Also known as the Titius-Bode Law or Titius's law. First postulated by Johann Daniel Titius of Wittenberg in 1766 and published by Johann Elert Bode in 1772.

0, 3, 6, 12, 24, 48, 96, 192, 384 ...

to each number add 4:

4, 7, 10, 16, 28, 52, 100, 196, 388 ...

Divide these numbers by 10:

0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6, 38.8 ...

And you wind up with close approximations of the distances of the planets from the Sun, in astronomical units.
Planet        Actual Distance(AU)    Predicted Distance(AU)
Mercury       .39                    0.4
Venus         .72                    0.7
Earth         1.0                    1.0
Mars          1.52                   1.6
Asteroid Belt                        2.8
Jupiter       5.2                    5.2
Saturn        9.54                   10.0
Uranus        19.19                  19.6
Neptune       30.06
Pluto         39.5294                38.8
Although Neptune and Pluto don't quite fit into this equation (Pluto being on average 39.5294 AU, and Neptune being on average 30.06 AU), their orbits are erratic, and sometimes Pluto is the 8th planet from the Sun. Many astronomers discount this as the reason for the discrepancy, citing the large gravitational pull generated by Jupiter and Saturn as why Neptune and Pluto are closer to the Sun than this equation predicts.

This equation led to the discovery of Ceres (the first discovered and largest known asteroid), and Uranus.

It is important to note that mathematical modelling of the origins of a solar system do not generally produce results which can be explained by this equation. This is not really a law, as it is not universal.

Expressed mathematically, Bode's Law is written as


  • Pn is the period of orbit of the nth planet
  • Po is the period of the sun's rotation
  • A is the semi-major axis of the orbit


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