |
Uranus is at 19.22 AU
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| 4 |
384 |
388 / 10 = 38.8 |
Pluto is at 39.44 AU
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| 4 |
768 |
772 / 10 = 77.2 |
****** is at 77.2 AU
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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.
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