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

**P**_{n}=P_{o}A^{n}
Where:

- P
_{n} is the period of orbit of the nth planet
- P
_{o} is the period of the sun's rotation
- A is the semi-major axis of the orbit

*references: www.britannica.com, www.nasa.gov, http://astrosun.tn.cornell.edu*