Editing Titius–Bode law (section)

==Original formulation==
The law relates the [[semi-major and semi-minor axes|semi-major axis]] <math>~a_n~</math> of each planet's orbit outward from the Sun in units such that the Earth's [[semi-major and semi-minor axes|semi-major axis]] is equal to 10:

<math display="block">~a = 4 + x~</math>

where <math>~x = 0, 3, 6, 12, 24, 48, 96, 192, 384, 768 \ldots~</math> such that, with the exception of the first step, each value is twice the previous value. There is another representation of the formula:

<math display="block">~a = 4 + 3 \times 2^n ~</math>

where <math>~n = -\infty, 0, 1, 2, \ldots~.</math>

The resulting values can be divided by 10 to convert them into [[astronomical unit]]s ({{sc|au}}), resulting in the expression:

<math display="block">a = 0.4 + 0.3 \times 2^n ~.</math>

For the far outer planets, beyond [[Saturn]], each planet is predicted to be roughly twice as far from the Sun as the previous object. Whereas the Titius–Bode law predicts [[Saturn]], [[Uranus]], [[Neptune]], and [[Pluto]] at about 10, 20, 39, and 77&nbsp;[[astronomical unit|AU]], the actual values are closer to 10, 19, 30, 40&nbsp;[[astronomical unit|AU]].{{efn|The spacing seems to transition from the complicated Titius–series to simple equal-spacing starting at Saturn, with [[Neptune]] being the first major planet that does not fit the Titius–Bode rule.}}