Friday, May 21, 2010

Bode's Law

Bode's Law, or Titus-Bode Law, is a now refuted law governing planet location with our Solar System. It presumes a relationship between all of the planets in their distances from the Sun.


The Law relates the semi-major axis, a, of each planet outward from the sun in units such that the Earth's semi-major axis = 10, with

a = n + 4
where n = 0, 3, 6, 12, 24, 48 ..., with each value of n > 3 twice the previous value. The resulting values can be divided by 10 to convert them into astronomical units (AU), which would result in the expression

a = 0.4 + 0.3 · 2 m
for m = , 0, 1, 2,...[1]

For the outer planets, each planet is 'predicted' to be roughly twice as far away from the Sun as the next inner object.


It's name comes from the fact that it was promoted by Johann Elert Bode when in 1768, he wrote the second edition of his astronomical compendium Anleitung zur Kenntniss des gestirnten Himmels, which states the following.
Let the distance from the Sun to Saturn be taken as 100, then Mercury is separated by 4 such parts from the Sun. Venus is 4+3=7. The Earth 4+6=10. Mars 4+12=16. Now comes a gap in this so orderly progression. After Mars there follows a space of 4+24=28 parts, in which no planet has yet been seen. Can one believe that the Founder of the universe had left this space empty? Certainly not. From here we come to the distance of Jupiter by 4+48=52 parts, and finally to that of Saturn by 4+96=100 parts.


At the time, Saturn was the farthest known planet. Bode's Law gained credibility when Uranus and then Ceres where discovered. These bodies happened to fall in line with predictions made by the formula. However, this Law become refuted when Neptune was discovered at a location from the Sun that was no where near its predicted location.

Also, to further refute Bode's Law is the fact that other systems exist in our Solar System which do not follow its formula. Although the moons around Jupiter, Saturn and Uranus do follow some sort of pattern, they do not follow Bode's Law; nor do they share patterns with each other.


The discovery of Pluto and more recently other Kuiper Belt objects have proven Bode's Law to be false. It appears that Bode's Law was a misguided attempt to explain an observation that did not have enough data. Given what is known now, it seems that perhaps there is some sort of rule that applies to naturally formed orbiting body systems, but there is no formula that can predict the arraignment of such. Perhaps Bode's Law can be useful in the future, not to predict planet placement in other extrasolar systems, but maybe to point us in the direction to understand planet formation and resonance. We can see there is some sort of resonance. We can also see that a particular resonance is not shared between different systems, and only applies in a limited fashion. It is not useful for anything else. Although it really cannot be called pseudo-science, since it was based on observation and did make some predictions that panned out, it is really not useful science today. Further complicating the issue is that the definition of planet has changed. Ceres and Pluto are no longer considered planets. This means that any use of Bode's Law in the context of what is now known can be called pseudo-science.

Planet Distances from the Sun (from

Mercury factor: 0
Bode’s Law: 0.4, Actual: 0.39

Venus factor: 1
Bode’s Law: 0.7, Actual: 0.72

Earth factor: 2
Bode’s Law: 1.0, Actual: 1.0

Mars factor: 4
Bode’s Law: 1.6, Actual: 1.52

Ceres factor: 8
Bode’s Law: 2.8, Actual: 2.77

Jupiter factor: 16
Bode’s Law: 5.2, Actual: 5.2

Saturn factor: 32
Bode’s Law: 10, Actual: 9.54

Uranus factor: 64
Bode’s Law: 19.6, Actual: 19.2

Neptune factor: 128
Bode’s Law: 38.8, Actual: 30.06

Pluto factor: 256
Bode’s Law: 77.2, Actual: 39.44

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