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© Copyright 2002, Jim Loy
Above, I show the relative distances within the Solar System. The S on the left is the Sun, then Mercury, Venus, Earth, etc. Ceres is the largest minor planet. A quick study of the distances might suggest that each planet is roughly double the distance from the sun, as the next nearest planet. A better fit was discovered by J. B. Titius (in 1766), and publicized by J. E. Bode (1772). This is often called Bode's Law, but Bode only quoted Titius. Translated into astronomical units (AU), where one AU is the mean distance of the Earth from the Sun, the law amounts to this. Make a seqence of numbers 0, 3, 6, 12, 24, ... (doubling each time, except for the first number), add 4, and divide by 10, and you get very close to the distance of each planet from the Sun in AU's (Titius and Bode seem to have actually used one tenth of an AU, which makes the arithmetic slightly simpler). Uranus, Neptune, and Pluto were not known at the time.
| distance from Sun (AU) |
double | x | (x+4)/10 | |
| Mercury | 0.387 | 0.25 | 0 | 0.4 |
| Venus | 0.723 | 0.5 | 3 | 0.7 |
| Earth | 1 | 1 | 6 | 1 |
| Mars | 1.524 | 2 | 12 | 1.6 |
| (Ceres) | 2.767 | 4 | 24 | 2.8 |
| Jupiter | 5.203 | 8 | 48 | 5.2 |
| Saturn | 9.539 | 16 | 96 | 10 |
| (Uranus) | 19.19 | 32 | 192 | 19.6 |
| (Neptune) | 30.06 | 64 | 384 | 38.8 |
| (Pluto) | 39.53 | 128 | 768 | 76.4 |
All well and good, except that there was a big gap between Mars and Jupiter. Titius and Bode decided to skip a number, making Jupiter a particularly good fit. This law was sometimes taken to predict that a planet would be found between Mars and Jupiter. Within a few years (1781), Uranus was discovered by Sir William Herschel, and it fit right into the law. This discovery made the law respectable, and the hunt for the missing planet began. In 1801, Giuseppe Piazzi discovered the minor planet Ceres, at just the right distance. Ceres was incredibly tiny for a planet. To date, more than 9000 minor planets (asteroids) have been discovered (See The Asteroid Belt). At first it was thought that a planet was destroyed by a collision, at that distance from the Sun. Now it is thought that the gravity of Jupiter prevented a planet from forming from the fragments there.
Neptune (discovered in Johann Galle in 1846) and Pluto (discovered by Clyde Tombaugh in 1930) do not fit the law very well. In fact, Pluto (in reality a minor planet) fits the spot where Neptune should be.
Why do the planets fit this law at all? The answer to that is not known precisely. But there is a clue. The minor planets exist in belts around the sun. At some distances (certain fractions of Jupiter's distance) there are no minor planets. And so, the various planets would seem to tug on each other to keep them at certain distances, or to eject planets from the Solar System if they wander too closely. So the Titius/Bode Law is perhaps not just a cosmic coincidence.