WOLFRAM|DEMONSTRATIONS PROJECT

Titius-Bode Law

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planet
zoom
Venus | Titius-Bode Law a = 0.70 | actual a = 0.72
orbit diagram
The Titius-Bode Law approximates the distance
a
from the Sun to the traditional planets. The Titius-Bode Law was formulated around 1770. There is no known scientific reason why the orbits of the primary planets seem to follow this relation. The law can be expressed as
a=0.4+(0.3)
n
2
where
n
is an integer representing the planet in question (0 for Venus, 1 for Earth, etc.). It is curious that Mercury needs the value
n=-∞
, the asteroid Ceres needs
n=3
, and the planet Neptune is skipped. At the time of discovery, Uranus and the more distant planets were not yet discovered.