Definition
The Titius-Bode law is the statement that the semimajor axes of planetary orbits in the solar system follow approximately a geometric progression when going from the innermost to the outermost planets. There is no real physical explanation for this law, which stems from observation only and was first introduced by the German astronomers Johann Daniel Titius and Johann Elert Bode around 1770.
The formula for the semimajor axis a reads: \( a=\left(0.4+0.3\times {2}^n\right) \) with n = −∞, 0, 1, 2, 3, … and a in astronomical units.
The formula is fairly correct for the planets that were known when it was proposed, and it correctly predicted the approximate orbit of objects in the asteroid belt (assumed to be a failed planet) and Uranus. However, it failed for Neptune’s orbit. Note also that for Mercury n = −∞ which breaks the logics of the law.
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Rouan, D. (2014). Titius-Bode Law. In: Amils, R., et al. Encyclopedia of Astrobiology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27833-4_1596-2
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DOI: https://doi.org/10.1007/978-3-642-27833-4_1596-2
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Publisher Name: Springer, Berlin, Heidelberg
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