To have a understanding of Bode’s Law or Titius-Bode’s Law, one needs to know the origins of our Solar System. It is old. Very old. It is estimated that our sun first formed around four and a half billion years ago. And that’s around the time when rough planetary material began to come together or coagulate. This was the birth of the System as we know it today. Technically, we have eight planets, but that’s excluding the ones that haven’t got a planetary status anymore or are very small to observe or even be classed as a planet. An example of the latter would be the planet Pluto, named after the Greek god of the Underworld. It was categorized as a dwarf planet as of mid-2000’s. The reason behind the demotion of Pluto’s planetary status was that several other so-called planets were found in the general locale of Pluto since the early 2000’s. We now believe and know that Pluto and its sister planets like Sedna, 50000 Quaoar and Eris are a part of a huge disk of rocks known as the Kuiper Belt. It is pretty much the trans-Neptunian equivalent of the Asteroid Belt.
Coming back to the topic at hand, the locations and orbits of these bodies which form our Solar System are theorized by Bode’s Law. Although, this Law only applies to certain star systems and one of them includes ours. Nonetheless, when it was was first hypothesized, it worked beautifully and was one of the contributing reasons for the discoveries of the planets beyond our own. Here’s an example of Titius-Bode’s Law as “perceived” in our Solar System with the current known planets and a couple of thought-to-be planets:
The Titius-Bode Law is a rule that predicts the spacing between the planets in the Solar System. To work out the distances, you first have to start with the following sequence of numbers:
0, 3, 6, 12, 24, 48, 96, 192, 384
As you can see, the numbers follow a sequence, as each number is double the value of the number before it, except for the first two numbers. A 4 is then added to each number.
4, 7, 10, 16, 28, 52, 100, 196, 388
Each number is then divided by 10.
0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6, 38.8
The end result is then applied to each of the planets, starting with Mercury, and radiating out towards Pluto. As can be seen in Table 1, the percentage in the error made using this rule is very small, especially when considering that at the time there were no telescopes. This made it much harder to observe the planets
During the creation of the rule, it was noted that there was a gap between Mars and Jupiter, and it was predicted that a planet existed within that area. However, it was not until 1801 that Giuseppe Piazzi discovered the small planet of Ceres to fill in the gap. To date there have been 9,000 minor planets found between Mars and Jupiter, and it is now thought that these are in fact asteroids that could have formed a proper planet, but could not because of the gravitational pull of Jupiter. Even though Titius and Bode did not know of the Asteroid Belt, the rule had predicted correctly that there was a large mass between Mars and Jupiter.
Table
Planet | k | T-B rule distance (AU) | Real distance (AU) | % error (using real distance as the accepted value) |
0 | 0.4 | 0.39 | 2.56 % | |
1 | 0.7 | 0.72 | 2.78 % | |
2 | 1.0 | 1.00 | 0.00 % | |
4 | 1.6 | 1.52 | 5.26 % | |
Asteroid Belt | 8 | 2.8 | 2.77 | 1.08 % |
16 | 5.2 | 5.20 | 0.00 % | |
32 | 10.0 | 9.54 | 4.82 % | |
64 | 19.6 | 19.2 | 2.08 % | |
128 | 38.8 | 30.06 | 29.08 % | |
256 | 77.22 | 39.44 | 95.75 % |
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