There is an undeniable Pythagorean bent to Kepler's laws. They contain a certain mathematical elegance. All three work from the same pattern. This pattern has led to the development of Bode's Law, which tells us that the planets are laid out mathematically. Below, the astronomical units are determined by fractions and multiples of the earth's mean distance from the sun (149 million km). This is used as the standard and so is listed as 1. The actual AU are given and compared to the theoretical AU in parentheses.

Mercury 0.38 (0.25)
Venus 0.72 (0.75)
Earth 1 (1)
Mars 1.52 (1.5)
Jupiter 5.2 (5)
Saturn 9.54 (10)
Uranus 19.22 (20)
Neptune 30.06 (30)

The differences between actual and theoretical vary less the farther we move away from the sun where the orbits are steadier. However, there seems to be an inexplicable gap between Mars and Jupiter. There should be an intermediate body there with an AU of about 3 otherwise we are hard pressed to explain the jump from 1.5 to 5. As luck would have it, the asteroid belt occupies this blank area. This has led some to believe that the asteroid belt is the remnants of a shattered planet.

While measuring the rate at which a planet moves at aphelion as opposed to perihelion, Kepler made yet more startling discoveries. He calculated these rates by measuring how far each planet travels in 24 hours (each hour becomes a degree and each degree is then broken into 60 minutes of arc and each minute is broken into 60 seconds of arc relative to the sun). Kepler found that Saturn progressed at aphelion by 106 inches per day and by 135 inches at perihelion. The ratio of 106/135 is 0.785185. A 2-seconds-of-arc difference from 0.8 which is the ratio of 4/5 which is the ratio of the major 3rd musical interval. Kepler found this worked for all the planets. He decided to compare the aphelion of one planet to the perihelion of another. To his astonishment, the musical intervals were even more precise and covered the entire musical scale! For example, Jupiter's aphelion divided by Mars's perihelion yielded the minor 3rd interval. Earth's aphelion divided by Venus's perihelion yielded a minor 6th.

Most modern astronomers mocked these discoveries and attributed them to pure chance. Yet the noted astronomer, Fred Hoyle, preformed his own calculations using the much more precise modern data and still found the musical intervals they describe "frighteningly good". Others such as Francis Warrain decided to use the data for Uranus, Neptune and Pluto and see if these worked since they were unknown to Kepler or anyone of his time. Once again, the musical intervals were so shockingly close as to preclude chance.