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Titius-Bode law (Bode's law) An empirical arithmetical relationship between the distances of the planets from the Sun. If the Sun-Earth distance is taken as 10, then the distances of Mercury, Venus, Earth Mars, Jupiter, and Saturn are approximately satisfied by the sequence: 4, 4 + 3, 4 + 6, 4 + 12, 4 + 48, and 4 + 96. The more accurate version of the ‘law’ is given by the function rn = ABn, where rn is the distance of the nth planet, A is a constant, and B = 1.73. This version is due to Mary Blagg (1858–1944). It is not clear that the ‘law’ has any fundamental significance, but may be merely a consequence of gravitational and tidal evolution following planetary and satellite formation. The asteroid belt occurs about 4 + 24, corresponding to the former ‘missing planet’ in the sequence, that was believed to exist for many years. Uranus, discovered in 1781, occurs close to the next term, 4 + 192, but the position of Neptune does not fit the ‘law’. The regular satellites of the giant planets fit modifications of the ‘law’. The ‘law’ was discovered in 1766 by J. D. Titius (1729–96) and was popularized by J. E. Bode (1747–1826).
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