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I am reading Heinlein's Time for the Stars(1956) and some of the characters are very excited about confirming Bode's law.

The formula suggests that, extending outward, each planet would be approximately twice as far from the Sun as the one before.

Wikipedia essentialy says it is no longer popular but is neither fully supported nor disproved.

The hypothesis correctly anticipated the orbits of Ceres (in the asteroid belt) and Uranus, but failed as a predictor of Neptune's orbit and has eventually been superseded as a theory of solar system formation.

Recent astronomical research suggests that planetary systems around some other stars may follow Titius–Bode-like laws.

It seems like we just don't have enough data to say for sure one way or the other. When will be able to to conclusively confirm or disprove Bode's law?

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  • $\begingroup$ I'm still wondering how it ever got promoted to "law" status to begin with, so I aksed! How and when did the Titius-Bode rule first become known as a "law"? I think it's really a bit of a misnomer. But I think your question is excellent - now that it is testable, let's see if it does in fact have any ability to predict or not. The answer below - that someone did - was a pleasant surprised. $\endgroup$ – uhoh Apr 2 '17 at 14:50
  • $\begingroup$ Bode's "Law" isn't even internally consistent; it includes an ugly special case for Mercury. The general formula is 3 * 2^n + 4, giving the distance in units of 0.1 AU (Venus = 7, Earth = 10, Mars = 16) -- but that gives a result of 5.5 for Mercury, when the actual value is about 0.4. Bode's Law is based on the idea that (0, 3, 6, 12, 24, ...) is a simple and logical progression, but if each value is double the previous one, the first should be 1.5, not 0. $\endgroup$ – Keith Thompson Apr 2 '17 at 20:50
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I would argue that it is disproven already. There have been studies done with Extrasolar planets, and it has been found to only apply in a very small number of instances. There might be some that follow the law, but the number is quite small. There are instances where it lines up nicely, but it seems like ultimately it fails most of the time.

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Bodes law is a little over stated. It's not a law per se but rather a rule of thumb or a rough guideline

It also doesn't work on our solar system exactly. For it to apply perfectly for our system you have to apply some modifiers for it to work out.

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To disprove a hypothesis, you need only one counter-example. The solar system is already one. Planetary semi-major distances do not follow a simple power-law rule.

A fraction of exoplanetary systems possesses resonant chains of planetary orbits (similar to the Laplace resonance for the Galileian satellites), which then give semi-major axes that follow a simple power-law rule, which is why the Titius-Bode-sequence is sometimes quoted in modern times in a exoplanetary context.

But the TB-sequence is far from being a law (it does not follow from Axioms, nor describe a general property of the Universe in any meaningful way), but is barely more than a first-semester student fitting a curve to data.

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