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Why did Bode’s law fail to predict Neptune’s distance from the Sun?
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Neptune
A photograph of clouds in Neptune's atmosphere, taken by Voyager 2 in August 1989. The view is from below the planet's equator, and north is up. The Great Dark Spot (center left) is 13,000 km (8,100 miles)—about the diameter of Earth—in its longer dimension. Accompanying it are bright, wispy clouds thought to comprise methane ice crystals. At higher southern latitudes lies a smaller, eye-shaped dark spot with a light core (bottom left). Just above that spot is a bright cloud dubbed Scooter. Each of these cloud features was seen to travel eastward but at a different rate, the Great Dark Spot moving the slowest.
Bode’s law failed to accurately predict the distance of Neptune because it is not a physical law, but rather an empirical, numerological curiosity with no scientific basis or underlying physical justification.12
While the formula successfully approximated the distances of the first seven planets and the asteroids in the solar system, it was never a reliable predictor. When Neptune was discovered in 1846, it was found to be approximately 30.1 AU from the Sun, a significant discrepancy from the 38.8 AU predicted by the equation for that position. This failure, along with the subsequent discovery of Pluto at a distance that also deviated sharply from the law's predictions, ultimately discredited the rule.132