MENTAL MODEL · M4574

Bode's Law

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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

An empirical formula discovered in the 18th century that can predict the distances of planets from the Sun with considerable accuracy: a = 0.4 + 0.3 × 2ⁿ (n = -∞, 0, 1, 2, 3...). Except for Neptune, all planets roughly conform to this rule.

SCAFFOLDING EFFECT

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Illustrates the value and limitations of empirical laws. Even without a theoretical basis, empirical formulas can guide discoveries (such as the discovery of Ceres and the asteroid belt). However, over-reliance on empirical laws can lead astray (as with Neptune's 'anomaly').

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Bode's law empirically fits planetary orbital radii with a simple geometric progression, providing an approximation for the planets known at the time (and later the asteroid belt). It lacks a dynamical foundation, being a 'descriptive law' whose coincidental fit reveals the predictive power and unreliability of empirical formulas.

MINIMUM ACTION

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Practice this model in one real situation:

When theory is lacking, one can first use empirical formulas to summarize and predict the unknown (e.g., searching for celestial bodies at missing orbital positions)
then test the formula with new discoveries
when anomalies arise (such as Neptune's deviation), be wary of the formula's scope rather than forcing a correction.

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Source support: Explicit

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en.wikipedia.orghttps://en.wikipedia.org/wiki/Titius%E2%80%93Bode_lawZH · Explicit
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