Titius–Bode law

The Titius - Bode series ( also titius - Bode series, bode - titiussche relationship, Bode's rule, and the like ) is an empirically discovered by Johann Daniel Titius and advertised by Johann Elert Bode numerical relationship, according to which the distances of most planets of the sun can be derived using a simple mathematical formula approximated solely from the number of your order.

Formula

Titius, the number sequence 0, 3, 6, 12, 24, 48, 96, etc., in which, after 3 each number is twice that of the previous, and added to each number 4 in the resulting sequence of numbers, he ordered the middle orbital radius of the Earth, the number to 10 and received with this measure the distances of all the known planets from the sun.

After formulation of Titius and Bode arises as the original formula:

The exponent n, starting at Mercury, for a value of the sequence - ∞, 0, 1, 2, 3, 4, 5, 6, etc. Thus arises from Mercury to Saturn, the number sequence 4, 7, 10, 16, 28, 52, 100 ...

Only in the modern form of the formula by Johann Friedrich worm from 1787 a is the mean distance of a planet from the sun, measured at the mean distance of the Earth in astronomical units:

Compared with measured values

The rule is true in most cases within a few percent in line with the actual conditions. However, there are some discrepancies:

• For Mercury would have the value of n according to the rest of the sequence is not - ∞, but -1.
• Between Mars and Jupiter is the asteroid belt. The largest body herein is Ceres, which is not a planet but a dwarf planet.
• Neptune has no place in this series. Instead, practically takes his place Pluto, whose status was however denied as a planet on August 24, 2006 by the IAU and changed into that of a dwarf planet.
• Pluto itself, in contrast to the inner planets, a highly eccentric path, which varies from 29.7 to 49.3 AU. This difference corresponds approximately to the diameter of Saturn's orbit or the distance of Uranus to the sun, inasmuch as the value of the prediction of the Titius - Bode series for the mean orbital radius of Pluto is still lower than in the rest of the planets.
• Eris is also a dwarf planet, is greater than Ceres and Pluto, but it fits in contrast to those not well in the series.

History

In 1723 calculated Christian Wolff for the average distances of the known planets a series of numbers, after which the mean orbital radius of the Earth is made up of ten units and for the planet Mercury to Saturn, the values ​​4, 7, 10, 15, 52 and 95 arise. Johann Daniel Titius in 1766 has created a formula for the closest possible distance range. Johann Elert Bode found in a footnote in the translated book by Titius Contemplation de la nature by Charles Bonnet and has made them well-known in his instructions to the attention of the gestirntes Heaven in 1772. He however did not mention the author of the accepted formulation, but later took the after. The accidental discovery of Uranus in 1781 by William Herschel meant a confirmation of this rule and let them appear for all the planets then known as law. Many astronomers now sought after a planet in the gap between Mars and Jupiter. Independently, then tracked down a celestial body on the night of January 1, 1801, Giuseppe Piazzi, you could assign this distance. It was the asteroid Ceres, the first asteroid discovered and by far the largest of these bodies also called planetoids, which closed this gap together with the entire asteroid belt. Since August 2006, Ceres has a new status of a dwarf planet.

Even Johannes Kepler had considered empirically a mathematical order of the planets. In this case it was a geometric relationship. In his 1596 published book mystery cosmographicum ( " The Secret of the World "), Kepler began the orbits of the known planets Mercury to Saturn as a cross-section of spherical shells with the surface of the five Platonic solids in relationship. Between the nested path spheres of six planets fit after some corrections, the individual surfaces of the five Platonic solids, depending on their form as spacers just so into it. In his 1619 published work Harmonice mundi ( " The Harmonies " ), he developed this theory further.

Controversy

For the Titius - Bode series there is no proven explanation as to why the distances of the planets can be displayed so and why this relationship looks just so and not otherwise. The numerical generally falls literally from the sky, without any reference is made ​​to physical principles or phenomena. Some feel that it is seen in an order where there is none, and still others suspect behind an underlying law of nature, perhaps even a new physics or at least a new cosmogony for the formation of the solar system. For the central and tacit assumption that always distinguish the distances of the planets from the sun by the same factor, no convincing physical justification is in sight.

Revealing for the organization of celestial mechanics of the solar system is the consideration of the orbital periods. The orbital periods of the adjacent planets are to each other in commensurability; that is, they are in a relationship based on a common measure and - partly approximate, sometimes quite precisely - can be expressed by small whole numbers:

Seen based former success of the Titius - Bode series generally commensurate to the circulation conditions and in detail on the empirical bending the uniform formula to capture all the different conditions with the highest possible accuracy. Simulations of the formation of planetary systems seem to confirm resonance effects between the planets as a possible cause.

Statistical tests showed, however, that almost always can be adapted to a hypothetical planetary system is a simple formula, if you allow similar deviations. Fall Even when the moon systems commensurabilities on and can be summarized by formulas similar series, but these series are different for each system; they give only number games that could still reveal no new sky mechanical law.

Assuming that this is not just a coincidence or just a statistical effect in the Titius - Bode series, numerous hypotheses for the above mentioned exceptions have been established. So you have seen in the objects of the asteroid belt, the fragments of a former planet which has entered into the scientific and fantastic literature under the name Phaeton. The investigations have shown over time that the total mass of all asteroids is only about five percent of the mass of the Moon and that many of the small bodies are more likely to emerge from different, once larger asteroid. Another hypothesis was assumed that the orbits of Neptune and Pluto may have been disturbed and altered by a close passing, massive object.

The cause of a possible distance order is generally seen in the formation of the solar system. The Titius - Bode series has lost for research in importance and is now only of historical importance.