Titius-Bode’s law

The Music of the spheres. …

Originally posted by Johann Daniel Titius:

Take notice of the distances of the planets from one another, and recognize that almost all are separated from one another in a proportion which matches their bodily magnitudes. Divide the distance from the Sun to Saturn into 100 parts; then Mercury is separated by four such parts from the Sun, Venus by 4+3=7 such parts, the Earth by 4+6=10, Mars by 4+12=16.

But notice that from Mars to Jupiter there comes a deviation from this so exact progression. From Mars there follows a space of 4+24=28 such parts, but so far no planet was sighted there. But should the Lord Architect have left that space empty? Not at all.

Let us therefore assume that this space without doubt belongs to the still undiscovered satellites of Mars, let us also add that perhaps Jupiter still has around itself some smaller ones which have not been sighted yet by any telescope. Next to this for us still unexplored space there rises Jupiter's sphere of influence at 4+48=52 parts; and that of Saturn at 4+96=100 parts.

4+0=4. Mercury
4+3=7. Venus
4+6=10. Earth
4+12=16. Mars
4+24=28. Asteroids then unknown.
4+48=52. Jupiter
4+96=100. Saturn

Neptune is said to be out of tune but Pluto isn't. Recently Pluto has been downgraded.

Or to put it another way we have progressed in our understanding of the solar system by one, two or three planets.

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2 thoughts on “Titius-Bode’s law

  1. Originally posted by Wikipedia:

    When originally published, the law was approximately satisfied by all the known planets — Mercury through Saturn — with a gap between the fourth and fifth planets. It was regarded as interesting, but of no great importance until the discovery of Uranus in 1781 which happens to fit neatly into the series. Based on this discovery, Bode urged a search for a fifth planet.Ceres, the largest object in the asteroid belt, was found at Bode's predicted position in 1801. Bode's law was then widely accepted until Neptune was discovered in 1846 and found not to satisfy Bode's law.Simultaneously, the large number of known asteroids in the belt resulted in Ceres no longer being considered a planet. (It is now understood that no planet could have formed in the belt, due to the gravitational influence of Jupiter.) Bode's law was discussed as an example of fallacious reasoning by the astronomer and logician Charles Sanders Peirce in 1898.The discovery of Pluto in 1930 confounded the issue still further. While nowhere near its position as predicted by Bode's law, it was roughly at the position the law had predicted for Neptune.However, the subsequent discovery of the Kuiper belt, and in particular of the object Eris, which is larger than Pluto yet does not fit Bode's law, have further discredited the formula.

    http://en.wikipedia.org/wiki/Titius-Bode_lawOn the other hand the fact that the asteroids cross the orbit of Neptune, extends the realm somewhat. With only the original threshold as a measure, we have no way to measure the yardstick.What if the rendition of the notes has a purpose?Suppose it is the engine that fires the sun.You would need massive shims for corrections now and again and the outer planets would seem the ideal place to put them.They would react to all the others inside them.To write it off as coincidence is to miss any available clue to its importance. It is not the job of science to sit on its fat arse and ignore things.

  2. More from the Wikipedia:

    Kepler discovered physical harmonies in planetary motion.He found that the difference between the maximum and minimum angular speeds of a planet in its orbit approximates a harmonic proportion. For instance, the maximum angular speed of the Earth as measured from the Sun varies by a semitone (a ratio of 16:15), from mi to fa, between aphelion and perihelion.Venus only varies by a tiny 25:24 interval (called a diesis in musical terms). Kepler explains the reason for the Earth's small harmonic range:"The Earth sings Mi, Fa, Mi: you may infer even from the syllables that in this our home misery and famine hold sway."

    When I first discovered declination I wondered if you could put the rate of climb or direction and speed, rather, in musical terms, change the distance covered in a day for a note or something.The moon changes it's angle of incidence by about 4 o5 degrees per day on average. Faster as it nears zero or the angle it makes with the Equator and slower as it reaches it's largest angle somewhere past or just under the tropic. (The maximum changes over about 11 years in a cycle.)I am no musician, I just know it would make a tune of some sort but I don't know how.

    Kepler also discovered that all but one of the ratios of the maximum and minimum speeds of planets on neighbouring orbits approximate musical harmonies within a margin of error of less than a diesis (a 25:24 interval).The orbits of Mars and Jupiter produce the one exception to this rule, creating the unharmonic ratio of 18:19. In fact, the cause of Kepler's dissonance might be explained by the fact that the asteroid belt separates those two planetary orbits, as discovered in 1801, 150 years after Kepler's death.

    http://en.wikipedia.org/wiki/Harmonices_MundiI have no idea how the discovery of the asteroids matters. The ratio isn't one of bode's law interactions is it?It concerns the varying speed of the unit around the sun.

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